build based on 20b6710

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-08-22T15:34:42","documenter_version":"1.6.0"}}
+{"documenter":{"julia_version":"1.10.4","generation_timestamp":"2024-08-23T09:29:28","documenter_version":"1.6.0"}}

dev/generated/examples/compressed_sensing/index.html

@@ -8,22 +8,22 @@
      1
      4
      5
-    10
-    17
-    18
-    19
-    20
-    21
-    26
+     6
+     7
+     9
+    11
+    12
+    22
+    25
      ⋮
- 65516
- 65517
- 65518
+ 65501
+ 65502
+ 65506
+ 65514
  65521
  65522
- 65528
- 65530
- 65532
+ 65526
+ 65529
  65534</code></pre><p>Afterwards we build a sampling operator which samples the image at the selected indices.</p><pre><code class="language-julia hljs">A = SamplingOp(eltype(image), pattern = sampledIndices , shape = size(image));</code></pre><p>Then we apply the sampling operator to the vectorized image to obtain the sampled measurement vector</p><pre><code class="language-julia hljs">b = A*vec(image);</code></pre><p>To visualize our image we can use CairoMakie:</p><pre><code class="language-julia hljs">using CairoMakie
 function plot_image(figPos, img; title = &quot;&quot;, width = 150, height = 150)
   ax = CairoMakie.Axis(figPos; yreversed=true, title, width, height)
@@ -36,30 +36,30 @@
 samplingMask[sampledIndices] .= true
 plot_image(fig[1,2], image .* samplingMask, title = &quot;Sampled Image&quot;)
 resize_to_layout!(fig)
-fig</code></pre><img src="214b8b4f.png" alt="Example block output"/><p>As we can see in the right image, only a third of the pixels are sampled. The goal of the inverse problem is to recover the original image from this measurement vector.</p><h2 id="Solving-the-Inverse-Problem"><a class="docs-heading-anchor" href="#Solving-the-Inverse-Problem">Solving the Inverse Problem</a><a id="Solving-the-Inverse-Problem-1"></a><a class="docs-heading-anchor-permalink" href="#Solving-the-Inverse-Problem" title="Permalink"></a></h2><p>To recover the image from the measurement vector, we solve the TV-regularized least squares problem:</p><p class="math-container">\[\begin{equation}
+fig</code></pre><img src="1e81714b.png" alt="Example block output"/><p>As we can see in the right image, only a third of the pixels are sampled. The goal of the inverse problem is to recover the original image from this measurement vector.</p><h2 id="Solving-the-Inverse-Problem"><a class="docs-heading-anchor" href="#Solving-the-Inverse-Problem">Solving the Inverse Problem</a><a id="Solving-the-Inverse-Problem-1"></a><a class="docs-heading-anchor-permalink" href="#Solving-the-Inverse-Problem" title="Permalink"></a></h2><p>To recover the image from the measurement vector, we solve the TV-regularized least squares problem:</p><p class="math-container">\[\begin{equation}
   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_2^2 + \vert\vert\mathbf{x}\vert\vert_{\lambda\text{TV}} .
 \end{equation}\]</p><p>For this purpose we build a TV regularizer with regularization parameter <span>$λ=0.01$</span></p><pre><code class="language-julia hljs">using RegularizedLeastSquares
 reg = TVRegularization(0.01; shape=size(image));</code></pre><p>We will use the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) to solve our inverse problem. Thus, we build the corresponding solver</p><pre><code class="language-julia hljs">solver = createLinearSolver(FISTA, A; reg=reg, iterations=20);</code></pre><p>and apply it to our measurement vector</p><pre><code class="language-julia hljs">img_approx = solve!(solver,b)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">65536-element Vector{Float32}:
- 1.1679568f-18
- 2.1116658f-18
- 4.5817737f-18
- 1.0172477f-17
- 2.268474f-17
- 5.0405303f-17
- 1.1135638f-16
- 2.4575f-16
- 5.3614856f-16
- 1.1372157f-15
+ 4.408601f-19
+ 8.141939f-19
+ 1.8912686f-18
+ 4.657992f-18
+ 1.13304495f-17
+ 2.6190603f-17
+ 5.750876f-17
+ 1.2296451f-16
+ 2.6434892f-16
+ 5.744004f-16
  ⋮
- 3.745113f-16
- 1.8518066f-16
- 8.505684f-17
- 3.59355f-17
- 1.43278f-17
- 5.6754496f-18
- 2.348305f-18
- 1.0605327f-18
- 6.0551384f-19</code></pre><p>To visualize the reconstructed image, we need to reshape the result vector to the correct shape. Afterwards we can use CairoMakie again:</p><pre><code class="language-julia hljs">img_approx = reshape(img_approx,size(image));
+ 5.001874f-16
+ 2.3916176f-16
+ 1.1642602f-16
+ 5.6809295f-17
+ 2.6450612f-17
+ 1.1868527f-17
+ 5.449228f-18
+ 2.69539f-18
+ 1.6241735f-18</code></pre><p>To visualize the reconstructed image, we need to reshape the result vector to the correct shape. Afterwards we can use CairoMakie again:</p><pre><code class="language-julia hljs">img_approx = reshape(img_approx,size(image));
 plot_image(fig[1,3], img_approx, title = &quot;Reconstructed Image&quot;)
 resize_to_layout!(fig)
-fig</code></pre><img src="cef6fff0.png" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../getting_started/">« Getting Started</a><a class="docs-footer-nextpage" href="../computed_tomography/">Computed Tomography »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Thursday 22 August 2024 15:34">Thursday 22 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+fig</code></pre><img src="9b2b83d3.png" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../getting_started/">« Getting Started</a><a class="docs-footer-nextpage" href="../computed_tomography/">Computed Tomography »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Friday 23 August 2024 09:29">Friday 23 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/generated/examples/computed_tomography/index.html

