+
@@ -648,14 +648,14 @@ This book jumps pretty quickly into concepts, for a quick overview of MRI, here’s my attempt to explain MRI in under 10 minutes:
How MRI Works (Explained In under 10 minutes)
+ +You can also access a full playlist of my lectures
If you would like to use the associated code that goes along with this book, it is available at the git repository LarsonLab/MRI-education-resources, and also the GitHub icon above. I recommend cloning the repository via the GitHub Desktop application, this way you get all the code at once and then can pull any updates made to the repository.
+This book is greatly influenced by many other great resources that I want to acknowledge up front:
@@ -460,8 +469,7 @@Miki Lustig’s MRI course notes
Educational resources from the Danish Research Centre for Magnetic Resonance, which includes a great on-line [Bloch Simulation] -(http://drcmr.dk/BlochSimulator/)
Educational resources from the Danish Research Centre for Magnetic Resonance, which includes a great on-line Bloch Simulator
+
@@ -648,14 +648,14 @@ 
-
-
+
-
+
+
diff --git a/_sources/Introduction.md b/_sources/Introduction.md
index 3af2118..5d005a2 100644
--- a/_sources/Introduction.md
+++ b/_sources/Introduction.md
@@ -26,10 +26,16 @@ This book jumps pretty quickly into concepts, for a quick overview of MRI, here'
[How MRI Works (Explained In under 10 minutes)](https://youtu.be/1Ku6-uXw7Ag)
+## Principles of MRI Course Lectures
+
You can also access a full playlist of my lectures
[Principles of MRI Recorded Lectures](https://www.youtube.com/playlist?list=PLjBt5Iq93BT9eXMsgevVTXKVv4BgVLB1X)
+## Using MRI-Education-Resources code
+
+If you would like to use the associated code that goes along with this book, it is available at the git repository https://github.com/LarsonLab/MRI-education-resources, and also the GitHub icon above. I recommend cloning the repository via the GitHub Desktop application, this way you get all the code at once and then can pull any updates made to the repository.
+
## Acknowledgements
This book is greatly influenced by many other great resources that I want to acknowledge up front:
@@ -37,6 +43,5 @@ This book is greatly influenced by many other great resources that I want to ack
* _Principles of Magnetic Resonance Imaging_ by Dwight Nishimura - I learned from this great text and borrowed a lot of its material. For some of my students with less engineering/signal processing background, this book on its own was challenging.
* Net magnetizations animation from Bill Overall and the [SpinBench](https://vista.ai/products/research-spinbench/) simulation and pulse sequence design tool
* Miki Lustig's MRI course notes
-* Educational resources from the [Danish Research Centre for Magnetic Resonance](https://www.drcmr.dk/MR), which includes a great on-line [Bloch Simulation]
-(http://drcmr.dk/BlochSimulator/)
+* Educational resources from the [Danish Research Centre for Magnetic Resonance](https://www.drcmr.dk/MR), which includes a great on-line [Bloch Simulator](http://drcmr.dk/BlochSimulator/)
diff --git a/reports/FOV and Resolution.err.log b/reports/FOV and Resolution.err.log
index c77fd28..45fd3aa 100644
--- a/reports/FOV and Resolution.err.log
+++ b/reports/FOV and Resolution.err.log
@@ -3,7 +3,7 @@ Traceback (most recent call last):
executenb(
File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 1305, in execute
return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute()
- File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 173, in wrapped
+ File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 165, in wrapped
return loop.run_until_complete(inner)
File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/asyncio/base_events.py", line 616, in run_until_complete
return future.result()
diff --git a/reports/Image Reconstruction.err.log b/reports/Image Reconstruction.err.log
index ac5c55a..d47fa6d 100644
--- a/reports/Image Reconstruction.err.log
+++ b/reports/Image Reconstruction.err.log
@@ -1,9 +1,9 @@
Traceback (most recent call last):
File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 778, in _async_poll_for_reply
msg = await ensure_async(self.kc.shell_channel.get_msg(timeout=new_timeout))
- File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 189, in ensure_async
+ File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 198, in ensure_async
result = await obj
- File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_client/channels.py", line 315, in get_msg
+ File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_client/channels.py", line 313, in get_msg
raise Empty
_queue.Empty
@@ -14,7 +14,7 @@ Traceback (most recent call last):
executenb(
File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/nbclient/client.py", line 1305, in execute
return NotebookClient(nb=nb, resources=resources, km=km, **kwargs).execute()
- File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 173, in wrapped
+ File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/jupyter_core/utils/__init__.py", line 165, in wrapped
return loop.run_until_complete(inner)
File "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/asyncio/base_events.py", line 616, in run_until_complete
return future.result()
diff --git a/searchindex.js b/searchindex.js
index 4b42b79..3a89d3f 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"docnames": ["Accelerated Imaging Methods", "Artifacts", "FOV and Resolution", "Fast Imaging Pulse Sequences", "Fun with RF Pulses", "Gradient and Spin Echoes", "Image Reconstruction", "Introduction", "MR Physics - Bloch Equation", "MRI Contrast", "MRI Math Concepts", "MRI Notation", "MRI Signal Equation", "MRI System", "Magnetic Fields and RF Coils", "Pulse Sequence", "Questions", "RF Pulses", "Signal to Noise Ratio", "Software_Resources", "Spatial Encoding", "Spectral-Spatial RF Pulses", "Spin Physics", "build_notes"], "filenames": ["Accelerated Imaging Methods.ipynb", "Artifacts.ipynb", "FOV and Resolution.ipynb", "Fast Imaging Pulse Sequences.ipynb", "Fun with RF Pulses.ipynb", "Gradient and Spin Echoes.ipynb", "Image Reconstruction.ipynb", "Introduction.md", "MR Physics - Bloch Equation.ipynb", "MRI Contrast.ipynb", "MRI Math Concepts.ipynb", "MRI Notation.ipynb", "MRI Signal Equation.ipynb", "MRI System.ipynb", "Magnetic Fields and RF Coils.ipynb", "Pulse Sequence.ipynb", "Questions.md", "RF Pulses.ipynb", "Signal to Noise Ratio.ipynb", "Software_Resources.md", "Spatial Encoding.ipynb", "Spectral-Spatial RF Pulses.ipynb", "Spin Physics.ipynb", "build_notes.md"], "titles": ["Accelerated Imaging Methods", "Artifacts", "Field of View (FOV) and Resolution", "Fast Imaging Pulse Sequences (Under Construction)", "Fun with RF Pulses?", "Gradient and Spin Echo Pulse Sequences", "Image Reconstruction", "Introduction to Principles of MRI", "Bloch Equation", "MRI Contrast", "MRI Math Concepts", "MRI Notation and Terminology", "The MRI Signal Equation and K-space", "The MRI System", "Magnetic fields in MRI", "The Pulse Sequence", "MRI Questions", "RF Pulses", "Signal to Noise Ratio (SNR)", "MRI Software Resources", "Spatial Encoding", "Spectral-Spatial RF Pulses", "Spin Physics", "<no title>"], "terms": {"scan": [0, 3, 6, 7, 13, 14, 16, 18], "can": [0, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "appli": [0, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 18, 20, 21, 22], "reduc": [0, 5, 6, 9, 16], "number": [0, 6, 8, 11, 12, 14, 15, 20, 21, 22], "sampl": [0, 2, 6, 12, 16, 19, 20, 21], "also": [0, 1, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 20, 21, 22], "known": [0, 3, 6, 10, 14, 20, 22], "undersampl": [0, 16], "These": [0, 2, 3, 4, 5, 6, 9, 12, 13, 14, 17, 20, 21, 22], "correspond": [0, 6, 16, 20], "advanc": [0, 6, 19], "allow": [0, 3, 9, 10, 17, 18], "The": [0, 1, 2, 4, 5, 6, 8, 9, 10, 11, 14, 16, 17, 18, 20, 21, 22], "techniqu": [0, 3, 6, 9], "cover": [0, 20, 22], "here": [0, 4, 7, 8, 10, 12, 15, 20, 22], "includ": [0, 1, 3, 5, 6, 7, 8, 10, 12, 13, 15, 18, 19, 20, 21, 22], "describ": [0, 2, 3, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "how": [0, 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "ar": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], "form": [0, 2, 3, 6, 7, 9, 12, 13, 15, 17, 20, 21, 22], "work": [0, 3, 7, 9, 13, 20, 21], "understand": [0, 3, 5, 7, 8, 11, 12, 14, 15, 17, 18, 20, 21, 22], "constraint": [0, 7, 12, 18], "tradeoff": [0, 7, 12, 18], "identifi": [0, 1, 3, 5, 7, 9, 12, 15, 16, 21], "when": [0, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22], "manipul": [0, 2, 3, 6, 7, 9, 12, 14, 15, 17, 18], "sequenc": [0, 2, 6, 7, 9, 11, 12, 14, 17, 18, 19, 20], "paramet": [0, 2, 3, 6, 7, 9, 12, 17, 18, 21], "improv": [0, 2, 3, 6, 7, 9, 12, 16, 17, 18], "perform": [0, 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20], "defin": [0, 2, 6, 10, 12, 14, 15, 17, 18, 20, 22], "which": [0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "modifi": 0, "analyz": [0, 6, 7, 8, 10, 12, 15, 17], "data": [0, 1, 3, 5, 7, 9, 13, 16], "an": [0, 5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "from": [0, 4, 6, 7, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 21, 22], "raw": [0, 6], "For": [0, 2, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 22], "help": [0, 11, 12, 15, 21, 22], "reformul": 0, "problem": [0, 6, 16], "linear": [0, 1, 6, 10, 12, 14, 17, 18, 20], "system": [0, 6, 10, 18, 19], "us": [0, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "standard": [0, 11], "mathemat": [0, 14], "notat": [0, 8, 12, 13, 20], "y": [0, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20], "mathbf": 0, "e": [0, 1, 6, 8, 12, 14, 15, 16, 17, 20, 22], "x": [0, 2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21], "n": [0, 1, 2, 8, 9, 12, 14, 15, 17, 20, 22], "where": [0, 8, 9, 10, 12, 14, 15, 17, 18, 20, 21, 22], "acquir": [0, 3, 5, 6, 9, 12, 13, 16, 18, 20], "encod": [0, 1, 5, 12, 13, 15], "matrix": [0, 6, 9, 20], "spatial": [0, 1, 5, 6, 10, 12, 13, 14, 15, 18], "distribut": [0, 18, 22], "transvers": [0, 5, 6, 8, 9, 11, 12, 14, 15, 16, 20, 21, 22], "magnet": [0, 1, 4, 5, 6, 7, 8, 9, 12, 16, 17, 19, 21], "g": [0, 1, 6, 10, 11, 12, 15, 16, 17, 20, 21], "nois": [0, 1, 14, 16], "In": [0, 2, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 22], "thi": [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22], "vector": [0, 4, 8, 14, 17, 22], "exampl": [0, 2, 4, 5, 6, 12, 14, 18, 19, 20, 21, 22, 23], "2d": [0, 5, 6, 14, 16, 20, 21], "ft": [0, 10, 16, 20], "would": [0, 6, 8, 13, 21, 22], "convert": [0, 6, 8, 17], "left": [0, 4, 6, 8, 10, 12, 14, 20], "begin": [0, 5, 8, 10, 11, 14, 18, 20, 22], "arrai": [0, 10, 14, 16], "c": [0, 1, 10, 16, 22, 23], "s_1": 0, "t_1": [0, 8, 9, 11, 12, 16, 18, 22], "t_2": [0, 5, 8, 9, 11, 12, 16, 20, 22], "vdot": 0, "t_": [0, 16, 17, 18], "nx": 0, "s_2": 0, "s_": [0, 5, 9, 12], "ny": 0, "end": [0, 2, 5, 8, 9, 10, 11, 14, 17, 18, 20, 21, 22], "right": [0, 4, 10, 12, 20, 22], "s_m": 0, "t_n": 0, "m": [0, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 20, 22], "th": [0, 6], "tr": [0, 3, 6, 12, 15, 16], "x_1": 0, "y_1": 0, "x_2": 0, "x_": 0, "1": [0, 1, 2, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22], "y_2": 0, "y_": 0, "x_i": 0, "y_i": 0, "equal": [0, 1, 2, 6, 9, 16, 17], "locat": [0, 1, 2, 5, 6, 8, 9, 10, 12, 13, 14, 17, 20, 22], "minimum": [0, 14, 15, 16], "discret": [0, 6], "fourier": [0, 9, 12, 16, 17, 20, 21], "transform": [0, 8, 9, 12, 16, 17, 20, 21], "f": [0, 1, 6, 9, 10, 12, 13, 16, 17, 20, 21, 22], "repres": [0, 5, 10, 12, 14, 16, 17, 20, 22], "our": [0, 2, 5, 6, 8, 9, 10, 12, 13, 14, 20, 22], "evalu": [0, 6, 20], "entri": [0, 1], "being": [0, 8, 12, 15, 17, 18, 22], "vec": [0, 4, 5, 6, 8, 10, 11, 12, 16, 20, 22], "_i": [0, 6], "r": [0, 5, 6, 8, 9, 11, 12, 16, 20, 22], "_j": 0, "_": [0, 6, 12, 15, 20], "i": [0, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21], "j": [0, 22], "exp": [0, 1, 5, 9, 10, 12, 16, 17, 18, 20], "2": [0, 1, 2, 4, 5, 6, 8, 9, 12, 14, 15, 16, 17, 18, 20, 21, 22], "pi": [0, 1, 5, 8, 9, 10, 12, 14, 16, 17, 18, 20, 21], "cdot": [0, 9, 10, 12, 14, 16, 17, 20], "case": [0, 9, 10, 12, 17, 18], "measur": [0, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 20, 22], "invers": [0, 1, 4, 6, 12, 16, 17, 20], "fulli": [0, 6, 9, 16, 20], "well": [0, 1, 5, 6, 9, 12, 14, 15, 17], "hat": [0, 9, 10, 12], "h": [0, 10, 16, 21, 22], "we": [0, 2, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22], "need": [0, 10, 13, 16, 18, 20, 22, 23], "consid": [0, 8, 12, 17, 18, 22], "coil": [0, 4, 6, 15, 17, 18, 20, 22], "sensit": [0, 13, 16, 20], "profil": [0, 6, 12, 17, 21], "_q": 0, "each": [0, 6, 9, 10, 12, 13, 14, 15, 18], "rf": [0, 1, 5, 6, 9, 11, 12, 18, 20], "along": [0, 4, 6, 8, 15, 16, 17, 22], "sub": [0, 11, 21], "oper": [0, 10, 12, 16], "s": [0, 1, 5, 6, 7, 8, 9, 11, 12, 14, 16, 18, 20, 21, 22], "y_q": 0, "n_q": 0, "c_q": 0, "diagon": 0, "diagnoal": 0, "0": [0, 1, 2, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22], "whether": 0, "expect": [0, 8, 9, 12, 15, 16, 18], "grid": [0, 