Notebook updates and Octave graphics fixes attempts

LarsonLab · Nov 11, 2023 · 3214c8e · 3214c8e
1 parent 6503e85
commit 3214c8e
Show file tree

Hide file tree

Showing 4 changed files with 148 additions and 17 deletions.
diff --git a/Notebooks/FOV and Resolution.ipynb b/Notebooks/FOV and Resolution.ipynb
@@ -14,25 +14,17 @@
     "    * Describe what determines the image FOV and resolution\n",
     "1. Manipulate MRI sequence parameters to improve performance\n",
     "    * Manipulate the gradients and k-space sampling to change the FOV and resolution\n",
-    "\n",
-    "## Field-of-View (FOV)\n",
-    "\n",
-    "The FOV is determined by the sample spacing in k-space, with the simple relationship based on the sample spacing, $\\Delta k$ as:\n",
-    "\n",
-    "$$ FOV = \\frac{1}{\\Delta k}$$\n",
-    "\n",
-    "\n",
-    "## Spatial Resolution\n",
-    "\n",
-    "The spatial resolution is determined by the maximum sample extent in k-space, with the simple relationship based on the maximum k-space sample locations, $k_{max}$ as:\n",
-    "\n",
-    "$$ \\Delta = \\frac{1}{2 k_{max}}$$\n"
+    "\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
+   "execution_count": null,
+   "metadata": {
+    "vscode": {
+     "languageId": "octave"
+    }
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -49,6 +41,143 @@
     "startup"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Field-of-View (FOV)\n",
+    "\n",
+    "The FOV is determined by the sample spacing in k-space, with the simple relationship based on the sample spacing, $\\Delta k$ as:\n",
+    "\n",
+    "$$ FOV = \\frac{1}{\\Delta k}$$\n",
+    "\n",
+    "For example, $FOV_{x} = \\frac{1}{\\Delta k_x}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "vscode": {
+     "languageId": "octave"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "% rectangular object to demonstrate FOV\n",
+    "\n",
+    "N = 256;\n",
+    "kx = [-N/2:N/2-1]/N;\n",
+    "N_rect = N/4;\n",
+    "kdata = sinc(kx *N_rect).' * sinc(kx *N_rect);\n",
+    "\n",
+    "rect_recon = ifft2c(kdata);\n",
+    "\n",
+    "subplot(221)\n",
+    "imagesc((abs(kdata)), [0 (1)])\n",
+    "colormap(gray), axis equal tight off\n",
+    "subplot(222)\n",
+    "imagesc(abs(rect_recon), [0 max(abs(rect_recon(:)))])\n",
+    "colormap(gray), axis equal tight off\n",
+    "title('Full FOV')\n",
+    "\n",
+    "kdata2 = kdata;\n",
+    "kdata2(1:2:end,:) = 0;\n",
+    "kdata2(:,1:2:end) = 0;\n",
+    "rect_recon2 = ifft2c(kdata2);\n",
+    "\n",
+    "subplot(221)\n",
+    "imagesc((abs(kdata2)), [0 (1)])\n",
+    "colormap(gray), axis equal tight off\n",
+    "subplot(222)\n",
+    "imagesc(abs(rect_recon2), [0 max(abs(rect_recon2(:)))])\n",
+    "colormap(gray), axis equal tight off\n",
+    "title('Doubled \\Delta k, Half FOV')\n",
+    "\n",
+    "kdata3 = kdata;\n",
+    "kdata2(1:3:end,:) = 0;\n",
+    "kdata2(2:3:end,:) = 0;\n",
+    "kdata2(:,1:3:end) = 0;\n",
+    "kdata2(:,2:3:end) = 0;\n",
+    "rect_recon3 = ifft2c(kdata3);\n",
+    "\n",
+    "subplot(221)\n",
+    "imagesc((abs(kdata3)), [0 (1)])\n",
+    "colormap(gray), axis equal tight off\n",
+    "subplot(222)\n",
+    "imagesc(abs(rect_recon3), [0 max(abs(rect_recon3(:)))])\n",
+    "colormap(gray), axis equal tight off\n",
+    "title('Tripled \\Delta k, One Third FOV')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Spatial Resolution\n",
+    "\n",
+    "The spatial resolution is determined by the maximum sample extent in k-space, with the simple relationship based on the maximum k-space sample locations, $k_{max}$ as:\n",
+    "\n",
+    "$$ \\delta = \\frac{1}{2 k_{max}}$$\n",
+    "\n",
+    "For example, $\\delta_x = \\frac{1}{2 k_{x,max}}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "vscode": {
+     "languageId": "octave"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "% rectangular object to demonstrate resolution\n",
+    "\n",
+    "N = 256;\n",
+    "kx = [-N/2:N/2-1]/N;\n",
+    "N_rect = N/2;\n",
+    "kdata = sinc(kx *N_rect).' * sinc(kx *N_rect);\n",
+    "\n",
+    "rect_recon = ifft2c(kdata);\n",
+    "\n",
+    "subplot(221)\n",
+    "imagesc((abs(kdata)), [0 (1)])\n",
+    "colormap(gray), axis equal tight off\n",
+    "subplot(222)\n",
+    "imagesc(abs(rect_recon), [0 max(abs(rect_recon(:)))])\n",
+    "colormap(gray), axis equal tight off\n",
+    "title('Full Resolution')\n",
+    "\n",
+    "kdata2 = kdata;\n",
+    "kdata2([[1:N/4],[3*N/4+1:N]],:) = 0;\n",
+    "kdata2(:,[[1:N/4],[3*N/4+1:N]]) = 0;\n",
+    "rect_recon2 = ifft2c(kdata2);\n",
+    "\n",
+    "subplot(221)\n",
+    "imagesc((abs(kdata2)), [0 (1)])\n",
+    "colormap(gray), axis equal tight off\n",
+    "subplot(222)\n",
+    "imagesc(abs(rect_recon2), [0 max(abs(rect_recon2(:)))])\n",
+    "colormap(gray), axis equal tight off\n",
+    "title('Half k_{max}, Double voxel size')\n",
+    "\n",
+    "kdata4 = kdata;\n",
+    "kdata4([[1:3*N/8],5*N/8+1:N]],:) = 0;\n",
+    "kdata4(:,[[1:3*N/8],5*N/8+1:N]]) = 0;\n",
+    "rect_recon4 = ifft2c(kdata4);\n",
+    "\n",
+    "subplot(221)\n",
+    "imagesc((abs(kdata4)), [0 (1)])\n",
+    "colormap(gray), axis equal tight off\n",
+    "subplot(222)\n",
+    "imagesc(abs(rect_recon4), [0 max(abs(rect_recon4(:)))])\n",
+    "colormap(gray), axis equal tight off\n",
+    "title('1/4 k_{max}, 4x voxel size')\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},