@@ -62,4 +62,4 @@
  0.0</code></pre><p>To visualize the reconstructed image, we need to reshape the result vector to the correct shape. Afterwards we can use CairoMakie again:</p><pre><code class="language-julia hljs">img_approx = reshape(img_approx,size(image));
 plot_image(fig[1,4], img_approx, title = &quot;Reconstructed Image&quot;)
 resize_to_layout!(fig)
-fig</code></pre><img src="97715265.png" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../compressed_sensing/">« Compressed Sensing</a><a class="docs-footer-nextpage" href="../../../solvers/">Solvers »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Thursday 22 August 2024 15:34">Thursday 22 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+fig</code></pre><img src="97715265.png" alt="Example block output"/><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../compressed_sensing/">« Compressed Sensing</a><a class="docs-footer-nextpage" href="../../../solvers/">Solvers »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Friday 23 August 2024 09:29">Friday 23 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/generated/examples/getting_started/index.html

@@ -9,4 +9,4 @@
   \underset{\mathbf{x}}{argmin} \frac{1}{2}\vert\vert \mathbf{A}\mathbf{x}-\mathbf{b} \vert\vert_2^2 + \vert\vert\mathbf{x}\vert\vert^2_2 .
 \end{equation}\]</p><p>The corresponding solver can be built with the L2 regularization term:</p><pre><code class="language-julia hljs">solver = createLinearSolver(CGNR, A; reg = L2Regularization(0.0001), iterations=32);
 x_approx = solve!(solver, b)
-isapprox(x, x_approx, rtol = 0.001)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../../">« Home</a><a class="docs-footer-nextpage" href="../compressed_sensing/">Compressed Sensing »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Thursday 22 August 2024 15:34">Thursday 22 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+isapprox(x, x_approx, rtol = 0.001)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../../">« Home</a><a class="docs-footer-nextpage" href="../compressed_sensing/">Compressed Sensing »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Friday 23 August 2024 09:29">Friday 23 August 2024</span>. Using Julia version 1.10.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>