6, 20], "wa": [0, 3, 5, 7], "It": [0, 5, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 22], "conveni": [0, 22], "fill": [0, 6], "point": [0, 18, 22], "return": [0, 8, 13, 22], "origin": [0, 3, 10, 12, 14, 22], "creat": [0, 2, 4, 5, 6, 7, 9, 12, 13, 15, 16, 17, 20, 21, 22], "augment": 0, "matric": [0, 9, 12], "concaten": 0, "element": [0, 12], "dimens": [0, 6, 9, 10, 12, 18, 20, 21], "ldot": 0, "y_n": 0, "_1": [0, 9], "_2": [0, 9], "_n": 0, "n_1": 0, "n_2": 0, "n_n": 0, "result": [0, 4, 6, 8, 9, 10, 12, 13, 17, 18, 20, 21, 22], "ex": [0, 17], "follow": [0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20], "optim": [0, 18], "arg": 0, "min_": 0, "frac": [0, 2, 5, 8, 9, 10, 16, 17, 18, 20, 22], "2_2": 0, "solv": [0, 12], "directli": [0, 9, 16], "pseudo": [0, 16], "calcul": [0, 8, 16], "pattern": [0, 2, 15, 16, 17, 20], "typic": [0, 4, 5, 6, 8, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21], "regular": 0, "mean": [0, 5, 6, 8, 9, 12, 14, 16, 17, 18, 20, 22], "consist": [0, 9, 13, 20, 21], "skip": 0, "line": [0, 1, 2, 3, 6, 7, 12, 15, 16, 20, 21], "grappa": 0, "util": 0, "kernel": [0, 12], "comput": [0, 10], "itself": 0, "captur": [0, 2, 9, 12, 13, 15, 18, 20], "lambda": 0, "tune": [0, 14], "ident": [0, 17], "simultan": [0, 16], "enforc": 0, "first": [0, 6, 8, 9, 15, 17, 20], "term": [0, 8, 9, 12, 16], "self": 0, "sescond": 0, "either": [0, 12, 16, 17, 18], "iter": 0, "estim": [0, 9], "while": [0, 5, 6, 8, 9, 12, 13, 17, 18, 21], "spirit": 0, "combin": [0, 12, 21], "full": [0, 2, 7, 11, 12, 16, 22], "center": [0, 6, 9, 12, 14, 15, 16, 17, 20], "There": [0, 5, 17, 18], "penalti": 0, "vari": [0, 8, 9, 11, 12, 13, 14, 17, 18, 20, 21, 22], "sever": [0, 5], "depend": [0, 5, 8, 9, 12, 14, 16, 20, 22], "condit": [0, 6, 9, 18, 22], "more": [0, 5, 6, 7, 8, 9, 12, 13, 15, 16, 17, 18, 19], "direct": [0, 4, 6, 8, 12, 13, 14, 16, 20, 21, 22], "lead": [0, 5, 10, 12, 17, 18, 20], "lower": [0, 9, 18], "convers": 0, "fewer": 0, "ill": 0, "higher": [0, 1, 9, 17, 18, 22], "penatli": 0, "region": [0, 1, 14], "littl": 0, "differ": [0, 1, 5, 6, 9, 12, 13, 14, 15, 16, 17, 18, 20, 22], "betweeen": 0, "bodi": [0, 14, 16, 17, 22], "tend": 0, "have": [0, 4, 8, 9, 14, 16, 17, 18, 20, 22], "larger": [0, 12, 14, 16], "character": [0, 5, 10, 12, 16, 17], "factor": [0, 12, 16, 18], "geq": [0, 6], "loss": [0, 1, 12, 16, 18], "load": [0, 1, 5, 6, 8, 9, 12, 13, 14, 17, 18, 21, 22], "geometri": 0, "appyl": 0, "total": [0, 16, 17, 18, 22], "readout": [0, 3, 6, 12, 16, 18, 20], "time": [0, 5, 6, 8, 10, 11, 12, 14, 15, 16, 20, 21, 22], "sqrt": [0, 9, 10, 14, 16, 17, 18], "relationship": [0, 2, 6, 9, 14, 17, 18], "snr_": [0, 16, 18], "appear": [0, 1, 9, 17], "alias": [0, 1, 16], "sometim": [0, 8, 15], "complet": [0, 5, 7, 8, 16, 20], "remov": [0, 5, 8, 9, 12, 17, 18, 21], "like": [0, 13, 17], "mismatch": 0, "between": [0, 5, 9, 12, 14, 15, 16, 17, 22], "cs": [0, 12], "theori": [0, 10], "sai": [0, 14], "some": [0, 4, 7, 12, 14, 15, 17, 18, 20], "domain": [0, 10, 16, 20], "subset": 0, "other": [0, 4, 6, 7, 8, 12, 13, 14, 17, 18, 20, 22], "word": [0, 4, 6, 13, 17, 20], "further": [0, 12], "acquisit": [0, 3, 5, 6, 9, 13, 16, 20], "specif": [0, 1, 5, 8, 12, 13, 20, 22], "ell_1": 0, "norm": 0, "sum_": [0, 10], "promot": 0, "sparsiti": 0, "solut": [0, 8, 12, 17], "lambda_": 0, "wx": 0, "multipli": [0, 9, 10, 12], "must": [0, 15, 16, 22, 23], "match": [0, 16, 18], "spars": [0, 16], "through": [0, 12, 14, 15, 17, 18, 21], "sparsifi": 0, "w": [0, 12, 16], "chosen": [0, 9], "balanc": [0, 16], "random": [0, 6, 16], "illustrat": 0, "diagram": [0, 5, 16], "below": [0, 1, 4, 5, 6, 8, 9, 10, 12, 14, 15, 17, 21, 22], "procedur": 0, "caption": 0, "figur": [0, 1, 2, 6, 8, 9, 10, 12, 14, 17, 18, 20, 21, 22], "http": [0, 1, 4, 5, 7, 8, 10, 11, 22], "doi": 0, "org": [0, 1, 10, 11], "10": [0, 7, 8, 9, 12, 13, 14, 16, 20, 21], "1109": 0, "msp": 0, "2007": 0, "914728": 0, "heurist": 0, "A": [0, 1, 5, 8, 10, 14, 15, 16, 17, 21, 22], "signal": [0, 1, 5, 6, 7, 8, 9, 10, 13, 15, 16, 17, 19, 21, 22], "8": [0, 2, 8, 9, 10, 14, 17, 20, 21, 22], "fold": [0, 1], "its": [0, 5, 7, 8, 9, 12, 16, 22], "d": [0, 5, 8, 12, 17, 18, 20], "b": [0, 8, 10, 11, 13, 14, 22], "equispac": 0, "prevent": 0, "recoveri": [0, 16], "incoher": 0, "interfer": [0, 1, 14], "strong": [0, 18, 22], "compon": [0, 7, 12, 14, 16, 22], "stick": 0, "abov": [0, 9, 10, 12, 14, 16, 17, 18, 20, 21, 22], "level": [0, 1], "detect": [0, 6, 13, 14, 16, 22], "recov": [0, 9, 22], "threshold": 0, "subtract": [0, 13, 14], "thu": [0, 6, 10, 12, 14, 16, 17, 20, 22], "enabl": [0, 3, 16], "weaker": 0, "popular": [0, 3, 5, 7, 19], "variat": [0, 4, 5, 13, 19, 20], "tv": 0, "tgv": 0, "wavelet": 0, "variabl": [0, 10], "densiti": [0, 16, 18, 22], "preferenti": [0, 13, 16, 22], "ha": [0, 5, 6, 7, 8, 9, 10, 12, 14, 15, 17, 20, 21, 22], "espirit": 0, "difficult": 0, "thei": [0, 4, 6, 7, 9, 13, 14, 15, 16, 17, 22], "inher": 0, "denois": 0, "constrain": 0, "base": [0, 2, 6, 7, 9, 10, 12, 14, 16, 17, 18, 20], "appar": [0, 20], "significantli": 0, "choic": [0, 9, 18], "most": [0, 3, 5, 6, 7, 8, 10, 12, 14, 15, 17, 20, 21, 22], "common": [0, 14, 20, 21], "come": [0, 6, 7, 9, 20], "overfit": 0, "over": [0, 6, 8, 11, 12, 14, 15, 18, 20], "smooth": 0, "unnatur": 0, "block": [0, 5, 15], "conceptu": 0, "train": [0, 16], "incorpor": [0, 10, 12, 18], "inform": [0, 6, 8, 9, 12, 14, 15, 16, 18, 20, 21, 22], "sinc": [0, 1, 2, 5, 6, 10, 12, 13, 14, 17, 18, 20], "real": [0, 6, 10, 16, 17, 20, 21, 22], "world": 0, "relev": [0, 10], "been": [0, 6, 9], "shown": [0, 5, 6, 8, 12, 14, 15, 17, 21, 22], "support": 0, "what": [0, 2, 5, 7, 8, 12, 13, 14, 15, 16, 20, 22], "within": [0, 3, 16, 17, 18, 20], "often": [0, 5, 10, 12, 15, 18], "least": [0, 14, 16], "squar": [0, 18], "object": [0, 1, 2, 6, 9, 10, 12, 20], "reg": 0, "mathcal": [0, 6, 9, 10, 12, 16, 20, 21], "implicitli": 0, "implement": [0, 17, 18], "via": 0, "machin": 0, "attempt": [0, 7], "straightforward": 0, "approach": [0, 18], "cnn": 0, "invert": [0, 5], "after": [0, 3, 5, 8, 9, 13, 14, 15, 16, 20, 22], "g_": [0, 16, 17, 20], "dnn": 0, "deeep": 0, "neural": 0, "network": [0, 16, 19], "nn": 0, "mani": [0, 7, 9, 10, 12, 14, 15, 16, 19, 22], "weight": [0, 5, 16, 18, 21], "prior": [0, 16, 20], "abl": [0, 22], "howev": [0, 5, 6, 9, 10, 12, 17, 18, 22], "so": [0, 5, 6, 8, 9, 12, 13, 14, 17, 18, 20, 21, 22], "call": [0, 3, 4, 5, 8, 9, 14, 17, 21, 22], "un": 0, "roll": 0, "becom": [0, 12, 17, 20], "better": 0, "compact": 0, "design": [0, 7, 8, 13, 14, 18, 19], "mimic": 0, "classic": 0, "algorithm": [0, 6, 10, 21], "seri": 0, "cascad": 0, "modl": 0, "varnet": 0, "regularl": 0, "model": [0, 10], "architectur": [0, 16], "singl": [0, 1, 3, 12, 14, 15, 16, 17, 20], "gradient": [0, 1, 2, 6, 9, 11, 12, 16, 17, 18, 21], "updat": [0, 6, 7, 8, 12, 14, 20, 21, 22], "descent": 0, "unet": [0, 16], "arxiv": 0, "ab": [0, 1, 2, 9, 10, 12, 17, 21], "2004": 0, "06688": 0, "e2": 0, "vn": 0, "take": [0, 4, 9, 17, 18, 20], "under": [0, 6, 7, 18, 22], "input": [0, 10], "ift": 0, "rss": 0, "bottom": [0, 4, 14], "dc": 0, "modul": [0, 1, 12, 17, 18, 20], "bring": [0, 13], "intermedi": [0, 17], "closer": [0, 22], "valu": [0, 6, 9, 10, 12, 16, 17, 18, 22], "refin": 0, "map": [0, 16, 19, 20], "multi": [0, 16], "one": [0, 6, 8, 10, 12, 14, 16, 18, 20, 21, 22], "u": [0, 23], "net": [0, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 19, 20, 22], "back": [0, 4, 6, 8, 9, 12, 14, 17, 20, 21, 22], "sme": 0, "step": [0, 16, 20, 21, 22], "_w": 0, "set": [0, 6, 7, 10], "structur": [0, 11, 22], "overal": [0, 5, 7, 9, 12, 15, 18, 21], "similar": [0, 10, 12], "both": [0, 5, 8, 15, 20, 21, 22], "unrol": [0, 16], "slightli": [0, 5, 6, 15, 17, 22], "lot": [0, 7], "4": [0, 2, 7, 10, 13, 14, 17, 18, 21], "radiolog": 0, "applic": [0, 22], "question": [0, 13], "answer": [0, 13, 16], "qualiti": [0, 12, 18], "supervis": 0, "realist": 0, "modif": [0, 16, 18], "exist": 0, "increas": [0, 14, 16, 17, 18, 22], "size": [0, 1, 2, 5, 6, 9, 10, 16, 18], "fastmri": 0, "provid": [0, 12, 14, 17, 18, 20, 21], "thousand": 0, "high": [0, 1, 12, 14, 15], "med": 0, "nyu": 0, "edu": 0, "48550": 0, "1811": 0, "08839": 0, "resnet": 0, "possibl": [0, 14, 16, 18], "gpu": 0, "essenti": 0, "send": 0, "forward": 0, "compar": [0, 11, 16, 17, 18, 22], "output": [0, 10], "propag": 0, "choos": [0, 9, 18, 22], "function": [0, 7, 8, 9, 12, 14, 16, 17, 20, 21], "l1": 0, "l2": 0, "batch": 0, "rate": [0, 5, 9, 11, 12, 15, 18, 21, 22], "etc": [0, 18], "challeng": [0, 7], "retain": 0, "textur": 0, "featur": [0, 17, 19], "anatomi": [0, 14, 16], "might": 0, "eras": 0, "hallucin": 0, "although": [0, 4, 22], "physic": [0, 18], "assur": 0, "recent": 0, "comprehens": [0, 1], "thes": 0, "reccommend": 0, "hammernik": 0, "k\u00fcstner": 0, "t": [0, 5, 6, 8, 9, 10, 11, 12, 16, 17, 20, 21, 22], "yaman": 0, "huang": 0, "z": [0, 4, 8, 9, 11, 13, 14, 15, 16, 17, 18, 21, 22], "rueckert": 0, "knoll": 0, "ak\u00e7akaya": 0, "driven": 0, "reson": [0, 1, 4, 6, 7, 8, 13, 15, 16, 20], "medic": 0, "ieee": 0, "process": [0, 5, 7, 8, 10, 14, 19, 22], "mag": 0, "2023": [0, 7], "jan": 0, "40": [0, 9], "98": 0, "114": 0, "2022": 0, "3215288": 0, "epub": 0, "pmid": 0, "37304755": 0, "pmcid": 0, "pmc10249732": 0, "pdf": 0, "2203": 0, "12215": 0, "setup": [1, 2, 5, 6, 8, 9, 12, 13, 14, 17, 18, 21, 22, 23], "mri": [1, 2, 3, 5, 8, 15, 17, 18, 21, 22], "educ": [1, 2, 5, 6, 7, 8, 9, 12, 13, 14, 17, 18, 19, 21, 22], "resourc": [1, 2, 5, 6, 7, 8, 9, 11, 12, 13, 14, 17, 18, 21, 22], "path": [1, 2, 5, 6, 8, 9, 12, 13, 14, 17, 18, 21, 22], "requir": [1, 2, 4, 5, 6, 8, 9, 12, 13, 14, 15, 16, 17, 18, 21, 22], "cd": [1, 2, 5, 6, 8, 9, 12, 13, 14, 17, 18, 21, 22], "startup": [1, 2, 5, 6, 8, 9, 12, 13, 14, 17, 18, 21, 22], "imag": [1, 2, 5, 7, 8, 10, 12, 13, 14, 15, 17, 18, 21, 22], "notebook": [1, 19], "variou": [1, 3, 5, 7, 9, 14, 15, 17], "wikipedia": [1, 10], "en": [1, 10], "wiki": [1, 10], "mri_artifact": 1, "veri": [1, 6, 9, 12, 15, 17, 18, 20], "mitig": [1, 3, 5, 7, 12, 21], "them": [1, 3, 5, 7, 12, 13, 14, 21, 22], "name": [1, 5, 8, 17, 20], "frequenc": [1, 4, 5, 6, 8, 10, 12, 13, 14, 15, 16, 17, 21], "phase": [1, 4, 5, 6, 12, 14, 16, 17], "across": [1, 5, 8, 11, 12, 13, 14, 16, 17], "spike": 1, "top": [1, 22], "entir": [1, 14, 19], "gibb": [1, 12, 16], "ring": [1, 10, 12, 16, 17], "truncat": [1, 16], "rippl": [1, 17], "sharp": [1, 10, 17], "edg": [1, 10, 12, 16], "zipper": 1, "noisi": 1, "At": [1, 16], "motion": [1, 16], "flow": [1, 12, 20], "copi": 1, "ghost": [1, 16], "chang": [1, 2, 4, 5, 6, 8, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "due": [1, 5, 12, 16, 18, 20], "displac": [1, 16, 21], "distort": [1, 3, 14, 16, 19], "shift": [1, 6, 9, 16, 21], "chemic": [1, 6, 16, 21], "fat": [1, 9, 12, 16, 21], "off": [1, 2, 4, 6, 13, 14, 15, 20, 22], "suscept": [1, 5, 12, 16, 19], "2dft": [1, 16], "epi": [1, 12, 16, 21], "t2": [1, 3, 8, 12, 16, 18, 19, 22], "around": [1, 4, 8, 13, 14, 15, 17, 22], "suscpet": 1, "implant": 1, "air": 1, "slice": [1, 15, 16, 21], "misregistr": 1, "dielectr": 1, "shade": 1, "particularli": [1, 12, 21], "larg": [1, 5, 13, 14, 17, 22], "fov": [1, 9, 13, 14], "b0": [1, 8, 14, 16], "boundari": 1, "artifici": 1, "dark": [1, 16], "tissu": [1, 9, 12, 16, 17, 22], "non": [1, 8, 17, 20, 22], "subject": [1, 5, 8, 12, 13, 22], "k": [1, 2, 3, 9, 16, 18, 21, 22], "space": [1, 2, 3, 9, 14, 16, 18, 21], "datanam": [1, 6], "se_t1_sag_data": [1, 6], "kdata": [1, 2, 6], "im_origin": [1, 6], "ifft2c": [1, 2, 6, 9, 12], "subplot": [1, 2, 6, 12, 14, 17, 18, 20, 21], "121": [1, 12, 18, 20, 21], "imagesc": [1, 2, 6, 9, 14, 21], "log": [1, 2], "max": [1, 2, 18, 21], "colormap": [1, 2, 6, 9, 14, 21], "grai": [1, 2, 6, 9, 14, 21], "axi": [1, 2, 4, 6, 8, 9, 14, 16, 22], "tight": [1, 2, 6, 9, 14], "122": [1, 12, 18, 20, 21], "warn": [1, 6, 8, 12, 14, 20, 21, 22], "user": 1, "plarson": 1, "document": 1, "github": 1, "mat": 1, "found": 1, "search": 1, "n_undersamp": 1, "data_undersamp": 1, "zero": [1, 8, 9, 17, 18, 21, 22], "iundersamp": 1, "round": [1, 14, 21], "im_undersamp": 1, "spike_loc": 1, "6": [1, 8, 10, 17, 18, 20, 21, 22], "53": 1, "data_spik": 1, "5": [1, 2, 8, 9, 10, 12, 13, 14, 17, 18, 20, 21, 22], "im_spik": 1, "rect": [1, 10], "32": [1, 10, 12], "kx": [1, 2, 9, 10, 12, 16, 20], "n_rect": [1, 2], "rect_ring": 1, "221": [1, 2, 17, 21], "222": [1, 2, 17], "ylabel": [1, 8, 9, 12, 14, 17, 18, 20, 21, 22], "kdata_window": 1, "ham": [1, 17], "rect_window": 1, "223": [1, 17, 21], "224": [1, 17], "window": [1, 6, 8, 12, 14, 17, 20, 21, 22, 23], "relative_rf_frequ": 1, "ph_int": 1, "rand": 1, "rfint": 1, "data_rfint": 1, "repmat": [1, 12, 17], "im_rfint": 1, "amplitud": [1, 4, 9, 12, 14, 15, 16, 17, 20, 22], "3": [1, 2, 8, 9, 13, 14, 17, 18, 21, 22], "randn": 1, "fundament": [2, 9, 22], "determin": [2, 10, 12, 13, 14, 16, 17, 20, 21], "cell": 2, "syntaxerror": 2, "invalid": 2, "syntax": 2, "simpl": [2, 18], "delta": [2, 5, 10, 12, 17, 20, 22], "fov_": 2, "k_x": [2, 10, 12, 16, 20], "rectangular": [2, 17], "demonstr": [2, 21], "256": [2, 