diff --git a/Notebooks/Signal to Noise Ratio.ipynb b/Notebooks/Signal to Noise Ratio.ipynb
@@ -29,7 +29,9 @@
     "\n",
     "The MRI signal is an integral over a volume of the transverse magnetization.  Therefore there is a linear dependency on the MRI signal and the volume of magnetization being examined.  So we have\n",
     "\n",
-    "$$SNR \\propto \\mathrm{Voxel\\ Volume} = \\Delta x\\ \\Delta y\\ \\Delta z$$\n",
+    "$$SNR \\propto \\mathrm{Voxel\\ Volume} = \\delta x\\ \\delta y\\ \\delta z$$\n",
+    "\n",
+    "where $\\delta x, \\delta y, \\delta z$ are the voxel dimensions in x, y, and z.\n",
     "\n",
     "### Data Acquisition Time\n",
     "\n",

diff --git a/apt.txt b/apt.txt
@@ -5,4 +5,3 @@ octave-signal
 octave-miscellaneous
 liboctave-dev
 ghostscript
-qt5-default
diff --git a/startup.m b/startup.m
@@ -40,5 +40,6 @@
         end
     end
 
+    graphics_toolkit('qt')
 end
 end
-Original file line number
+Diff line change
@@ Expand Up / @@ -40,5 +40,6 @@ @@
             end
         end
+        graphics_toolkit('qt')
     end
     end