9], "rect_recon": 2, "titl": [2, 6, 8, 9, 10, 12, 14, 17, 18, 20, 21, 22], "kdata2": 2, "rect_recon2": 2, "doubl": 2, "half": [2, 6, 16], "kdata3": 2, "rect_recon3": 2, "tripl": 2, "One": [2, 4, 14, 18, 22], "third": 2, "maximum": [2, 13, 14, 16, 18], "extent": [2, 14], "k_": 2, "delta_x": [2, 16, 18], "kdata4": 2, "rect_recon4": 2, "4x": 2, "voxel": [2, 5, 11, 16], "kdata8": 2, "7": [2, 14], "16": [2, 10], "9": [2, 8, 22], "rect_recon8": 2, "8x": 2, "modern": 3, "reli": [3, 16], "heavili": 3, "primarili": [3, 7, 15], "method": [3, 5, 6, 15, 18, 19, 20], "multipl": [3, 5, 10, 15, 16, 17], "acronym": [3, 5, 7], "acceler": 3, "artifact": [3, 5, 7, 10, 12, 14, 19, 21], "blur": [3, 12, 16], "row": 3, "faster": [3, 6, 16], "refocus": [3, 4, 16, 17, 21], "exict": 3, "dure": [3, 5, 6, 7, 9, 14, 15, 16, 17, 18, 20, 21], "rapid": 3, "relax": [3, 7, 11, 15, 16, 18, 20], "enhanc": [3, 12], "rare": 3, "scanner": [3, 15, 16, 22], "ge": [3, 9, 16], "healthcar": 3, "siemen": 3, "healthin": 3, "field": [3, 4, 5, 8, 12, 16, 17, 18, 22], "tfe": [3, 20], "philip": 3, "ye": 4, "you": [4, 5, 7, 9, 11, 22], "heard": 4, "me": 4, "mayb": 4, "special": [4, 6], "type": [4, 5, 7, 9, 11, 12, 15, 16, 17, 18, 20], "person": 4, "think": 4, "check": 4, "out": [4, 5, 6, 11, 12, 16, 18, 20], "interest": [4, 14, 18], "movi": [4, 20], "spinbench": [4, 7], "heartvista": 4, "ai": 4, "class": [4, 5], "basic": [4, 9, 10, 15, 19], "insensit": 4, "b_1": [4, 11, 17, 21, 22], "inhomongen": 4, "similarli": [4, 10, 18], "even": 4, "transmit": [4, 11, 13, 16], "mostli": 4, "effect": [4, 10, 12, 18], "180": [4, 5, 8, 9, 16, 17, 18], "degre": [4, 5, 8, 16, 17, 18], "flip": [4, 5, 14, 15, 16, 18, 21], "angl": [4, 5, 14, 15, 16, 18, 22], "purpos": [4, 13, 14, 15, 17, 19], "spin": [4, 8, 9, 11, 12, 13, 14, 16, 17, 18], "echo": [4, 9, 11, 12, 15, 16, 18, 20, 21], "unwant": 4, "show": [4, 6, 8, 9, 10, 12, 14, 15, 17, 20], "simul": [4, 7, 9, 17, 19, 20], "two": [4, 5, 18, 21, 22], "sweep": 4, "again": [4, 12, 22], "second": [4, 9, 15], "yellow": 4, "b1": 4, "white": [4, 9], "rang": [4, 7, 13, 14, 16, 17, 19], "larmor": [4, 8, 14, 15, 16, 17, 22], "plot": [4, 6, 8, 9, 10, 12, 14, 17, 18, 20, 21, 22], "corner": 4, "continu": [4, 10, 22], "constant": [4, 5, 9, 16, 17, 20, 22], "hard": [4, 5, 8, 16], "frequneci": [4, 12, 20], "rotat": [4, 12, 14, 15, 16, 17, 20, 22], "broad": [5, 7], "simpler": 5, "addit": [5, 6, 8, 12, 16, 17, 18, 20], "elimin": [5, 9, 16, 21], "undesir": 5, "contrast": [5, 7, 8, 12, 15, 17, 22], "build": [5, 12, 17, 19, 23], "excit": [5, 6, 9, 11, 13, 16, 20, 21], "g_x": [5, 11, 16, 20], "cancel": 5, "section": [5, 9, 20], "anoth": [5, 8, 9, 17, 22], "recal": [5, 6], "And": [5, 12, 14, 18, 22], "simplifi": [5, 8, 12, 20, 22], "exhibit": 5, "explain": [5, 7, 8], "propto": [5, 9, 17, 18], "m_0": [5, 8, 9, 11, 16, 18, 22], "te": [5, 12, 15, 16, 18], "ideal": [5, 6, 9, 10, 15], "uniform": 5, "absens": [5, 22], "ani": [5, 8, 9, 12, 16, 18, 20, 22], "practic": [5, 6, 10, 18, 20], "unavoid": 5, "refer": [5, 8, 13, 17, 20, 22], "f_r": [5, 12], "imperfect": [5, 12], "main": [5, 8, 9, 11, 12, 15, 16, 21, 22], "b_0": [5, 8, 11, 16, 22], "decai": [5, 9, 16, 22], "everi": [5, 9, 14, 15, 16, 18], "contain": [5, 6, 16, 17], "smallest": 5, "sum": [5, 12, 17, 20, 21, 22], "align": [5, 6, 13, 14, 16, 20, 22], "mathrm": [5, 6, 9, 10, 13, 15, 18, 20], "int_": [5, 10, 18, 20], "m_": [5, 6, 8, 11, 12, 15, 16, 17, 20, 21, 22], "xy": [5, 6, 8, 11, 12, 14, 15, 17, 20, 21, 22], "note": [5, 6, 7, 9, 10, 12, 14, 15, 16, 17, 18, 20], "reconstruct": [5, 9, 10, 12, 19, 20], "mechan": 5, "precess": [5, 12, 14, 16, 20], "de": 5, "averag": [5, 18], "magnitud": [5, 13, 16, 17], "illustr": [5, 6, 8, 9, 10, 17, 19, 20, 22], "gener": [5, 9, 11, 12, 16, 19, 20], "t2star_spinecho_illustr": 5, "No": 5, "80": [5, 8, 9, 22], "ms": [5, 8, 9, 12, 14, 17, 18, 21], "mild": 5, "approxim": [5, 16, 17, 18, 21], "dephas": [5, 16, 20], "broken": 5, "up": [5, 7, 9, 12, 14, 16, 17, 22], "separ": [5, 12, 13, 14, 16, 21, 22], "leq": 5, "revers": [5, 10, 20], "accumul": [5, 6, 12, 20], "easili": [5, 18, 21], "doe": [5, 12, 16, 18, 23], "make": 5, "revert": 5, "To": [5, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22], "try": [5, 8, 10], "visit": 5, "drcmr": [5, 7, 8, 22], "dk": [5, 7, 8, 22], "blochsimul": [5, 7, 8], "scene": 5, "inhomogen": [5, 12, 16], "90x": 5, "180y": 5, "happen": [5, 16, 17], "180x": 5, "Is": 5, "still": [5, 6, 10], "repeat": [5, 9, 13, 15, 16, 20, 21, 22], "order": [5, 6, 9, 20, 21, 22], "refocu": [5, 16], "pure": 5, "all": [5, 6, 8, 10, 12, 13, 14, 15, 16, 18, 22], "becaus": [5, 8, 13, 16, 22], "give": [5, 13, 14, 16], "gnuplot": [6, 8, 12, 14, 20, 21, 22], "graphic": [6, 8, 12, 14, 20, 21, 22], "toolkit": [6, 8, 12, 14, 20, 21, 22], "discourag": [6, 8, 12, 14, 20, 21, 22], "activ": [6, 8, 12, 14, 20, 21, 22, 23], "maintain": [6, 8, 12, 14, 20, 21, 22], "limit": [6, 8, 10, 12, 14, 16, 17, 18, 20, 21, 22], "ulik": [6, 8, 12, 14, 20, 21, 22], "fix": [6, 8, 12, 14, 17, 20, 21, 22], "commun": [6, 8, 12, 14, 20, 21, 22], "pipe": [6, 8, 12, 14, 20, 21, 22], "pass": [6, 8, 12, 14, 20, 21, 22], "octav": [6, 8, 12, 14, 20, 21, 22], "interpret": [6, 8, 12, 14, 20, 21, 22], "made": [6, 8, 12, 14, 20, 21, 22], "interact": [6, 8, 12, 14, 16, 20, 21, 22], "reflect": [6, 8, 12, 14, 20, 21, 22], "properti": [6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22], "manag": [6, 8, 12, 14, 20, 21, 22], "close": [6, 8, 12, 14, 20, 21, 22], "mous": [6, 8, 12, 14, 20, 21, 22], "click": [6, 8, 12, 14, 20, 21, 22], "notifi": [6, 8, 12, 14, 20, 21, 22], "intern": [6, 8, 12, 14, 20, 21, 22], "list": [6, 8, 11, 12, 14, 20, 21, 22], "open": [6, 8, 12, 13, 14, 20, 21, 22], "recommend": [6, 8, 12, 14, 20, 21, 22], "qt": [6, 8, 12, 14, 20, 21, 22], "instead": [6, 8, 12, 14, 20, 21, 22], "collect": [6, 16], "cartesian": [6, 12], "done": [6, 12, 15, 18, 21, 22], "anticip": 6, "formul": [6, 10, 12, 20, 21, 22], "introduc": [6, 9, 15, 17, 20, 22], "proport": [6, 9, 14, 16, 17, 18, 20, 22], "s_i": 6, "denot": [6, 10, 12, 14], "subscript": 6, "trajectori": [6, 12, 21], "raster": [6, 20], "fashion": [6, 15], "knowledg": [6, 12], "mr": [6, 9, 11, 14, 18, 20, 21, 22], "store": [6, 16, 20], "onc": [6, 9, 12, 18, 22], "simpli": [6, 10, 12, 13, 14, 22], "3d": [6, 20, 22], "fast": [6, 10, 12], "fft": [6, 10, 17], "anim": [6, 7, 8, 17], "fraction": 6, "nex": [6, 16], "wai": [6, 9, 14, 15, 16, 20], "amount": [6, 9, 10, 15, 17], "state": [6, 9, 16, 22], "posit": [6, 14, 16, 17, 20, 21], "complex": [6, 8, 9, 11, 12], "conjug": [6, 16], "neg": [6, 20], "im": 6, "m_x": [6, 8, 11, 22], "puls": [6, 7, 9, 11, 12, 18, 19, 20], "just": [6, 14, 19], "satisfi": 6, "taken": [6, 18], "togeth": [6, 9, 14, 17, 18], "onli": [6, 10, 15, 16, 17, 21, 22], "sourc": [6, 8, 9, 13, 22], "violat": [6, 21], "global": 6, "offset": [6, 18], "m_y": [6, 8, 11, 22], "correct": [6, 8, 14, 16, 17, 22], "problemat": 6, "low": [6, 9, 12, 22], "central": 6, "than": [6, 9, 14, 16], "project": 6, "onto": [6, 12], "convex": 6, "poc": 6, "homodyn": 6, "suitabl": 6, "short": [7, 9, 17], "book": [7, 11, 23], "associ": [7, 16, 17], "code": [7, 19, 20, 21], "larsonlab": 7, "repositori": 7, "helper": [7, 9], "built": 7, "cours": [7, 19], "about": [7, 15, 17, 22], "decad": 7, "teach": 7, "1st": 7, "year": 7, "graduat": 7, "student": 7, "background": [7, 14], "natur": 7, "scienc": 7, "engin": 7, "undergo": 7, "fall": 7, "quarter": 7, "promin": 7, "role": 7, "my": [7, 19], "upon": 7, "should": [7, 8, 14, 17, 18, 21, 22], "achiev": [7, 8, 9, 13, 16, 17, 22], "fundmanet": [7, 13, 14], "why": [7, 13, 14], "necessari": [7, 10, 13, 14, 15, 17], "concept": [7, 8, 12, 16, 19, 20, 22], "polar": [7, 8, 11, 13, 14, 16, 20], "jump": 7, "pretti": 7, "quickli": [7, 17], "quick": 7, "overview": 7, "minut": 7, "access": 7, "playlist": 7, "lectur": [7, 19], "record": [7, 15], "greatli": [7, 8, 12], "influenc": [7, 12, 18], "great": 7, "want": 7, "front": 7, "dwight": 7, "nishimura": 7, "text": 7, "borrow": 7, "materi": 7, "less": [7, 17, 22], "own": [7, 12], "bill": 7, "tool": [7, 10, 15, 19], "miki": 7, "lustig": 7, "danish": 7, "research": 7, "centr": 7, "bloch": [7, 12, 16, 17, 22], "physicist": 8, "felix": 8, "who": 8, "won": 8, "nobel": 8, "prize": 8, "discoveri": 8, "phenomena": 8, "almost": 8, "behavior": [8, 12, 15, 17], "seen": [8, 9], "deriv": [8, 10, 12, 22], "kei": [8, 12, 14, 17], "respons": [8, 17], "vast": 8, "major": [8, 17, 18], "present": [8, 9, 10, 14, 20], "experi": [8, 12, 14, 15, 18, 20, 22], "dt": [8, 9, 12, 17, 20, 21], "gamma": [8, 11, 12, 13, 14, 16, 17, 20, 21, 22], "bmatrix": [8, 11, 14, 22], "beavhior": 8, "equilibrium": [8, 9, 11, 13, 14], "longitudin": [8, 9, 16, 22], "m_z": [8, 9, 11, 16, 17, 22], "lattic": [8, 16, 22], "valuabl": [8, 22], "hand": [8, 14], "observ": [8, 10, 22], "neglect": [8, 12, 16, 20], "rightarrow": [8, 10], "infti": [8, 10, 20], "5e3": 8, "1500": [8, 9], "mt": [8, 12, 13, 14, 17], "unit": [8, 9, 11, 14, 17], "bloch_rot": [8, 17], "start": [8, 10, 12, 13, 16, 20, 22], "mstart": 8, "bstatic": 8, "1e": [8, 14], "ns": 8, "300": 8, "mall": [8, 22], "xlabel": [8, 9, 10, 12, 14, 17, 18, 20, 21, 22], "legend": [8, 9, 17, 18, 21, 22], "north": [8, 22], "boxoff": [8, 22], "5540": [8, 22], "occur": [8, 12, 16, 18, 22], "oscil": [8, 14, 16, 21, 22], "orthogon": 8, "If": [8, 10, 13, 22], "b_": [8, 14, 16], "co": [8, 9, 10, 14, 16, 18], "bar": [8, 11, 13, 14, 22], "sin": [8, 9, 10, 14, 18], "energi": [8, 13, 14, 17, 21, 22], "good": [8, 9, 11, 17], "progress": 8, "awai": [8, 9, 14, 22], "simplif": [8, 20], "f_0": [8, 12, 14, 22], "visual": [8, 17, 20, 22], "math": 8, "stationari": 8, "represent": [8, 15, 16, 20], "now": [8, 12, 17, 20, 21, 22], "do": [8, 9, 12, 13], "analysi": [8, 12], "option": [8, 20], "45": [8, 16], "90": [8, 16, 17, 18], "creation": 8, "omega_0": 8, "With": [8, 21], "final": [8, 12, 14], "clearli": 8, "gammabar": [8, 12, 17], "42": [8, 12, 17, 20, 21, 22], "58": [8, 12, 17, 20, 21], "khz": [8, 12, 13, 16, 17], "simplic": [8, 12], "f0": [8, 17], "m0": [8, 9, 17, 18, 22], "m_equilibrium": [8, 17], "paaramet": 8, "t_rf": 8, "linspac": [8, 9, 10, 14, 17, 18, 20, 21, 22], "4000": 8, "rf_flip_angl": 8, "radian": [8, 16], "b10": [8, 17], "425": 8, "8713e": 8, "03": 8, "length": [8, 9, 14, 17, 18, 20, 21, 22], "12": [8, 14, 16, 21], "513": 8, "ones": [8, 9, 10, 17, 20, 21], "northwest": 8, "192": 8, "438": 8, "equilibriuam": 8, "ultim": [8, 13], "orient": [8, 13, 14, 22], "same": [8, 9, 12, 14, 16, 17], "without": [8, 12], "shorthand": [8, 11], "t1": [8, 16, 18, 19, 22], "durat": [8, 12, 16, 17, 18], "millitesla": [8, 14], "tip": [8, 11, 15, 17, 22], "m_start": [8, 22], "bloch_rftip": 8, "bloch_relax": [8, 22], "1232e": 8, "17": 8, "0000e": 8, "00": 8, "num2str": [8, 9, 10, 14, 18], "657": 8, "rich": 9, "varieti": 9, "arguabl": [9, 17], "advantag": [9, 16, 17], "gd": 9, "ti": [9, 16], "desir": [9, 17, 18], "therefor": [9, 13, 18, 20, 22], "control": [9, 17, 18], "se": [9, 16], "200": 9, "t2v": 9, "30": 9, "60": [9, 17], "100": [9, 12, 13, 14, 16, 17], "130": 9, "meshgrid": [9, 12, 17, 20], "s_te": 9, "int2str": [9, 12, 17, 18, 20], "versu": [9, 12], "150": 9, "mesh": [9, 12], "view": [9, 13, 16, 18, 20], "155": 9, "zlabel": 9, "colorbar": [9, 14, 21], "given": [9, 16, 17, 20, 22], "repetit": [9, 15, 16], "incomplet": 9, "Then": [9, 12, 21], "simplest": 9, "reach": 9, "steadi": [9, 16], "2nd": [9, 20], "evolut": 9, "400": [9, 18], "800": [9, 18], "1200": 9, "2000": 9, "ntr": 9, "500": [9, 21], "nt_per_tr": 9, "t_per_tr": 9, "t_minu": 9, "t_plu": 9, "befor": [9, 16, 17, 20], "mz_minu": 9, "mz_plu": 9, "initi": [9, 12, 20], "ep": [9, 17], "mz_all": 9, "o": 9, "t1v": 9, "s_tr": 9, "2500": 9, "110": 9, "effici": [9, 16], "acqrui": 9, "per": 9, "theta": [9, 15, 16, 17, 18], "s_flip": 9, "By": [9, 14, 20], "long": [9, 18], "enough": [9, 13, 15], "see": [9, 12, 13, 15, 18, 20, 22], "matter": 9, "approx": [9, 13, 20, 22], "cerebrospin": 9, "fluid": 9, "brain": 9, "rel": [9, 10, 13, 14, 15, 18], "therebi": 9, "longer": [9, 16, 18], "shorter": [9, 12, 16, 18], "discuss": [9, 14], "later": [9, 12, 15, 22], "principl": [9, 12, 14], "muscl": 9, "smaller": [9, 14], "boost": 9, "leav": 9, "small": [9, 13, 14, 17, 19, 22], "certain": [9, 13], "ratio": [9, 11, 14, 22], "zoom": 9, "area": [9, 10, 16, 18, 20], "delai": 9, "strategi": [9, 12], "commonli": [9, 10, 13, 16], "null": 9, "stir": 9, "attenu": 9, "flair": 9, "ir": 9, "flip1": 9, "flip2": 9, "750": 9, "mz1_minu": 9, "mz2_minu": 9, "mz1_plu": 9, "mz2_plu": 9, "t1_minu": 9, "t1_plu": 9, "t2_minu": 9, "t2_plu": 9, "evolv": [9, 21], "period": [9, 17], "find": [9, 10, 21], "2001": 9, "4001": 9, "6001": 9, "751": 9, "2751": 9, "4751": 9, "vs": [9, 17], "s_ti": 9, "gadolinium": 9, "chelat": 9, "superparamagnet": 9, "iron": 9, "oxid": 9, "shorten": 9, "wherev": 9, "quantifi": 9, "r_1": 9, "r_2": 9, "typiclali": 9, "l": [9, 10], "mmol": 9, "cm": [9, 14, 21], "concentr": 9, "mm": 9, "1300": 9, "csf": 9, "3700": 9, "1700": 9, "1000": [9, 16], "liver": 9, "cartilag": 9, "pictur": 9, "three": [9, 18], "circular": 9, "jinc": 9, "circl": 9, "circ": 9, "k_r": 9, "scheme": 9, "signal_gr": 9, "mrsignal_spoiled_gradient_echo": [9, 18], "contrast_phantom": 9, "nphan": 9, "xc": 9, "yc": 9, "25": 9, "1e3": [9, 12, 21], "06": 9, "64": [9, 10, 14], "ball": 9, "radiu": [9, 14], "20": [9, 17, 21], "160": 9, "3000": 9, "ky": [9, 12, 20], "coordin": 9, "ad": [9, 15, 16, 17], "individu": [9, 12, 14, 22], "exponenti": [9, 22], "displai": 9, "phi": [10, 20], "tan": 10, "funcion": 10, "ne": 10, "dx": 10, "ax": [10, 15], "ast": 10, "dirac": 10, "comb": 10, "sha": 10, "\u0448": 10, "rectangl": [10, 15], "sqcap": 10, "quad": 10, "linewidth": [10, 20], "normal": [10, 18], "tau": [10, 12, 16, 17, 18, 20], "intuit": [10, 12], "slid": 10, "nice": [10, 19], "unitari": 10, "ordinari": 10, "swap": 10, "dk_x": 10, "k_y": [10, 12, 16, 20], "dy": 10, "f_x": 10, "f_y": 10, "finit": 10, "kspace": 10, "width": 10, "w_": [10, 16], "accord": [10, 16], "convolv": [10, 12], "notabl": 10, "decomposit": 10, "512": 10, "kxmax": 10, "128": 10, "kxmax_trunc": 10, "fftshift": [10, 17], "ifft": 10, "ifftshift": 10, "power": [10, 12, 14, 16, 17, 18, 19, 20], "actual": [10, 15], "dft": 10, "x_n": 10, "coeffici": [10, 18], "k_n": 10, "formula": 10, "extrem": [10, 18, 22], "extend": [10, 18], "si": 11, "gyromagnet": [11, 14, 22], "hz": [11, 12, 13, 16, 21, 22], "receiv": [11, 12, 13, 15, 16, 20], "g_y": [11, 16, 20], "g_z": [11, 16, 21], "b_x": [11, 14], "b_y": [11, 14], "b_z": [11, 14, 20], "jargon": 11, "intimid": [11, 12], "imped": 11, "luckili": 11, "coupl": 11, "radiopaedia": 11, "articl": 11, "abbrevi": 11, "vendor": 11, "com": 11, "serv1": 11, "php": 11, "cam": 11, "format": 12, "equiat": 12, "impact": [12, 18], "affect": [12, 18], "resonnac": 12, "obtain": 12, "int": 12, "int_0": [12, 17, 18, 20], "reason": [12, 18], "clear": 12, "soon": [12, 20], "situat": [12, 16], "add": [12, 13, 14, 21], "simllifi": 12, "easiest": 12, "c_n": 12, "s_n": 12, "receiev": 12, "filter": [12, 16, 21], "integr": [12, 17, 18, 20], "upsilon": 12, "gxr": [12, 16], "kx0": 12, "upsilon_cartesian": 12, "tesp": 12, "dky": 12, "assum": 12, "deadtim": 12, "tall": 12, "upsilon_epi": 12, "reshap": 12, "planar": [12, 16, 20, 21], "corrupt": 12, "convolut": 12, "snr": 12, "w_cartesian": 12, "w_epi": 12, "x0": 12, "height": 12, "peak": [12, 17], "outsid": [12, 17], "get": [12, 15, 22], "wors": 12, "much": [12, 14, 15, 16, 17, 22], "macroscop": 12, "f_": [12, 18], "speci": 12, "examin": [12, 18], "could": 12, "index": 12, "complic": 12, "gain": [12, 16, 18], "spiral": [12, 20], "radial": [12, 20], "look": [12, 13, 15, 16, 17, 22], "_0": [12, 20], "r_0": 12, "star": 12, "df": [12, 17, 21], "frfom": 12, "residu": 12, "side": [12, 14, 18], "lobe": 12, "interpol": [12, 18], "write": 12, "version": [12, 21], "numer": [12, 18], "solver": 12, "graph": 12, "As": [12, 17, 22], "framework": [12, 20], "express": 12, "boil": 12, "down": [12, 17, 22], "decompos": [12, 18], "m_i": 12, "w_i": 12, "sum_i": 12, "divid": [12, 14, 22], "water": [12, 16, 21, 22], "m_1": 12, "m_2": 12, "w_1": 12, "w_2": 12, "accur": 12, "thw": 12, "ssfp": 12, "diffus": [12, 18, 19, 21], "explor": 13, "deconstruct": 13, "insid": 13, "insight": 13, "hardwar": 13, "loud": 13, "danger": 13, "metal": 13, "cut": 13, "nuclear": 13, "greater": 13, "stronger": [13, 14], "tesla": 13, "alwai": [13, 14, 16, 20, 22], "homogen": [13, 14], "manget": [13, 22], "superconduct": 13, "alloi": 13, "bath": 13, "liquid": 13, "helium": 13, "recept": 13, "deposit": [13, 21], "perturb": [13, 14, 22], "caus": [13, 17, 22], "releas": 13, "radio": [13, 14], "mhz": [13, 14, 16], "excitaiton": [13, 16], "thermal": [13, 22], "Thes": 13, "linearli": [13, 18, 20], "place": [13, 14, 16, 22], "fiel": 13, "distinguish": 13, "summar": [13, 18], "tabl": 13, "strength": [13, 16, 18], "mu": [13, 14, 16, 22], "critic": [14, 18], "wire": 14, "govern": [14, 22], "electromagnet": [14, 22], "maxwel": 14, "equat": [14, 16, 17, 20], "rule": 14, "link": 14, "solenoid": 14, "volum": [14, 20], "psace": [14, 21], "ensur": 14, "usual": [14, 15, 16], "convent": [14, 20, 22], "50": 14, "05": [14, 20], "switch": [14, 15, 17, 22], "few": [14, 17, 19], "Their": 14, "00001": 14, "perpedicularli": 14, "plane": [14, 15, 16], "reactiv": 14, "capacitor": 14, "inductor": 14, "kw": 14, "surround": 14, "mv": 14, "aris": [14, 16], "channel": 14, "put": [14, 18, 20], "electr": 14, "i0": 14, "amp": 14, "mu0": 14, "401": 14, "bz": 14, "211": [14, 17, 21], "212": [14, 17, 21], "resons": 14, "event": 14, "amplifi": 14, "digit": 14, "tell": 14, "far": [14, 20], "birdcag": 14, "perpendicular": [14, 16, 22], "tailor": 14, "knee": 14, "abdomen": 14, "head": 14, "configur": [14, 16], "isol": 14, "decoupl": 14, "detun": 14, "turn": [14, 15, 16, 20, 22], "don": 14, "senit": 14, "move": [14, 16, 22], "brightest": 14, "closest": 14, "biot": 14, "savart": 14, "law": 14, "flag_2d": 14, "bx": 14, "BY": 14, "xp": 14, "yp": [14, 20], "zp": 14, "loop_coil_field": 14, "quiver": [14, 20], "18": 14, "bmag": 14, "xhalf": 14, "chapter": [15, 22], "select": [15, 16, 19, 21], "import": [15, 17, 18], "indic": 15, "conjunct": 15, "remeb": 15, "incred": [15, 20], "convei": 15, "signific": 15, "experiment": 15, "speed": 15, "drawn": 15, "bracket": 15, "particular": 15, "simlifi": 15, "crusher": 15, "destruct": 15, "shape": [15, 21], "instantan": 15, "realiti": 15, "slew": [15, 21], "trapezoid": 15, "mai": 16, "clinic": 16, "3t": 16, "5t": 16, "xrai": 16, "visibl": 16, "light": 16, "fm": 16, "am": 16, "proper": 16, "assign": 16, "conduct": 16, "calibr": 16, "isotop": 16, "cannot": [16, 22], "1h": 16, "13": [16, 22], "19": [16, 22], "2h": 16, "human": [16, 22], "diamagnet": 16, "paramagnet": 16, "ferromagnet": 16, "proton": [16, 18, 21, 22], "immedi": 16, "equilibirum": 16, "static": 16, "parallel": [16, 20], "lab": [16, 17], "frame": [16, 17], "flux": 16, "benefit": 16, "compress": [16, 19], "sens": [16, 19], "doesn": 16, "contribut": [16, 22], "highest": 16, "spoil": [16, 18], "2e": 16, "pdw": 16, "t1w": 16, "t2w": 16, "dixon": 16, "prepar": 16, "additoin": 16, "suppress": [16, 21], "daq": 16, "serv": 16, "mxy": [16, 20], "statement": 16, "true": 16, "overlap": 16, "prewind": 16, "gre": [16, 18], "\u03b8": 16, "twice": 16, "thinner": 16, "decreas": 16, "bandwidth": 16, "bw_": [16, 17], "bw": [16, 17], "nyquist": 16, "theorem": 16, "avoid": 16, "lowest": 16, "oversampl": 16, "multislic": 16, "next": [16, 20], "3dft": 16, "hold": 16, "rbw": 16, "anti": 16, "xr": [16, 20], "read": [16, 18, 20], "fov_x": 16, "n_": [16, 22], "fe": 16, "none": 16, "stretch": [16, 17], "pile": 16, "bright": 16, "band": 16, "sequenti": 16, "sar": [16, 17], "rapidli": 16, "robust": 16, "intravoxel": 16, "free": 16, "bssfp": 16, "partial": 16, "deep": 16, "learn": 16, "symmetri": 16, "gather": 16, "databas": 16, "outer": 16, "amplif": 16, "acquist": 16, "Of": 16, "regardless": 16, "dataset": 16, "develop": 16, "000": 16, "decod": 16, "recurr": 16, "appl": 17, "equival": [17, 18, 20], "aim": [17, 21], "tbw": [17, 21], "detail": 17, "ss": 17, "distanc": 17, "absorb": 17, "heat": 17, "safeti": 17, "minim": 17, "sinusoid": 17, "002": 17, "tmax": 17, "rf_sinusoid": 17, "ft_sinusoid": 17, "imaginari": 17, "xlim": [17, 20], "tmat": 17, "dfmat": 17, "rf_all": 17, "rf_n": 17, "ft_n": 17, "fwidth": 17, "11": [17, 21], "rf_sinc": 17, "ft_sinc": 17, "gz": [17, 21], "poorli": 17, "uniformli": 17, "forth": [17, 22], "substanti": 17, "presenc": 17, "meanwhil": 17, "wide": [17, 18], "spread": 17, "wherea": [17, 22], "precis": 17, "360": 17, "address": 17, "avail": [17, 19, 22], "impli": [17, 18], "shrunk": 17, "goe": 17, "bwplot": 17, "IN": 17, "rf_shape": 17, "trf": 17, "bwrf": 17, "plai": 17, "notic": [17, 22], "sharper": 17, "But": [17, 18], "break": 17, "sophist": 17, "account": [17, 18], "shinnar": 17, "le": 17, "roux": 17, "slr": 17, "dzrf": [17, 21], "isn": 17, "issu": 17, "themselv": 17, "subtli": 17, "degrad": 17, "inv": 17, "characterist": 18, "theoret": 18, "foundat": 18, "delta_i": 18, "delta_z": 18, "gaussian": 18, "root": 18, "sigma": 18, "mea": 18, "downtim": 18, "seq": 18, "especi": [18, 19], "ernst": 18, "theta_": 18, "intrigu": 18, "trdt1": 18, "01": 18, "1600": 18, "inf": 18, "theta_optim": 18, "snr_effici": 18, "it1": 18, "aco": 18, "ylim": [18, 20], "drop": 18, "stabl": 18, "finer": 18, "coarser": 18, "nativ": 18, "pad": 18, "nearbi": 18, "scale": [18, 21], "distinct": 18, "care": 18, "alon": [18, 20], "demonin": 18, "tread": 18, "snr_t2s_onesid": 18, "imax_onesid": 18, "snr_t2s_twosid": 18, "imax_twosid": 18, "disp": 18, "2806": 18, "4907": 18, "ve": 19, "favorit": 19, "focus": 19, "kmjohnson3": 19, "intro": 19, "python": 19, "jupyt": [19, 23], "introduct": 19, "mribri999": 19, "mrsignalsseq": 19, "introductori": 19, "marku": 19, "nilsson": 19, "matlab": 19, "mikgroup": 19, "sigpi": 19, "packag": 19, "mrirecon": 19, "bart": 19, "toolbox": 19, "qmrlab": 19, "quantit": 19, "fit": 19, "transfer": 19, "ismrm": 19, "mrhub": 19, "hub": 19, "worth": 19, "brows": 19, "delv": [19, 22], "topic": 19, "omega": 20, "basi": [20, 22], "cumul": 20, "stop": 20, "undo": 20, "k_z": [20, 21], "motiv": 20, "local": 20, "rather": 20, "textrm": 20, "i2": 20, "amaz": 20, "appropri": 20, "fact": 20, "regularli": 20, "increment": 20, "1d": 20, "splot": 20, "kfe": 20, "phase_x": 20, "mxy_f": [20, 21], "drawnow": 20, "3rd": 20, "t_y": 20, "kpe": 20, "tpe": 20, "ip": 20, "phase_i": 20, "mxy_p": 20, "spatial_encoding_mxy_illustr": 20, "blade": 20, "kx_ep": 20, "ky_ep": 20, "k_theta": 20, "k_radial": 20, "201": [20, 21], "nturn": 20, "k_spiral": 20, "molecul": 21, "lipid": [21, 22], "fmri": 21, "spectroscopi": 21, "relat": 21, "reveal": 21, "travers": 21, "trick": 21, "compil": 21, "abr": 21, "mex": 21, "file": 21, "error": 21, "re": 21, "run": 21, "abrx": 21, "31": [21, 22], "column": 21, "trajectoi": 21, "nlobe": 21, "nspec": 21, "nramp": 21, "ramp": 21, "g1": 21, "gamp": 21, "95": 21, "mod": 21, "nrw": 21, "grw": 21, "cumsum": 21, "k_f": 21, "h_f": 21, "h_z": 21, "envelop": 21, "subpuls": 21, "4258": 21, "slewmax": 21, "15e3": 21, "gmax": 21, "20e": 21, "sbw": 21, "dz": 21, "resolut": 21, "10e": 21, "verse_frac": 21, "nspat": 21, "nwait": 21, "rfspec": 21, "gf": 21, "ab2ex": 21, "g_f": 21, "rfspat": 21, "min": 21, "ceil": 21, "floor": 21, "vers": 21, "rfspatv": 21, "isnan": 21, "g1z": 21, "mxy_z": 21, "flip_scal": 21, "rfscaleg": 21, "plot3": 21, "589": 21, "mxy_2d": 21, "m_xy": 21, "watch": 21, "behav": 22, "phenomenom": 22, "nucleu": 22, "angular": 22, "momentum": 22, "moment": 22, "act": 22, "respond": 22, "tyipcal": 22, "hydrogen": 22, "nuclei": 22, "atom": 22, "primari": 22, "23": 22, "na": 22, "p": 22, "abund": 22, "absenc": 22, "randomli": 22, "ensembl": 22, "arrow": 22, "vertic": 22, "www": 22, "i_z": 22, "planck": 22, "63e": 22, "34": 22, "58e6": 22, "boltzmann": 22, "62e": 22, "ev": 22, "38e": 22, "temperatur": 22, "310": 22, "prefer": 22, "boltzman": 22, "uparrow": 22, "downarrow": 22, "kt": 22, "expon": 22, "strongli": 22, "analog": 22, "swing": 22, "your": 22, "leg": 22, "wrong": 22, "compassmr": 22, "default": 22, "compass": 22, "mode": 22, "slider": 22, "adjust": 22, "freq": 22, "uenci": 22, "new": 22, "checkbox": 22, "part": 22, "hit": 22, "push": 22, "button": 22, "needl": 22, "blue": 22, "trace": 22, "highlight": 22, "composit": 22, "last": 22, "mx": 22, "anaconda": 23, "prompt": 23, "FOR": 23, "conda": 23, "wintest": 23, "environ": 23, "pip": 23, "instal": 23, "forg": 23, "octave_kernel": 23, "jb": 23, "booknam": 23, "runjb": 23, "quantecon": 23, "mini": 23, "seem": 23}, "objects": {}, "objtypes": {}, "objnames": {}, "titleterms": {"acceler": [0, 16], "imag": [0, 3, 6, 9, 16, 20], "method": [0, 16], "learn": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 17, 18, 20, 21, 22], "goal": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 17, 18, 20, 21, 22], "gener": 0, "formul": 0, "mri": [0, 6, 7, 9, 10, 11, 12, 13, 14, 16, 19, 20], "reconstruct": [0, 6, 16], "parallel": 0, "space": [0, 6, 10, 11, 12, 20], "auto": 0, "calibr": 0, "k": [0, 6, 10, 12, 20], "snr": [0, 16, 18], "artifact": [0, 1, 16], "compress": 0, "sens": 0, "deep": 0, "requir": 0, "dl": 0, "refer": 0, "comparison": 1, "simul": [1, 5, 8, 14, 22], "field": [2, 11, 13, 14, 15, 20], "view": 2, "fov": [2, 16], "resolut": [2, 16, 18], "spatial": [2, 16, 20, 21], "fast": [3, 16], "puls": [3, 4, 5, 8, 15, 16, 17, 21], "sequenc": [3, 5, 15, 16], "under": 3, "construct": 3, "echo": [3, 5], "planar": 3, "epi": 3, "turbo": 3, "spin": [3, 5, 22], "fse": 3, "tse": 3, "fun": 4, "rf": [4, 8, 13, 14, 15, 16, 17, 21], "adiabat": 4, "pretti": 4, "pictur": 4, "gradient": [5, 13, 14, 15, 20], "ge": 5, "gre": 5, "off": [5, 12, 17], "reson": [5, 12, 14, 17, 22], "effect": [5, 20], "t2": [5, 9], "refocus": 5, "visual": 5, "se": 5, "sort": 6, "data": [6, 10, 12, 15, 18, 20], "fourier": [6, 10], "transform": [6, 10], "partial": 6, "introduct": 7, "principl": 7, "get": 7, "start": 7, "acknowledg": 7, "bloch": 8, "equat": [8, 12, 18, 22], "THE": 8, "precess": [8, 22], "excit": [8, 14, 15, 17, 22], "exampl": [8, 9, 10], "constant": 8, "amplitud": 8, "lab": 8, "versu": [8, 17, 18], "rotat": 8, "frame": 8, "common": 8, "flip": [8, 9, 17], "angl": [8, 9, 17], "relax": [8, 9, 12, 22], "contrast": [9, 16], "te": 9, "tr": [9, 18], "t1": 9, "90": 9, "degre": 9, "proton": 9, "densiti": 9, "weight": [9, 12], "pd": 9, "invers": [9, 10], "recoveri": 9, "agent": 9, "typic": 9, "time": [9, 17, 18], "3t": 9, "simpl": 9, "phantom": 9, "challeng": 9, "yourself": 9, "math": 10, "concept": 10, "complex": 10, "number": 10, "impuls": 10, "function": 10, "train": 10, "sampl": [10, 15], "other": 10, "convolut": 10, "2": 10, "d": 10, "n": 10, "dualiti": 10, "separ": 10, "ident": 10, "pair": 10, "truncat": 10, "point": 10, "spread": 10, "psf": 10, "analysi": 10, "discret": 10, "notat": 11, "terminolog": 11, "definit": 11, "posit": 11, "net": 11, "magnet": [11, 13, 14, 15, 18, 20, 22], "acronym": 11, "glossari": 11, "The": [12, 13, 15], "signal": [12, 14, 18, 20], "ideal": 12, "ad": 12, "coil": [12, 13, 14, 16], "sensit": [12, 14], "dure": 12, "acquisit": [12, 15, 18], "chemic": 12, "shift": [12, 17], "complet": 12, "system": [13, 14, 16], "compon": [13, 15], "scanner": 13, "main": [13, 14], "b_0": [13, 14], "radiofrequ": [13, 14], "b_1": [13, 14], "vec": [13, 14], "r": [13, 14], "t": [13, 14], "g": [13, 14], "fundament": 13, "experi": 13, "procedur": 13, "loop": 14, "current": 14, "transmit": 14, "tx": 14, "receiv": 14, "rx": 14, "recept": 14, "creat": 14, "reciproc": 14, "profil": 14, "element": 14, "local": 15, "g_x": 15, "g_y": 15, "g_z": 15, "window": 15, "daq": 15, "diagram": 15, "annot": 15, "simplifi": 15, "kei": 15, "paramet": 15, "question": 16, "mr": 16, "physic": [16, 22], "encod": [16, 20], "characterist": 16, "properti": 17, "bandwidth": 17, "product": 17, "slice": 17, "thick": 17, "specif": 17, "absorpt": 17, "rate": 17, "select": 17, "hard": 17, "shape": 17, "On": 17, "design": [17, 21], "high": 17, "nois": 18, "ratio": 18, "depend": 18, "voxel": 18, "volum": 18, "transvers": 18, "effici": 18, "post": 18, "process": 18, "upsampl": 18, "downsampl": 18, "t_2": 18, "decai": 18, "softwar": 19, "resourc": 19, "from": 20, "cartesian": 20, "frequenc": [20, 22], "phase": 20, "2dft": 20, "trajectori": 20, "spectral": 21, "nuclear": 22, "polar": 22, "equilibrium": 22, "fraction": 22}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 6, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx": 56}})
\ No newline at end of file
+Search.setIndex({"docnames": ["Accelerated Imaging Methods", "Artifacts", "FOV and Resolution", "Fast Imaging Pulse Sequences", "Fun with RF Pulses", "Gradient and Spin Echoes", "Image Reconstruction", "Introduction", "MR Physics - Bloch Equation", "MRI Contrast", "MRI Math Concepts", "MRI Notation", "MRI Signal Equation", "MRI System", "Magnetic Fields and RF Coils", "Pulse Sequence", "Questions", "RF Pulses", "Signal to Noise Ratio", "Software_Resources", "Spatial Encoding", "Spectral-Spatial RF Pulses", "Spin Physics", "build_notes"], "filenames": ["Accelerated Imaging Methods.ipynb", "Artifacts.ipynb", "FOV and Resolution.ipynb", "Fast Imaging Pulse Sequences.ipynb", "Fun with RF Pulses.ipynb", "Gradient and Spin Echoes.ipynb", "Image Reconstruction.ipynb", "Introduction.md", "MR Physics - Bloch Equation.ipynb", "MRI Contrast.ipynb", "MRI Math Concepts.ipynb", "MRI Notation.ipynb", "MRI Signal Equation.ipynb", "MRI System.ipynb", "Magnetic Fields and RF Coils.ipynb", "Pulse Sequence.ipynb", "Questions.md", "RF Pulses.ipynb", "Signal to Noise Ratio.ipynb", "Software_Resources.md", "Spatial Encoding.ipynb", "Spectral-Spatial RF Pulses.ipynb", "Spin Physics.ipynb", "build_notes.md"], "titles": ["Accelerated Imaging Methods", "Artifacts", "Field of View (FOV) and Resolution", "Fast Imaging Pulse Sequences (Under Construction)", "Fun with RF Pulses?", "Gradient and Spin Echo Pulse Sequences", "Image Reconstruction", "Introduction to Principles of MRI", "Bloch Equation", "MRI Contrast", "MRI Math Concepts", "MRI Notation and Terminology", "The MRI Signal Equation and K-space", "The MRI System", "Magnetic fields in MRI", "The Pulse Sequence", "MRI Questions", "RF Pulses", "Signal to Noise Ratio (SNR)", "MRI Software Resources", "Spatial Encoding", "Spectral-Spatial RF Pulses", "Spin Physics", "<no title>"], "terms": {"scan": [0, 3, 6, 7, 13, 14, 16, 18], "can": [0, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "appli": [0, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 18, 20, 21, 22], "reduc": [0, 5, 6, 9, 16], "number": [0, 6, 8, 11, 12, 14, 15, 20, 21, 22], "sampl": [0, 2, 6, 12, 16, 19, 20, 21], "also": [0, 1, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 20, 21, 22], "known": [0, 3, 6, 10, 14, 20, 22], "undersampl": [0, 16], "These": [0, 2, 3, 4, 5, 6, 9, 12, 13, 14, 17, 20, 21, 22], "correspond": [0, 6, 16, 20], "advanc": [0, 6, 19], "allow": [0, 3, 9, 10, 17, 18], "The": [0, 1, 2, 4, 5, 6, 8, 9, 10, 11, 14, 16, 17, 18, 20, 21, 22], "techniqu": [0, 3, 6, 9], "cover": [0, 20, 22], "here": [0, 4, 7, 8, 10, 12, 15, 20, 22], "includ": [0, 1, 3, 5, 6, 7, 8, 10, 12, 13, 15, 18, 19, 20, 21, 22], "describ": [0, 2, 3, 5, 6, 7, 8, 9, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "how": [0, 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "ar": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], "form": [0, 2, 3, 6, 7, 9, 12, 13, 15, 17, 20, 21, 22], "work": [0, 3, 7, 9, 13, 20, 21], "understand": [0, 3, 5, 7, 8, 11, 12, 14, 15, 17, 18, 20, 21, 22], "constraint": [0, 7, 12, 18], "tradeoff": [0, 7, 12, 18], "identifi": [0, 1, 3, 5, 7, 9, 12, 15, 16, 21], "when": [0, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22], "manipul": [0, 2, 3, 6, 7, 9, 12, 14, 15, 17, 18], "sequenc": [0, 2, 6, 7, 9, 11, 12, 14, 17, 18, 19, 20], "paramet": [0, 2, 3, 6, 7, 9, 12, 17, 18, 21], "improv": [0, 2, 3, 6, 7, 9, 12, 16, 17, 18], "perform": [0, 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20], "defin": [0, 2, 6, 10, 12, 14, 15, 17, 18, 20, 22], "which": [0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "modifi": 0, "analyz": [0, 6, 7, 8, 10, 12, 15, 17], "data": [0, 1, 3, 5, 7, 9, 13, 16], "an": [0, 5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "from": [0, 4, 6, 7, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 21, 22], "raw": [0, 6], "For": [0, 2, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 22], "help": [0, 11, 12, 15, 21, 22], "reformul": 0, "problem": [0, 6, 16], "linear": [0, 1, 6, 10, 12, 14, 17, 18, 20], "system": [0, 6, 10, 18, 19], "us": [0, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "standard": [0, 11], "mathemat": [0, 14], "notat": [0, 8, 12, 13, 20], "y": [0, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20], "mathbf": 0, "e": [0, 1, 6, 8, 12, 14, 15, 16, 17, 20, 22], "x": [0, 2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 21], "n": [0, 1, 2, 8, 9, 12, 14, 15, 17, 20, 22], "where": [0, 8, 9, 10, 12, 14, 15, 17, 18, 20, 21, 22], "acquir": [0, 3, 5, 6, 9, 12, 13, 16, 18, 20], "encod": [0, 1, 5, 12, 13, 15], "matrix": [0, 6, 9, 20], "spatial": [0, 1, 5, 6, 10, 12, 13, 14, 15, 18], "distribut": [0, 18, 22], "transvers": [0, 5, 6, 8, 9, 11, 12, 14, 15, 16, 20, 21, 22], "magnet": [0, 1, 4, 5, 6, 7, 8, 9, 12, 16, 17, 19, 21], "g": [0, 1, 6, 10, 11, 12, 15, 16, 17, 20, 21], "nois": [0, 1, 14, 16], "In": [0, 2, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 20, 22], "thi": [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22], "vector": [0, 4, 8, 14, 17, 22], "exampl": [0, 2, 4, 5, 6, 12, 14, 18, 19, 20, 21, 22, 23], "2d": [0, 5, 6, 14, 16, 20, 21], "ft": [0, 10, 16, 20], "would": [0, 6, 7, 8, 13, 21, 22], "convert": [0, 6, 8, 17], "left": [0, 4, 6, 8, 10, 12, 14, 20], "begin": [0, 5, 8, 10, 11, 14, 18, 20, 22], "arrai": [0, 10, 14, 16], "c": [0, 1, 10, 16, 22, 23], "s_1": 0, "t_1": [0, 8, 9, 11, 12, 16, 18, 22], "t_2": [0, 5, 8, 9, 11, 12, 16, 20, 22], "vdot": 0, "t_": [0, 16, 17, 18], "nx": 0, "s_2": 0, "s_": [0, 5, 9, 12], "ny": 0, "end": [0, 2, 5, 8, 9, 10, 11, 14, 17, 18, 20, 21, 22], "right": [0, 4, 10, 12, 20, 22], "s_m": 0, "t_n": 0, "m": [0, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 20, 22], "th": [0, 6], "tr": [0, 3, 6, 12, 15, 16], "x_1": 0, "y_1": 0, "x_2": 0, "x_": 0, "1": [0, 1, 2, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 21, 22], "y_2": 0, "y_": 0, "x_i": 0, "y_i": 0, "equal": [0, 1, 2, 6, 9, 16, 17], "locat": [0, 1, 2, 5, 6, 8, 9, 10, 12, 13, 14, 17, 20, 22], "minimum": [0, 14, 15, 16], "discret": [0, 6], "fourier": [0, 9, 12, 16, 17, 20, 21], "transform": [0, 8, 9, 12, 16, 17, 20, 21], "f": [0, 1, 6, 9, 10, 12, 13, 16, 17, 20, 21, 22], "repres": [0, 5, 10, 12, 14, 16, 17, 20, 22], "our": [0, 2, 5, 6, 8, 9, 10, 12, 13, 14, 20, 22], "evalu": [0, 6, 20], "entri": [0, 1], "being": [0, 8, 12, 15, 17, 18, 22], "vec": [0, 4, 5, 6, 8, 10, 11, 12, 16, 20, 22], "_i": [0, 6], "r": [0, 5, 6, 8, 9, 11, 12, 16, 20, 22], "_j": 0, "_": [0, 6, 12, 15, 20], "i": [0, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21], "j": [0, 22], "exp": [0, 1, 5, 9, 10, 12, 16, 17, 18, 20], "2": [0, 1, 2, 4, 5, 6, 8, 9, 12, 14, 15, 16, 17, 18, 20, 21, 22], "pi": [0, 1, 5, 8, 9, 10, 12, 14, 16, 17, 18, 20, 21], "cdot": [0, 9, 10, 12, 14, 16, 17, 20], "case": [0, 9, 10, 12, 17, 18], "measur": [0, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 20, 22], "invers": [0, 1, 4, 6, 12, 16, 17, 20], "fulli": [0, 6, 9, 16, 20], "well": [0, 1, 5, 6, 9, 12, 14, 15, 17], "hat": [0, 9, 10, 12], "h": [0, 10, 16, 21, 22], "we": [0, 2, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22], "need": [0, 10, 13, 16, 18, 20, 22, 23], "consid": [0, 8, 12, 17, 18, 22], "coil": [0, 4, 6, 15, 17, 18, 20, 22], "sensit": [0, 13, 16, 20], "profil": [0, 6, 12, 17, 21], "_q": 0, "each": [0, 6, 9, 10, 12, 13, 14, 15, 18], "rf": [0, 1, 5, 6, 9, 11, 12, 18, 20], "along": [0, 4, 6, 7, 8, 15, 16, 17, 22], "sub": [0, 11, 21], "oper": [0, 10, 12, 16], "s": [0, 1, 5, 6, 7, 8, 9, 11, 12, 14, 16, 18, 20, 21, 22], "y_q": 0, "n_q": 0, "c_q": 0, "diagon": 0, "diagnoal": 0, "0": [0, 1, 2, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22], "whether": 0, "expect": [0, 8, 9, 12, 15, 16, 18], "grid": [0, 6, 20], "wa": [0, 3, 5, 7], "It": [0, 5, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 20, 22], "conveni": [0, 22], "fill": [0, 6], "point": [0, 18, 22], "return": [0, 8, 13, 22], "origin": [0, 3, 10, 12, 14, 22], "creat": [0, 2, 4, 5, 6, 7, 9, 12, 13, 15, 16, 17, 20, 21, 22], "augment": 0, "matric": [0, 9, 12], "concaten": 0, "element": [0, 12], "dimens": [0, 6, 9, 10, 12, 18, 20, 21], "ldot": 0, "y_n": 0, "_1": [0, 9], "_2": [0, 9], "_n": 0, "n_1": 0, "n_2": 0, "n_n": 0, "result": [0, 4, 6, 8, 9, 10, 12, 13, 17, 18, 20, 21, 22], "ex": [0, 17], "follow": [0, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20], "optim": [0, 18], "arg": 0, "min_": 0, "frac": [0, 2, 5, 8, 9, 10, 16, 17, 18, 20, 22], "2_2": 0, "solv": [0, 12], "directli": [0, 9, 16], "pseudo": [0, 16], "calcul": [0, 8, 16], "pattern": [0, 2, 15, 16, 17, 20], "typic": [0, 4, 5, 6, 8, 10, 12, 13, 14, 15, 16, 17, 18, 20, 21], "regular": 0, "mean": [0, 5, 6, 8, 9, 12, 14, 16, 17, 18, 20, 22], "consist": [0, 9, 13, 20, 21], "skip": 0, "line": [0, 1, 2, 3, 6, 7, 12, 15, 16, 20, 21], "grappa": 0, "util": 0, "kernel": [0, 12], "comput": [0, 10], "itself": 0, "captur": [0, 2, 9, 12, 13, 15, 18, 20], "lambda": 0, "tune": [0, 14], "ident": [0, 17], "simultan": [0, 16], "enforc": 0, "first": [0, 6, 8, 9, 15, 17, 20], "term": [0, 8, 9, 12, 16], "self": 0, "sescond": 0, "either": [0, 12, 16, 17, 18], "iter": 0, "estim": [0, 9], "while": [0, 5, 6, 8, 9, 12, 13, 17, 18, 21], "spirit": 0, "combin": [0, 12, 21], "full": [0, 2, 7, 11, 12, 16, 22], "center": [0, 6, 9, 12, 14, 15, 16, 17, 20], "There": [0, 5, 17, 18], "penalti": 0, "vari": [0, 8, 9, 11, 12, 13, 14, 17, 18, 20, 21, 22], "sever": [0, 5], "depend": [0, 5, 8, 9, 12, 14, 16, 20, 22], "condit": [0, 6, 9, 18, 22], "more": [0, 5, 6, 7, 8, 9, 12, 13, 15, 16, 17, 18, 19], "direct": [0, 4, 6, 8, 12, 13, 14, 16, 20, 21, 22], "lead": [0, 5, 10, 12, 17, 18, 20], "lower": [0, 9, 18], "convers": 0, "fewer": 0, "ill": 0, "higher": [0, 1, 9, 17, 18, 22], "penatli": 0, "region": [0, 1, 14], "littl": 0, "differ": [0, 1, 5, 6, 9, 12, 13, 14, 15, 16, 17, 18, 20, 22], "betweeen": 0, "bodi": [0, 14, 16, 17, 22], "tend": 0, "have": [0, 4, 8, 9, 14, 16, 17, 18, 20, 22], "larger": [0, 12, 14, 16], "character": [0, 5, 10, 12, 16, 17], "factor": [0, 12, 16, 18], "geq": [0, 6], "loss": [0, 1, 12, 16, 18], "load": [0, 1, 5, 6, 8, 9, 12, 13, 14, 17, 18, 21, 22], "geometri": 0, "appyl": 0, "total": [0, 16, 17, 18, 22], "readout": [0, 3, 6, 12, 16, 18, 20], "time": [0, 5, 6, 8, 10, 11, 12, 14, 15, 16, 20, 21, 22], "sqrt": [0, 9, 10, 14, 16, 17, 18], "relationship": [0, 2, 6, 9, 14, 17, 18], "snr_": [0, 16, 18], "appear": [0, 1, 9, 17], "alias": [0, 1, 16], "sometim": [0, 8, 15], "complet": [0, 5, 7, 8, 16, 20], "remov": [0, 5, 8, 9, 12, 17, 18, 21], "like": [0, 7, 13, 17], "mismatch": 0, "between": [0, 5, 9, 12, 14, 15, 16, 17, 22], "cs": [0, 12], "theori": [0, 10], "sai": [0, 14], "some": [0, 4, 7, 12, 14, 15, 17, 18, 20], "domain": [0, 10, 16, 20], "subset": 0, "other": [0, 4, 6, 7, 8, 12, 13, 14, 17, 18, 20, 22], "word": [0, 4, 6, 13, 17, 20], "further": [0, 12], "acquisit": [0, 3, 5, 6, 9, 13, 16, 20], "specif": [0, 1, 5, 8, 12, 13, 20, 22], "ell_1": 0, "norm": 0, "sum_": [0, 10], "promot": 0, "sparsiti": 0, "solut": [0, 8, 12, 17], "lambda_": 0, "wx": 0, "multipli": [0, 9, 10, 12], "must": [0, 15, 16, 22, 23], "match": [0, 16, 18], "spars": [0, 16], "through": [0, 12, 14, 15, 17, 18, 21], "sparsifi": 0, "w": [0, 12, 16], "chosen": [0, 9], "balanc": [0, 16], "random": [0, 6, 16], "illustrat": 0, "diagram": [0, 5, 16], "below": [0, 1, 4, 5, 6, 8, 9, 10, 12, 14, 15, 17, 21, 22], "procedur": 0, "caption": 0, "figur": [0, 1, 2, 6, 8, 9, 10, 12, 14, 17, 18, 20, 21, 22], "http": [0, 1, 4, 5, 8, 10, 11, 22], "doi": 0, "org": [0, 1, 10, 11], "10": [0, 7, 8, 9, 12, 13, 14, 16, 20, 21], "1109": 0, "msp": 0, "2007": 0, "914728": 0, "heurist": 0, "A": [0, 1, 5, 8, 10, 14, 15, 16, 17, 21, 22], "signal": [0, 1, 5, 6, 7, 8, 9, 10, 13, 15, 16, 17, 19, 21, 22], "8": [0, 2, 8, 9, 10, 14, 17, 20, 21, 22], "fold": [0, 1], "its": [0, 5, 7, 8, 9, 12, 16, 22], "d": [0, 5, 8, 12, 17, 18, 20], "b": [0, 8, 10, 11, 13, 14, 22], "equispac": 0, "prevent": 0, "recoveri": [0, 16], "incoher": 0, "interfer": [0, 1, 14], "strong": [0, 18, 22], "compon": [0, 7, 12, 14, 16, 22], "stick": 0, "abov": [0, 7, 9, 10, 12, 14, 16, 17, 18, 20, 21, 22], "level": [0, 1], "detect": [0, 6, 13, 14, 16, 22], "recov": [0, 9, 22], "threshold": 0, "subtract": [0, 13, 14], "thu": [0, 6, 10, 12, 14, 16, 17, 20, 22], "enabl": [0, 3, 16], "weaker": 0, "popular": [0, 3, 5, 7, 19], "variat": [0, 4, 5, 13, 19, 20], "tv": 0, "tgv": 0, "wavelet": 0, "variabl": [0, 10], "densiti": [0, 16, 18, 22], "preferenti": [0, 13, 16, 22], "ha": [0, 5, 6, 7, 8, 9, 10, 12, 14, 15, 17, 20, 21, 22], "espirit": 0, "difficult": 0, "thei": [0, 4, 6, 7, 9, 13, 14, 15, 16, 17, 22], "inher": 0, "denois": 0, "constrain": 0, "base": [0, 2, 6, 7, 9, 10, 12, 14, 16, 17, 18, 20], "appar": [0, 20], "significantli": 0, "choic": [0, 9, 18], "most": [0, 3, 5, 6, 7, 8, 10, 12, 14, 15, 17, 20, 21, 22], "common": [0, 14, 20, 21], "come": [0, 6, 7, 9, 20], "overfit": 0, "over": [0, 6, 8, 11, 12, 14, 15, 18, 20], "smooth": 0, "unnatur": 0, "block": [0, 5, 15], "conceptu": 0, "train": [0, 16], "incorpor": [0, 10, 12, 18], "inform": [0, 6, 8, 9, 12, 14, 15, 16, 18, 20, 21, 22], "sinc": [0, 1, 2, 5, 6, 10, 12, 13, 14, 17, 18, 20], "real": [0, 6, 10, 16, 17, 20, 21, 22], "world": 0, "relev": [0, 10], "been": [0, 6, 9], "shown": [0, 5, 6, 8, 12, 14, 15, 17, 21, 22], "support": 0, "what": [0, 2, 5, 7, 8, 12, 13, 14, 15, 16, 20, 22], "within": [0, 3, 16, 17, 18, 20], "often": [0, 5, 10, 12, 15, 18], "least": [0, 14, 16], "squar": [0, 18], "object": [0, 1, 2, 6, 9, 10, 12, 20], "reg": 0, "mathcal": [0, 6, 9, 10, 12, 16, 20, 21], "implicitli": 0, "implement": [0, 17, 18], "via": [0, 7], "machin": 0, "attempt": [0, 7], "straightforward": 0, "approach": [0, 18], "cnn": 0, "invert": [0, 5], "after": [0, 3, 5, 8, 9, 13, 14, 15, 16, 20, 22], "g_": [0, 16, 17, 20], "dnn": 0, "deeep": 0, "neural": 0, "network": [0, 16, 19], "nn": 0, "mani": [0, 7, 9, 10, 12, 14, 15, 16, 19, 22], "weight": [0, 5, 16, 18, 21], "prior": [0, 16, 20], "abl": [0, 22], "howev": [0, 5, 6, 9, 10, 12, 17, 18, 22], "so": [0, 5, 6, 8, 9, 12, 13, 14, 17, 18, 20, 21, 22], "call": [0, 3, 4, 5, 8, 9, 14, 17, 21, 22], "un": 0, "roll": 0, "becom": [0, 12, 17, 20], "better": 0, "compact": 0, "design": [0, 7, 8, 13, 14, 18, 19], "mimic": 0, "classic": 0, "algorithm": [0, 6, 10, 21], "seri": 0, "cascad": 0, "modl": 0, "varnet": 0, "regularl": 0, "model": [0, 10], "architectur": [0, 16], "singl": [0, 1, 3, 12, 14, 15, 16, 17, 20], "gradient": [0, 1, 2, 6, 9, 11, 12, 16, 17, 18, 21], "updat": [0, 6, 7, 8, 12, 14, 20, 21, 22], "descent": 0, "unet": [0, 16], "arxiv": 0, "ab": [0, 1, 2, 9, 10, 12, 17, 21], "2004": 0, "06688": 0, "e2": 0, "vn": 0, "take": [0, 4, 9, 17, 18, 20], "under": [0, 6, 7, 18, 22], "input": [0, 10], "ift": 0, "rss": 0, "bottom": [0, 4, 14], "dc": 0, "modul": [0, 1, 12, 17, 18, 20], "bring": [0, 13], "intermedi": [0, 17], "closer": [0, 22], "valu": [0, 6, 9, 10, 12, 16, 17, 18, 22], "refin": 0, "map": [0, 16, 19, 20], "multi": [0, 16], "one": [0, 6, 8, 10, 12, 14, 16, 18, 20, 21, 22], "u": [0, 23], "net": [0, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 19, 20, 22], "back": [0, 4, 6, 8, 9, 12, 14, 17, 20, 21, 22], "sme": 0, "step": [0, 16, 20, 21, 22], "_w": 0, "set": [0, 6, 7, 10], "structur": [0, 11, 22], "overal": [0, 5, 7, 9, 12, 15, 18, 21], "similar": [0, 10, 12], "both": [0, 5, 8, 15, 20, 21, 22], "unrol": [0, 16], "slightli": [0, 5, 6, 15, 17, 22], "lot": [0, 7], "4": [0, 2, 7, 10, 13, 14, 17, 18, 21], "radiolog": 0, "applic": [0, 7, 22], "question": [0, 13], "answer": [0, 13, 16], "qualiti": [0, 12, 18], "supervis": 0, "realist": 0, "modif": [0, 16, 18], "exist": 0, "increas": [0, 14, 16, 17, 18, 22], "size": [0, 1, 2, 5, 6, 9, 10, 16, 18], "fastmri": 0, "provid": [0, 12, 14, 17, 18, 20, 21], "thousand": 0, "high": [0, 1, 12, 14, 15], "med": 0, "nyu": 0, "edu": 0, "48550": 0, "1811": 0, "08839": 0, "resnet": 0, "possibl": [0, 14, 16, 18], "gpu": 0, "essenti": 0, "send": 0, "forward": 0, "compar": [0, 11, 16, 17, 18, 22], "output": [0, 10], "propag": 0, "choos": [0, 9, 18, 22], "function": [0, 7, 8, 9, 12, 14, 16, 17, 20, 21], "l1": 0, "l2": 0, "batch": 0, "rate": [0, 5, 9, 11, 12, 15, 18, 21, 22], "etc": [0, 18], "challeng": [0, 7], "retain": 0, "textur": 0, "featur": [0, 17, 19], "anatomi": [0, 14, 16], "might": 0, "eras": 0, "hallucin": 0, "although": [0, 4, 22], "physic": [0, 18], "assur": 0, "recent": 0, "comprehens": [0, 1], "thes": 0, "reccommend": 0, "hammernik": 0, "k\u00fcstner": 0, "t": [0, 5, 6, 8, 9, 10, 11, 12, 16, 17, 20, 21, 22], "yaman": 0, "huang": 0, "z": [0, 4, 8, 9, 11, 13, 14, 15, 16, 17, 18, 21, 22], "rueckert": 0, "knoll": 0, "ak\u00e7akaya": 0, "driven": 0, "reson": [0, 1, 4, 6, 7, 8, 13, 15, 16, 20], "medic": 0, "ieee": 0, "process": [0, 5, 7, 8, 10, 14, 19, 22], "mag": 0, "2023": [0, 7], "jan": 0, "40": [0, 9], "98": 0, "114": 0, "2022": 0, "3215288": 0, "epub": 0, "pmid": 0, "37304755": 0, "pmcid": 0, "pmc10249732": 0, "pdf": 0, "2203": 0, "12215": 0, "setup": [1, 2, 5, 6, 8, 9, 12, 13, 14, 17, 18, 21, 22, 23], "mri": [1, 2, 3, 5, 8, 15, 17, 18, 21, 22], "educ": [1, 2, 5, 6, 8, 9, 12, 13, 14, 17, 18, 19, 21, 22], "resourc": [1, 2, 5, 6, 8, 9, 11, 12, 13, 14, 17, 18, 21, 22], "path": [1, 2, 5, 6, 8, 9, 12, 13, 14, 17, 18, 21, 22], "requir": [1, 2, 4, 5, 6, 8, 9, 12, 13, 14, 15, 16, 17, 18, 21, 22], "cd": [1, 2, 5, 6, 8, 9, 12, 13, 14, 17, 18, 21, 22], "startup": [1, 2, 5, 6, 8, 9, 12, 13, 14, 17, 18, 21, 22], "imag": [1, 2, 5, 7, 8, 10, 12, 13, 14, 15, 17, 18, 21, 22], "notebook": [1, 19], "variou": [1, 3, 5, 7, 9, 14, 15, 17], "wikipedia": [1, 10], "en": [1, 10], "wiki": [1, 10], "mri_artifact": 1, "veri": [1, 6, 9, 12, 15, 17, 18, 20], "mitig": [1, 3, 5, 7, 12, 21], "them": [1, 3, 5, 7, 12, 13, 14, 21, 22], "name": [1, 5, 8, 17, 20], "frequenc": [1, 4, 5, 6, 8, 10, 12, 13, 14, 15, 16, 17, 21], "phase": [1, 4, 5, 6, 12, 14, 16, 17], "across": [1, 5, 8, 11, 12, 13, 14, 16, 17], "spike": 1, "top": [1, 22], "entir": [1, 14, 19], "gibb": [1, 12, 16], "ring": [1, 10, 12, 16, 17], "truncat": [1, 16], "rippl": [1, 17], "sharp": [1, 10, 17], "edg": [1, 10, 12, 16], "zipper": 1, "noisi": 1, "At": [1, 16], "motion": [1, 16], "flow": [1, 12, 20], "copi": 1, "ghost": [1, 16], "chang": [1, 2, 4, 5, 6, 8, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22], "due": [1, 5, 12, 16, 18, 20], "displac": [1, 16, 21], "distort": [1, 3, 14, 16, 19], "shift": [1, 6, 9, 16, 21], "chemic": [1, 6, 16, 21], "fat": [1, 9, 12, 16, 21], "off": [1, 2, 4, 6, 13, 14, 15, 20, 22], "suscept": [1, 5, 12, 16, 19], "2dft": [1, 16], "epi": [1, 12, 16, 21], "t2": [1, 3, 8, 12, 16, 18, 19, 22], "around": [1, 4, 8, 13, 14, 15, 17, 22], "suscpet": 1, "implant": 1, "air": 1, "slice": [1, 15, 16, 21], "misregistr": 1, "dielectr": 1, "shade": 1, "particularli": [1, 12, 21], "larg": [1, 5, 13, 14, 17, 22], "fov": [1, 9, 13, 14], "b0": [1, 8, 14, 16], "boundari": 1, "artifici": 1, "dark": [1, 16], "tissu": [1, 9, 12, 16, 17, 22], "non": [1, 8, 17, 20, 22], "subject": [1, 5, 8, 12, 13, 22], "k": [1, 2, 3, 9, 16, 18, 21, 22], "space": [1, 2, 3, 9, 14, 16, 18, 21], "datanam": [1, 6], "se_t1_sag_data": [1, 6], "kdata": [1, 2, 6], "im_origin": [1, 6], "ifft2c": [1, 2, 6, 9, 12], "subplot": [1, 2, 6, 12, 14, 17, 18, 20, 21], "121": [1, 12, 18, 20, 21], "imagesc": [1, 2, 6, 9, 14, 21], "log": [1, 2], "max": [1, 2, 18, 21], "colormap": [1, 2, 6, 9, 14, 21], "grai": [1, 2, 6, 9, 14, 21], "axi": [1, 2, 4, 6, 8, 9, 14, 16, 22], "tight": [1, 2, 6, 9, 14], "122": [1, 12, 18, 20, 21], "warn": [1, 6, 8, 12, 14, 20, 21, 22], "user": 1, "plarson": 1, "document": 1, "github": [1, 7], "mat": 1, "found": 1, "search": 1, "n_undersamp": 1, "data_undersamp": 1, "zero": [1, 8, 9, 17, 18, 21, 22], "iundersamp": 1, "round": [1, 14, 21], "im_undersamp": 1, "spike_loc": 1, "6": [1, 8, 10, 17, 18, 20, 21, 22], "53": 1, "data_spik": 1, "5": [1, 2, 8, 9, 10, 12, 13, 14, 17, 18, 20, 21, 22], "im_spik": 1, "rect": [1, 10], "32": [1, 10, 12], "kx": [1, 2, 9, 10, 12, 16, 20], "n_rect": [1, 2], "rect_ring": 1, "221": [1, 2, 17, 21], "222": [1, 2, 17], "ylabel": [1, 8, 9, 12, 14, 17, 18, 20, 21, 22], "kdata_window": 1, "ham": [1, 17], "rect_window": 1, "223": [1, 17, 21], "224": [1, 17], "window": [1, 6, 8, 12, 14, 17, 20, 21, 22, 23], "relative_rf_frequ": 1, "ph_int": 1, "rand": 1, "rfint": 1, "data_rfint": 1, "repmat": [1, 12, 17], "im_rfint": 1, "amplitud": [1, 4, 9, 12, 14, 15, 16, 17, 20, 22], "3": [1, 2, 8, 9, 13, 14, 17, 18, 21, 22], "randn": 1, "fundament": [2, 9, 22], "determin": [2, 10, 12, 13, 14, 16, 17, 20, 21], "cell": 2, "syntaxerror": 2, "invalid": 2, "syntax": 2, "simpl": [2, 18], "delta": [2, 5, 10, 12, 17, 20, 22], "fov_": 2, "k_x": [2, 10, 12, 16, 20], "rectangular": [2, 17], "demonstr": [2, 21], "256": [2, 9], "rect_recon": 2, "titl": [2, 6, 8, 9, 10, 12, 14, 17, 18, 20, 21, 22], "kdata2": 2, "rect_recon2": 2, "doubl": 2, "half": [2, 6, 16], "kdata3": 2, "rect_recon3": 2, "tripl": 2, "One": [2, 4, 14, 18, 22], "third": 2, "maximum": [2, 13, 14, 16, 18], "extent": [2, 14], "k_": 2, "delta_x": [2, 16, 18], "kdata4": 2, "rect_recon4": 2, "4x": 2, "voxel": [2, 5, 11, 16], "kdata8": 2, "7": [2, 14], "16": [2, 10], "9": [2, 8, 22], "rect_recon8": 2, "8x": 2, "modern": 3, "reli": [3, 16], "heavili": 3, "primarili": [3, 7, 15], "method": [3, 5, 6, 15, 18, 19, 20], "multipl": [3, 5, 10, 15, 16, 17], "acronym": [3, 5, 7], "acceler": 3, "artifact": [3, 5, 7, 10, 12, 14, 19, 21], "blur": [3, 12, 16], "row": 3, "faster": [3, 6, 16], "refocus": [3, 4, 16, 17, 21], "exict": 3, "dure": [3, 5, 6, 7, 9, 14, 15, 16, 17, 18, 20, 21], "rapid": 3, "relax": [3, 7, 11, 15, 16, 18, 20], "enhanc": [3, 12], "rare": 3, "scanner": [3, 15, 16, 22], "ge": [3, 9, 16], "healthcar": 3, "siemen": 3, "healthin": 3, "field": [3, 4, 5, 8, 12, 16, 17, 18, 22], "tfe": [3, 20], "philip": 3, "ye": 4, "you": [4, 5, 7, 9, 11, 22], "heard": 4, "me": 4, "mayb": 4, "special": [4, 6], "type": [4, 5, 7, 9, 11, 12, 15, 16, 17, 18, 20], "person": 4, "think": 4, "check": 4, "out": [4, 5, 6, 11, 12, 16, 18, 20], "interest": [4, 14, 18], "movi": [4, 20], "spinbench": [4, 7], "heartvista": 4, "ai": 4, "class": [4, 5], "basic": [4, 9, 10, 15, 19], "insensit": 4, "b_1": [4, 11, 17, 21, 22], "inhomongen": 4, "similarli": [4, 10, 18], "even": 4, "transmit": [4, 11, 13, 16], "mostli": 4, "effect": [4, 10, 12, 18], "180": [4, 5, 8, 9, 16, 17, 18], "degre": [4, 5, 8, 16, 17, 18], "flip": [4, 5, 14, 15, 16, 18, 21], "angl": [4, 5, 14, 15, 16, 18, 22], "purpos": [4, 13, 14, 15, 17, 19], "spin": [4, 8, 9, 11, 12, 13, 14, 16, 17, 18], "echo": [4, 9, 11, 12, 15, 16, 18, 20, 21], "unwant": 4, "show": [4, 6, 8, 9, 10, 12, 14, 15, 17, 20], "simul": [4, 7, 9, 17, 19, 20], "two": [4, 5, 18, 21, 22], "sweep": 4, "again": [4, 12, 22], "second": [4, 9, 15], "yellow": 4, "b1": 4, "white": [4, 9], "rang": [4, 7, 13, 14, 16, 17, 19], "larmor": [4, 8, 14, 15, 16, 17, 22], "plot": [4, 6, 8, 9, 10, 12, 14, 17, 18, 20, 21, 22], "corner": 4, "continu": [4, 10, 22], "constant": [4, 5, 9, 16, 17, 20, 22], "hard": [4, 5, 8, 16], "frequneci": [4, 12, 20], "rotat": [4, 12, 14, 15, 16, 17, 20, 22], "broad": [5, 7], "simpler": 5, "addit": [5, 6, 8, 12, 16, 17, 18, 20], "elimin": [5, 9, 16, 21], "undesir": 5, "contrast": [5, 7, 8, 12, 15, 17, 22], "build": [5, 12, 17, 19, 23], "excit": [5, 6, 9, 11, 13, 16, 20, 21], "g_x": [5, 11, 16, 20], "cancel": 5, "section": [5, 9, 20], "anoth": [5, 8, 9, 17, 22], "recal": [5, 6], "And": [5, 12, 14, 18, 22], "simplifi": [5, 8, 12, 20, 22], "exhibit": 5, "explain": [5, 7, 8], "propto": [5, 9, 17, 18], "m_0": [5, 8, 9, 11, 16, 18, 22], "te": [5, 12, 15, 16, 18], "ideal": [5, 6, 9, 10, 15], "uniform": 5, "absens": [5, 22], "ani": [5, 7, 8, 9, 12, 16, 18, 20, 22], "practic": [5, 6, 10, 18, 20], "unavoid": 5, "refer": [5, 8, 13, 17, 20, 22], "f_r": [5, 12], "imperfect": [5, 12], "main": [5, 8, 9, 11, 12, 15, 16, 21, 22], "b_0": [5, 8, 11, 16, 22], "decai": [5, 9, 16, 22], "everi": [5, 9, 14, 15, 16, 18], "contain": [5, 6, 16, 17], "smallest": 5, "sum": [5, 12, 17, 20, 21, 22], "align": [5, 6, 13, 14, 16, 20, 22], "mathrm": [5, 6, 9, 10, 13, 15, 18, 20], "int_": [5, 10, 18, 20], "m_": [5, 6, 8, 11, 12, 15, 16, 17, 20, 21, 22], "xy": [5, 6, 8, 11, 12, 14, 15, 17, 20, 21, 22], "note": [5, 6, 7, 9, 10, 12, 14, 15, 16, 17, 18, 20], "reconstruct": [5, 9, 10, 12, 19, 20], "mechan": 5, "precess": [5, 12, 14, 16, 20], "de": 5, "averag": [5, 18], "magnitud": [5, 13, 16, 17], "illustr": [5, 6, 8, 9, 10, 17, 19, 20, 22], "gener": [5, 9, 11, 12, 16, 19, 20], "t2star_spinecho_illustr": 5, "No": 5, "80": [5, 8, 9, 22], "ms": [5, 8, 9, 12, 14, 17, 18, 21], "mild": 5, "approxim": [5, 16, 17, 18, 21], "dephas": [5, 16, 20], "broken": 5, "up": [5, 7, 9, 12, 14, 16, 17, 22], "separ": [5, 12, 13, 14, 16, 21, 22], "leq": 5, "revers": [5, 10, 20], "accumul": [5, 6, 12, 20], "easili": [5, 18, 21], "doe": [5, 12, 16, 18, 23], "make": 5, "revert": 5, "To": [5, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22], "try": [5, 8, 10], "visit": 5, "drcmr": [5, 8, 22], "dk": [5, 8, 22], "blochsimul": [5, 8], "scene": 5, "inhomogen": [5, 12, 16], "90x": 5, "180y": 5, "happen": [5, 16, 17], "180x": 5, "Is": 5, "still": [5, 6, 10], "repeat": [5, 9, 13, 15, 16, 20, 21, 22], "order": [5, 6, 9, 20, 21, 22], "refocu": [5, 16], "pure": 5, "all": [5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 18, 22], "becaus": [5, 8, 13, 16, 22], "give": [5, 13, 14, 16], "gnuplot": [6, 8, 12, 14, 20, 21, 22], "graphic": [6, 8, 12, 14, 20, 21, 22], "toolkit": [6, 8, 12, 14, 20, 21, 22], "discourag": [6, 8, 12, 14, 20, 21, 22], "activ": [6, 8, 12, 14, 20, 21, 22, 23], "maintain": [6, 8, 12, 14, 20, 21, 22], "limit": [6, 8, 10, 12, 14, 16, 17, 18, 20, 21, 22], "ulik": [6, 8, 12, 14, 20, 21, 22], "fix": [6, 8, 12, 14, 17, 20, 21, 22], "commun": [6, 8, 12, 14, 20, 21, 22], "pipe": [6, 8, 12, 14, 20, 21, 22], "pass": [6, 8, 12, 14, 20, 21, 22], "octav": [6, 8, 12, 14, 20, 21, 22], "interpret": [6, 8, 12, 14, 20, 21, 22], "made": [6, 7, 8, 12, 14, 20, 21, 22], "interact": [6, 8, 12, 14, 16, 20, 21, 22], "reflect": [6, 8, 12, 14, 20, 21, 22], "properti": [6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22], "manag": [6, 8, 12, 14, 20, 21, 22], "close": [6, 8, 12, 14, 20, 21, 22], "mous": [6, 8, 12, 14, 20, 21, 22], "click": [6, 8, 12, 14, 20, 21, 22], "notifi": [6, 8, 12, 14, 20, 21, 22], "intern": [6, 8, 12, 14, 20, 21, 22], "list": [6, 8, 11, 12, 14, 20, 21, 22], "open": [6, 8, 12, 13, 14, 20, 21, 22], "recommend": [6, 7, 8, 12, 14, 20, 21, 22], "qt": [6, 8, 12, 14, 20, 21, 22], "instead": [6, 8, 12, 14, 20, 21, 22], "collect": [6, 16], "cartesian": [6, 12], "done": [6, 12, 15, 18, 21, 22], "anticip": 6, "formul": [6, 10, 12, 20, 21, 22], "introduc": [6, 9, 15, 17, 20, 22], "proport": [6, 9, 14, 16, 17, 18, 20, 22], "s_i": 6, "denot": [6, 10, 12, 14], "subscript": 6, "trajectori": [6, 12, 21], "raster": [6, 20], "fashion": [6, 15], "knowledg": [6, 12], "mr": [6, 9, 11, 14, 18, 20, 21, 22], "store": [6, 16, 20], "onc": [6, 7, 9, 12, 18, 22], "simpli": [6, 10, 12, 13, 14, 22], "3d": [6, 20, 22], "fast": [6, 10, 12], "fft": [6, 10, 17], "anim": [6, 7, 8, 17], "fraction": 6, "nex": [6, 16], "wai": [6, 7, 9, 14, 15, 16, 20], "amount": [6, 9, 10, 15, 17], "state": [6, 9, 16, 22], "posit": [6, 14, 16, 17, 20, 21], "complex": [6, 8, 9, 11, 12], "conjug": [6, 16], "neg": [6, 20], "im": 6, "m_x": [6, 8, 11, 22], "puls": [6, 7, 9, 11, 12, 18, 19, 20], "just": [6, 14, 19], "satisfi": 6, "taken": [6, 18], "togeth": [6, 9, 14, 17, 18], "onli": [6, 10, 15, 16, 17, 21, 22], "sourc": [6, 8, 9, 13, 22], "violat": [6, 21], "global": 6, "offset": [6, 18], "m_y": [6, 8, 11, 22], "correct": [6, 8, 14, 16, 17, 22], "problemat": 6, "low": [6, 9, 12, 22], "central": 6, "than": [6, 9, 14, 16], "project": 6, "onto": [6, 12], "convex": 6, "poc": 6, "homodyn": 6, "suitabl": 6, "short": [7, 9, 17], "book": [7, 11, 23], "associ": [7, 16, 17], "larsonlab": 7, "repositori": 7, "helper": [7, 9], "built": 7, "about": [7, 15, 17, 22], "decad": 7, "teach": 7, "1st": 7, "year": 7, "graduat": 7, "student": 7, "background": [7, 14], "natur": 7, "scienc": 7, "engin": 7, "undergo": 7, "fall": 7, "quarter": 7, "promin": 7, "role": 7, "my": [7, 19], "upon": 7, "should": [7, 8, 14, 17, 18, 21, 22], "achiev": [7, 8, 9, 13, 16, 17, 22], "fundmanet": [7, 13, 14], "why": [7, 13, 14], "necessari": [7, 10, 13, 14, 15, 17], "concept": [7, 8, 12, 16, 19, 20, 22], "polar": [7, 8, 11, 13, 14, 16, 20], "jump": 7, "pretti": 7, "quickli": [7, 17], "quick": 7, "overview": 7, "minut": 7, "access": 7, "playlist": 7, "record": [7, 15], "If": [7, 8, 10, 13, 22], "goe": [7, 17], "avail": [7, 17, 19, 22], "git": 7, "icon": 7, "clone": 7, "desktop": 7, "pull": 7, "greatli": [7, 8, 12], "influenc": [7, 12, 18], "great": 7, "want": 7, "front": 7, "dwight": 7, "nishimura": 7, "text": 7, "borrow": 7, "materi": 7, "less": [7, 17, 22], "own": [7, 12], "bill": 7, "tool": [7, 10, 15, 19], "miki": 7, "lustig": 7, "danish": 7, "research": 7, "centr": 7, "bloch": [7, 12, 16, 17, 22], "physicist": 8, "felix": 8, "who": 8, "won": 8, "nobel": 8, "prize": 8, "discoveri": 8, "phenomena": 8, "almost": 8, "behavior": [8, 12, 15, 17], "seen": [8, 9], "deriv": [8, 10, 12, 22], "kei": [8, 12, 14, 17], "respons": [8, 17], "vast": 8, "major": [8, 17, 18], "present": [8, 9, 10, 14, 20], "experi": [8, 12, 14, 15, 18, 20, 22], "dt": [8, 9, 12, 17, 20, 21], "gamma": [8, 11, 12, 13, 14, 16, 17, 20, 21, 22], "bmatrix": [8, 11, 14, 22], "beavhior": 8, "equilibrium": [8, 9, 11, 13, 14], "longitudin": [8, 9, 16, 22], "m_z": [8, 9, 11, 16, 17, 22], "lattic": [8, 16, 22], "valuabl": [8, 22], "hand": [8, 14], "observ": [8, 10, 22], "neglect": [8, 12, 16, 20], "rightarrow": [8, 10], "infti": [8, 10, 20], "5e3": 8, "1500": [8, 9], "mt": [8, 12, 13, 14, 17], "unit": [8, 9, 11, 14, 17], "bloch_rot": [8, 17], "start": [8, 10, 12, 13, 16, 20, 22], "mstart": 8, "bstatic": 8, "1e": [8, 14], "ns": 8, "300": 8, "mall": [8, 22], "xlabel": [8, 9, 10, 12, 14, 17, 18, 20, 21, 22], "legend": [8, 9, 17, 18, 21, 22], "north": [8, 22], "boxoff": [8, 22], "5540": [8, 22], "occur": [8, 12, 16, 18, 22], "oscil": [8, 14, 16, 21, 22], "orthogon": 8, "b_": [8, 14, 16], "co": [8, 9, 10, 14, 16, 18], "bar": [8, 11, 13, 14, 22], "sin": [8, 9, 10, 14, 18], "energi": [8, 13, 14, 17, 21, 22], "good": [8, 9, 11, 17], "progress": 8, "awai": [8, 9, 14, 22], "simplif": [8, 20], "f_0": [8, 12, 14, 22], "visual": [8, 17, 20, 22], "math": 8, "stationari": 8, "represent": [8, 15, 16, 20], "now": [8, 12, 17, 20, 21, 22], "do": [8, 9, 12, 13], "analysi": [8, 12], "option": [8, 20], "45": [8, 16], "90": [8, 16, 17, 18], "creation": 8, "omega_0": 8, "With": [8, 21], "final": [8, 12, 14], "clearli": 8, "gammabar": [8, 12, 17], "42": [8, 12, 17, 20, 21, 22], "58": [8, 12, 17, 20, 21], "khz": [8, 12, 13, 16, 17], "simplic": [8, 12], "f0": [8, 17], "m0": [8, 9, 17, 18, 22], "m_equilibrium": [8, 17], "paaramet": 8, "t_rf": 8, "linspac": [8, 9, 10, 14, 17, 18, 20, 21, 22], "4000": 8, "rf_flip_angl": 8, "radian": [8, 16], "b10": [8, 17], "425": 8, "8713e": 8, "03": 8, "length": [8, 9, 14, 17, 18, 20, 21, 22], "12": [8, 14, 16, 21], "513": 8, "ones": [8, 9, 10, 17, 20, 21], "northwest": 8, "192": 8, "438": 8, "equilibriuam": 8, "ultim": [8, 13], "orient": [8, 13, 14, 22], "same": [8, 9, 12, 14, 16, 17], "without": [8, 12], "shorthand": [8, 11], "t1": [8, 16, 18, 19, 22], "durat": [8, 12, 16, 17, 18], "millitesla": [8, 14], "tip": [8, 11, 15, 17, 22], "m_start": [8, 22], "bloch_rftip": 8, "bloch_relax": [8, 22], "1232e": 8, "17": 8, "0000e": 8, "00": 8, "num2str": [8, 9, 10, 14, 18], "657": 8, "rich": 9, "varieti": 9, "arguabl": [9, 17], "advantag": [9, 16, 17], "gd": 9, "ti": [9, 16], "desir": [9, 17, 18], "therefor": [9, 13, 18, 20, 22], "control": [9, 17, 18], "se": [9, 16], "200": 9, "t2v": 9, "30": 9, "60": [9, 17], "100": [9, 12, 13, 14, 16, 17], "130": 9, "meshgrid": [9, 12, 17, 20], "s_te": 9, "int2str": [9, 12, 17, 18, 20], "versu": [9, 12], "150": 9, "mesh": [9, 12], "view": [9, 13, 16, 18, 20], "155": 9, "zlabel": 9, "colorbar": [9, 14, 21], "given": [9, 16, 17, 20, 22], "repetit": [9, 15, 16], "incomplet": 9, "Then": [9, 12, 21], "simplest": 9, "reach": 9, "steadi": [9, 16], "2nd": [9, 20], "evolut": 9, "400": [9, 18], "800": [9, 18], "1200": 9, "2000": 9, "ntr": 9, "500": [9, 21], "nt_per_tr": 9, "t_per_tr": 9, "t_minu": 9, "t_plu": 9, "befor": [9, 16, 17, 20], "mz_minu": 9, "mz_plu": 9, "initi": [9, 12, 20], "ep": [9, 17], "mz_all": 9, "o": 9, "t1v": 9, "s_tr": 9, "2500": 9, "110": 9, "effici": [9, 16], "acqrui": 9, "per": 9, "theta": [9, 15, 16, 17, 18], "s_flip": 9, "By": [9, 14, 20], "long": [9, 18], "enough": [9, 13, 15], "see": [9, 12, 13, 15, 18, 20, 22], "matter": 9, "approx": [9, 13, 20, 22], "cerebrospin": 9, "fluid": 9, "brain": 9, "rel": [9, 10, 13, 14, 15, 18], "therebi": 9, "longer": [9, 16, 18], "shorter": [9, 12, 16, 18], "discuss": [9, 14], "later": [9, 12, 15, 22], "principl": [9, 12, 14], "muscl": 9, "smaller": [9, 14], "boost": 9, "leav": 9, "small": [9, 13, 14, 17, 19, 22], "certain": [9, 13], "ratio": [9, 11, 14, 22], "zoom": 9, "area": [9, 10, 16, 18, 20], "delai": 9, "strategi": [9, 12], "commonli": [9, 10, 13, 16], "null": 9, "stir": 9, "attenu": 9, "flair": 9, "ir": 9, "flip1": 9, "flip2": 9, "750": 9, "mz1_minu": 9, "mz2_minu": 9, "mz1_plu": 9, "mz2_plu": 9, "t1_minu": 9, "t1_plu": 9, "t2_minu": 9, "t2_plu": 9, "evolv": [9, 21], "period": [9, 17], "find": [9, 10, 21], "2001": 9, "4001": 9, "6001": 9, "751": 9, "2751": 9, "4751": 9, "vs": [9, 17], "s_ti": 9, "gadolinium": 9, "chelat": 9, "superparamagnet": 9, "iron": 9, "oxid": 9, "shorten": 9, "wherev": 9, "quantifi": 9, "r_1": 9, "r_2": 9, "typiclali": 9, "l": [9, 10], "mmol": 9, "cm": [9, 14, 21], "concentr": 9, "mm": 9, "1300": 9, "csf": 9, "3700": 9, "1700": 9, "1000": [9, 16], "liver": 9, "cartilag": 9, "pictur": 9, "three": [9, 18], "circular": 9, "jinc": 9, "circl": 9, "circ": 9, "k_r": 9, "scheme": 9, "signal_gr": 9, "mrsignal_spoiled_gradient_echo": [9, 18], "contrast_phantom": 9, "nphan": 9, "xc": 9, "yc": 9, "25": 9, "1e3": [9, 12, 21], "06": 9, "64": [9, 10, 14], "ball": 9, "radiu": [9, 14], "20": [9, 17, 21], "160": 9, "3000": 9, "ky": [9, 12, 20], "coordin": 9, "ad": [9, 15, 16, 17], "individu": [9, 12, 14, 22], "exponenti": [9, 22], "displai": 9, "phi": [10, 20], "tan": 10, "funcion": 10, "ne": 10, "dx": 10, "ax": [10, 15], "ast": 10, "dirac": 10, "comb": 10, "sha": 10, "\u0448": 10, "rectangl": [10, 15], "sqcap": 10, "quad": 10, "linewidth": [10, 20], "normal": [10, 18], "tau": [10, 12, 16, 17, 18, 20], "intuit": [10, 12], "slid": 10, "nice": [10, 19], "unitari": 10, "ordinari": 10, "swap": 10, "dk_x": 10, "k_y": [10, 12, 16, 20], "dy": 10, "f_x": 10, "f_y": 10, "finit": 10, "kspace": 10, "width": 10, "w_": [10, 16], "accord": [10, 16], "convolv": [10, 12], "notabl": 10, "decomposit": 10, "512": 10, "kxmax": 10, "128": 10, "kxmax_trunc": 10, "fftshift": [10, 17], "ifft": 10, "ifftshift": 10, "power": [10, 12, 14, 16, 17, 18, 19, 20], "actual": [10, 15], "dft": 10, "x_n": 10, "coeffici": [10, 18], "k_n": 10, "formula": 10, "extrem": [10, 18, 22], "extend": [10, 18], "si": 11, "gyromagnet": [11, 14, 22], "hz": [11, 12, 13, 16, 21, 22], "receiv": [11, 12, 13, 15, 16, 20], "g_y": [11, 16, 20], "g_z": [11, 16, 21], "b_x": [11, 14], "b_y": [11, 14], "b_z": [11, 14, 20], "jargon": 11, "intimid": [11, 12], "imped": 11, "luckili": 11, "coupl": 11, "radiopaedia": 11, "articl": 11, "abbrevi": 11, "vendor": 11, "com": 11, "serv1": 11, "php": 11, "cam": 11, "format": 12, "equiat": 12, "impact": [12, 18], "affect": [12, 18], "resonnac": 12, "obtain": 12, "int": 12, "int_0": [12, 17, 18, 20], "reason": [12, 18], "clear": 12, "soon": [12, 20], "situat": [12, 16], "add": [12, 13, 14, 21], "simllifi": 12, "easiest": 12, "c_n": 12, "s_n": 12, "receiev": 12, "filter": [12, 16, 21], "integr": [12, 17, 18, 20], "upsilon": 12, "gxr": [12, 16], "kx0": 12, "upsilon_cartesian": 12, "tesp": 12, "dky": 12, "assum": 12, "deadtim": 12, "tall": 12, "upsilon_epi": 12, "reshap": 12, "planar": [12, 16, 20, 21], "corrupt": 12, "convolut": 12, "snr": 12, "w_cartesian": 12, "w_epi": 12, "x0": 12, "height": 12, "peak": [12, 17], "outsid": [12, 17], "get": [12, 15, 22], "wors": 12, "much": [12, 14, 15, 16, 17, 22], "macroscop": 12, "f_": [12, 18], "speci": 12, "examin": [12, 18], "could": 12, "index": 12, "complic": 12, "gain": [12, 16, 18], "spiral": [12, 20], "radial": [12, 20], "look": [12, 13, 15, 16, 17, 22], "_0": [12, 20], "r_0": 12, "star": 12, "df": [12, 17, 21], "frfom": 12, "residu": 12, "side": [12, 14, 18], "lobe": 12, "interpol": [12, 18], "write": 12, "version": [12, 21], "numer": [12, 18], "solver": 12, "graph": 12, "As": [12, 17, 22], "framework": [12, 20], "express": 12, "boil": 12, "down": [12, 17, 22], "decompos": [12, 18], "m_i": 12, "w_i": 12, "sum_i": 12, "divid": [12, 14, 22], "water": [12, 16, 21, 22], "m_1": 12, "m_2": 12, "w_1": 12, "w_2": 12, "accur": 12, "thw": 12, "ssfp": 12, "diffus": [12, 18, 19, 21], "explor": 13, "deconstruct": 13, "insid": 13, "insight": 13, "hardwar": 13, "loud": 13, "danger": 13, "metal": 13, "cut": 13, "nuclear": 13, "greater": 13, "stronger": [13, 14], "tesla": 13, "alwai": [13, 14, 16, 20, 22], "homogen": [13, 14], "manget": [13, 22], "superconduct": 13, "alloi": 13, "bath": 13, "liquid": 13, "helium": 13, "recept": 13, "deposit": [13, 21], "perturb": [13, 14, 22], "caus": [13, 17, 22], "releas": 13, "radio": [13, 14], "mhz": [13, 14, 16], "excitaiton": [13, 16], "thermal": [13, 22], "Thes": 13, "linearli": [13, 18, 20], "place": [13, 14, 16, 22], "fiel": 13, "distinguish": 13, "summar": [13, 18], "tabl": 13, "strength": [13, 16, 18], "mu": [13, 14, 16, 22], "critic": [14, 18], "wire": 14, "govern": [14, 22], "electromagnet": [14, 22], "maxwel": 14, "equat": [14, 16, 17, 20], "rule": 14, "link": 14, "solenoid": 14, "volum": [14, 20], "psace": [14, 21], "ensur": 14, "usual": [14, 15, 16], "convent": [14, 20, 22], "50": 14, "05": [14, 20], "switch": [14, 15, 17, 22], "few": [14, 17, 19], "Their": 14, "00001": 14, "perpedicularli": 14, "plane": [14, 15, 16], "reactiv": 14, "capacitor": 14, "inductor": 14, "kw": 14, "surround": 14, "mv": 14, "aris": [14, 16], "channel": 14, "put": [14, 18, 20], "electr": 14, "i0": 14, "amp": 14, "mu0": 14, "401": 14, "bz": 14, "211": [14, 17, 21], "212": [14, 17, 21], "resons": 14, "event": 14, "amplifi": 14, "digit": 14, "tell": 14, "far": [14, 20], "birdcag": 14, "perpendicular": [14, 16, 22], "tailor": 14, "knee": 14, "abdomen": 14, "head": 14, "configur": [14, 16], "isol": 14, "decoupl": 14, "detun": 14, "turn": [14, 15, 16, 20, 22], "don": 14, "senit": 14, "move": [14, 16, 22], "brightest": 14, "closest": 14, "biot": 14, "savart": 14, "law": 14, "flag_2d": 14, "bx": 14, "BY": 14, "xp": 14, "yp": [14, 20], "zp": 14, "loop_coil_field": 14, "quiver": [14, 20], "18": 14, "bmag": 14, "xhalf": 14, "chapter": [15, 22], "select": [15, 16, 19, 21], "import": [15, 17, 18], "indic": 15, "conjunct": 15, "remeb": 15, "incred": [15, 20], "convei": 15, "signific": 15, "experiment": 15, "speed": 15, "drawn": 15, "bracket": 15, "particular": 15, "simlifi": 15, "crusher": 15, "destruct": 15, "shape": [15, 21], "instantan": 15, "realiti": 15, "slew": [15, 21], "trapezoid": 15, "mai": 16, "clinic": 16, "3t": 16, "5t": 16, "xrai": 16, "visibl": 16, "light": 16, "fm": 16, "am": 16, "proper": 16, "assign": 16, "conduct": 16, "calibr": 16, "isotop": 16, "cannot": [16, 22], "1h": 16, "13": [16, 22], "19": [16, 22], "2h": 16, "human": [16, 22], "diamagnet": 16, "paramagnet": 16, "ferromagnet": 16, "proton": [16, 18, 21, 22], "immedi": 16, "equilibirum": 16, "static": 16, "parallel": [16, 20], "lab": [16, 17], "frame": [16, 17], "flux": 16, "benefit": 16, "compress": [16, 19], "sens": [16, 19], "doesn": 16, "contribut": [16, 22], "highest": 16, "spoil": [16, 18], "2e": 16, "pdw": 16, "t1w": 16, "t2w": 16, "dixon": 16, "prepar": 16, "additoin": 16, "suppress": [16, 21], "daq": 16, "serv": 16, "mxy": [16, 20], "statement": 16, "true": 16, "overlap": 16, "prewind": 16, "gre": [16, 18], "\u03b8": 16, "twice": 16, "thinner": 16, "decreas": 16, "bandwidth": 16, "bw_": [16, 17], "bw": [16, 17], "nyquist": 16, "theorem": 16, "avoid": 16, "lowest": 16, "oversampl": 16, "multislic": 16, "next": [16, 20], "3dft": 16, "hold": 16, "rbw": 16, "anti": 16, "xr": [16, 20], "read": [16, 18, 20], "fov_x": 16, "n_": [16, 22], "fe": 16, "none": 16, "stretch": [16, 17], "pile": 16, "bright": 16, "band": 16, "sequenti": 16, "sar": [16, 17], "rapidli": 16, "robust": 16, "intravoxel": 16, "free": 16, "bssfp": 16, "partial": 16, "deep": 16, "learn": 16, "symmetri": 16, "gather": 16, "databas": 16, "outer": 16, "amplif": 16, "acquist": 16, "Of": 16, "regardless": 16, "dataset": 16, "develop": 16, "000": 16, "decod": 16, "recurr": 16, "appl": 17, "equival": [17, 18, 20], "aim": [17, 21], "tbw": [17, 21], "detail": 17, "ss": 17, "distanc": 17, "absorb": 17, "heat": 17, "safeti": 17, "minim": 17, "sinusoid": 17, "002": 17, "tmax": 17, "rf_sinusoid": 17, "ft_sinusoid": 17, "imaginari": 17, "xlim": [17, 20], "tmat": 17, "dfmat": 17, "rf_all": 17, "rf_n": 17, "ft_n": 17, "fwidth": 17, "11": [17, 21], "rf_sinc": 17, "ft_sinc": 17, "gz": [17, 21], "poorli": 17, "uniformli": 17, "forth": [17, 22], "substanti": 17, "presenc": 17, "meanwhil": 17, "wide": [17, 18], "spread": 17, "wherea": [17, 22], "precis": 17, "360": 17, "address": 17, "impli": [17, 18], "shrunk": 17, "bwplot": 17, "IN": 17, "rf_shape": 17, "trf": 17, "bwrf": 17, "plai": 17, "notic": [17, 22], "sharper": 17, "But": [17, 18], "break": 17, "sophist": 17, "account": [17, 18], "shinnar": 17, "le": 17, "roux": 17, "slr": 17, "dzrf": [17, 21], "isn": 17, "issu": 17, "themselv": 17, "subtli": 17, "degrad": 17, "inv": 17, "characterist": 18, "theoret": 18, "foundat": 18, "delta_i": 18, "delta_z": 18, "gaussian": 18, "root": 18, "sigma": 18, "mea": 18, "downtim": 18, "seq": 18, "especi": [18, 19], "ernst": 18, "theta_": 18, "intrigu": 18, "trdt1": 18, "01": 18, "1600": 18, "inf": 18, "theta_optim": 18, "snr_effici": 18, "it1": 18, "aco": 18, "ylim": [18, 20], "drop": 18, "stabl": 18, "finer": 18, "coarser": 18, "nativ": 18, "pad": 18, "nearbi": 18, "scale": [18, 21], "distinct": 18, "care": 18, "alon": [18, 20], "demonin": 18, "tread": 18, "snr_t2s_onesid": 18, "imax_onesid": 18, "snr_t2s_twosid": 18, "imax_twosid": 18, "disp": 18, "2806": 18, "4907": 18, "ve": 19, "favorit": 19, "focus": 19, "kmjohnson3": 19, "intro": 19, "python": 19, "jupyt": [19, 23], "introduct": 19, "mribri999": 19, "mrsignalsseq": 19, "cours": 19, "code": [19, 20, 21], "lectur": 19, "introductori": 19, "marku": 19, "nilsson": 19, "matlab": 19, "mikgroup": 19, "sigpi": 19, "packag": 19, "mrirecon": 19, "bart": 19, "toolbox": 19, "qmrlab": 19, "quantit": 19, "fit": 19, "transfer": 19, "ismrm": 19, "mrhub": 19, "hub": 19, "worth": 19, "brows": 19, "delv": [19, 22], "topic": 19, "omega": 20, "basi": [20, 22], "cumul": 20, "stop": 20, "undo": 20, "k_z": [20, 21], "motiv": 20, "local": 20, "rather": 20, "textrm": 20, "i2": 20, "amaz": 20, "appropri": 20, "fact": 20, "regularli": 20, "increment": 20, "1d": 20, "splot": 20, "kfe": 20, "phase_x": 20, "mxy_f": [20, 21], "drawnow": 20, "3rd": 20, "t_y": 20, "kpe": 20, "tpe": 20, "ip": 20, "phase_i": 20, "mxy_p": 20, "spatial_encoding_mxy_illustr": 20, "blade": 20, "kx_ep": 20, "ky_ep": 20, "k_theta": 20, "k_radial": 20, "201": [20, 21], "nturn": 20, "k_spiral": 20, "molecul": 21, "lipid": [21, 22], "fmri": 21, "spectroscopi": 21, "relat": 21, "reveal": 21, "travers": 21, "trick": 21, "compil": 21, "abr": 21, "mex": 21, "file": 21, "error": 21, "re": 21, "run": 21, "abrx": 21, "31": [21, 22], "column": 21, "trajectoi": 21, "nlobe": 21, "nspec": 21, "nramp": 21, "ramp": 21, "g1": 21, "gamp": 21, "95": 21, "mod": 21, "nrw": 21, "grw": 21, "cumsum": 21, "k_f": 21, "h_f": 21, "h_z": 21, "envelop": 21, "subpuls": 21, "4258": 21, "slewmax": 21, "15e3": 21, "gmax": 21, "20e": 21, "sbw": 21, "dz": 21, "resolut": 21, "10e": 21, "verse_frac": 21, "nspat": 21, "nwait": 21, "rfspec": 21, "gf": 21, "ab2ex": 21, "g_f": 21, "rfspat": 21, "min": 21, "ceil": 21, "floor": 21, "vers": 21, "rfspatv": 21, "isnan": 21, "g1z": 21, "mxy_z": 21, "flip_scal": 21, "rfscaleg": 21, "plot3": 21, "589": 21, "mxy_2d": 21, "m_xy": 21, "watch": 21, "behav": 22, "phenomenom": 22, "nucleu": 22, "angular": 22, "momentum": 22, "moment": 22, "act": 22, "respond": 22, "tyipcal": 22, "hydrogen": 22, "nuclei": 22, "atom": 22, "primari": 22, "23": 22, "na": 22, "p": 22, "abund": 22, "absenc": 22, "randomli": 22, "ensembl": 22, "arrow": 22, "vertic": 22, "www": 22, "i_z": 22, "planck": 22, "63e": 22, "34": 22, "58e6": 22, "boltzmann": 22, "62e": 22, "ev": 22, "38e": 22, "temperatur": 22, "310": 22, "prefer": 22, "boltzman": 22, "uparrow": 22, "downarrow": 22, "kt": 22, "expon": 22, "strongli": 22, "analog": 22, "swing": 22, "your": 22, "leg": 22, "wrong": 22, "compassmr": 22, "default": 22, "compass": 22, "mode": 22, "slider": 22, "adjust": 22, "freq": 22, "uenci": 22, "new": 22, "checkbox": 22, "part": 22, "hit": 22, "push": 22, "button": 22, "needl": 22, "blue": 22, "trace": 22, "highlight": 22, "composit": 22, "last": 22, "mx": 22, "anaconda": 23, "prompt": 23, "FOR": 23, "conda": 23, "wintest": 23, "environ": 23, "pip": 23, "instal": 23, "forg": 23, "octave_kernel": 23, "jb": 23, "booknam": 23, "runjb": 23, "quantecon": 23, "mini": 23, "seem": 23}, "objects": {}, "objtypes": {}, "objnames": {}, "titleterms": {"acceler": [0, 16], "imag": [0, 3, 6, 9, 16, 20], "method": [0, 16], "learn": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 17, 18, 20, 21, 22], "goal": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 15, 17, 18, 20, 21, 22], "gener": 0, "formul": 0, "mri": [0, 6, 7, 9, 10, 11, 12, 13, 14, 16, 19, 20], "reconstruct": [0, 6, 16], "parallel": 0, "space": [0, 6, 10, 11, 12, 20], "auto": 0, "calibr": 0, "k": [0, 6, 10, 12, 20], "snr": [0, 16, 18], "artifact": [0, 1, 16], "compress": 0, "sens": 0, "deep": 0, "requir": 0, "dl": 0, "refer": 0, "comparison": 1, "simul": [1, 5, 8, 14, 22], "field": [2, 11, 13, 14, 15, 20], "view": 2, "fov": [2, 16], "resolut": [2, 16, 18], "spatial": [2, 16, 20, 21], "fast": [3, 16], "puls": [3, 4, 5, 8, 15, 16, 17, 21], "sequenc": [3, 5, 15, 16], "under": 3, "construct": 3, "echo": [3, 5], "planar": 3, "epi": 3, "turbo": 3, "spin": [3, 5, 22], "fse": 3, "tse": 3, "fun": 4, "rf": [4, 8, 13, 14, 15, 16, 17, 21], "adiabat": 4, "pretti": 4, "pictur": 4, "gradient": [5, 13, 14, 15, 20], "ge": 5, "gre": 5, "off": [5, 12, 17], "reson": [5, 12, 14, 17, 22], "effect": [5, 20], "t2": [5, 9], "refocus": 5, "visual": 5, "se": 5, "sort": 6, "data": [6, 10, 12, 15, 18, 20], "fourier": [6, 10], "transform": [6, 10], "partial": 6, "introduct": 7, "principl": 7, "get": 7, "start": 7, "cours": 7, "lectur": 7, "us": 7, "educ": 7, "resourc": [7, 19], "code": 7, "acknowledg": 7, "bloch": 8, "equat": [8, 12, 18, 22], "THE": 8, "precess": [8, 22], "excit": [8, 14, 15, 17, 22], "exampl": [8, 9, 10], "constant": 8, "amplitud": 8, "lab": 8, "versu": [8, 17, 18], "rotat": 8, "frame": 8, "common": 8, "flip": [8, 9, 17], "angl": [8, 9, 17], "relax": [8, 9, 12, 22], "contrast": [9, 16], "te": 9, "tr": [9, 18], "t1": 9, "90": 9, "degre": 9, "proton": 9, "densiti": 9, "weight": [9, 12], "pd": 9, "invers": [9, 10], "recoveri": 9, "agent": 9, "typic": 9, "time": [9, 17, 18], "3t": 9, "simpl": 9, "phantom": 9, "challeng": 9, "yourself": 9, "math": 10, "concept": 10, "complex": 10, "number": 10, "impuls": 10, "function": 10, "train": 10, "sampl": [10, 15], "other": 10, "convolut": 10, "2": 10, "d": 10, "n": 10, "dualiti": 10, "separ": 10, "ident": 10, "pair": 10, "truncat": 10, "point": 10, "spread": 10, "psf": 10, "analysi": 10, "discret": 10, "notat": 11, "terminolog": 11, "definit": 11, "posit": 11, "net": 11, "magnet": [11, 13, 14, 15, 18, 20, 22], "acronym": 11, "glossari": 11, "The": [12, 13, 15], "signal": [12, 14, 18, 20], "ideal": 12, "ad": 12, "coil": [12, 13, 14, 16], "sensit": [12, 14], "dure": 12, "acquisit": [12, 15, 18], "chemic": 12, "shift": [12, 17], "complet": 12, "system": [13, 14, 16], "compon": [13, 15], "scanner": 13, "main": [13, 14], "b_0": [13, 14], "radiofrequ": [13, 14], "b_1": [13, 14], "vec": [13, 14], "r": [13, 14], "t": [13, 14], "g": [13, 14], "fundament": 13, "experi": 13, "procedur": 13, "loop": 14, "current": 14, "transmit": 14, "tx": 14, "receiv": 14, "rx": 14, "recept": 14, "creat": 14, "reciproc": 14, "profil": 14, "element": 14, "local": 15, "g_x": 15, "g_y": 15, "g_z": 15, "window": 15, "daq": 15, "diagram": 15, "annot": 15, "simplifi": 15, "kei": 15, "paramet": 15, "question": 16, "mr": 16, "physic": [16, 22], "encod": [16, 20], "characterist": 16, "properti": 17, "bandwidth": 17, "product": 17, "slice": 17, "thick": 17, "specif": 17, "absorpt": 17, "rate": 17, "select": 17, "hard": 17, "shape": 17, "On": 17, "design": [17, 21], "high": 17, "nois": 18, "ratio": 18, "depend": 18, "voxel": 18, "volum": 18, "transvers": 18, "effici": 18, "post": 18, "process": 18, "upsampl": 18, "downsampl": 18, "t_2": 18, "decai": 18, "softwar": 19, "from": 20, "cartesian": 20, "frequenc": [20, 22], "phase": 20, "2dft": 20, "trajectori": 20, "spectral": 21, "nuclear": 22, "polar": 22, "equilibrium": 22, "fraction": 22}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 6, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx": 56}})
\ No newline at end of file