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{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-03T00:01:58","documenter_version":"1.2.0"}}
{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-03T15:24:07","documenter_version":"1.2.0"}}
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Function Docstrings · RadonKA.jl</title><meta name="title" content="Function Docstrings · RadonKA.jl"/><meta property="og:title" content="Function Docstrings · RadonKA.jl"/><meta property="twitter:title" content="Function Docstrings · RadonKA.jl"/><meta name="description" content="Documentation for RadonKA.jl."/><meta property="og:description" content="Documentation for RadonKA.jl."/><meta property="twitter:description" content="Documentation for RadonKA.jl."/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">RadonKA.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">RadonKA.jl</a></li><li class="is-active"><a class="tocitem" href>Function Docstrings</a><ul class="internal"><li><a class="tocitem" href="#Radon"><span>Radon</span></a></li><li><a class="tocitem" href="#IRadon"><span>IRadon</span></a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Function Docstrings</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Function Docstrings</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/roflmaostc/RadonKA.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/roflmaostc/RadonKA.jl/blob/main/docs/src/functions.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h2 id="Radon"><a class="docs-heading-anchor" href="#Radon">Radon</a><a id="Radon-1"></a><a class="docs-heading-anchor-permalink" href="#Radon" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="RadonKA.radon" href="#RadonKA.radon"><code>RadonKA.radon</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">radon(I, θs; backend=CPU())</code></pre><p>Calculates the parallel Radon transform of the three dimensional AbstractArray <code>I</code>. The first two dimensions are y and x. The third dimension is z, the rotational axis. Works either with a <code>AbstractArray{T, 3}</code> or <code>AbstractArray{T, 2}</code>.</p><p><code>θs</code> is a vector or range storing the angles in radians.</p><p><code>backend</code> can be either <code>CPU()</code> for multithreaded CPU execution or <code>CUDABackend()</code> for CUDA execution. In principle, all backends of KernelAbstractions.jl should work but are not tested</p><p>Please note: the implementation is not quite optimized for cache efficiency and it is a very naive algorithm. But still, it is fast!</p><p>See also <a href="#RadonKA.iradon"><code>iradon</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/roflmaostc/RadonKA.jl/blob/a98ae81981102d2a9063957c8ddacccf4572198b/src/radon.jl#L12-L30">source</a></section></article><h2 id="IRadon"><a class="docs-heading-anchor" href="#IRadon">IRadon</a><a id="IRadon-1"></a><a class="docs-heading-anchor-permalink" href="#IRadon" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="RadonKA.iradon" href="#RadonKA.iradon"><code>RadonKA.iradon</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">iradon(sinogram, θs; backend=CPU())</code></pre><p>Calculates the parallel inverse Radon transform of the <code>sinogram</code>. The first two dimensions are y and x. The third dimension is z, the rotational axis. Works either with a <code>AbstractArray{T, 3}</code> or <code>AbstractArray{T, 2}</code>.</p><p><code>θs</code> is a vector or range storing the angles in radians.</p><p><code>backend</code> can be either <code>CPU()</code> for multithreaded CPU execution or <code>CUDABackend()</code> for CUDA execution. In principle, all backends of KernelAbstractions.jl should work but are not tested.</p><p>See also <a href="#RadonKA.radon"><code>radon</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/roflmaostc/RadonKA.jl/blob/a98ae81981102d2a9063957c8ddacccf4572198b/src/iradon.jl#L26-L40">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="RadonKA.filtered_backprojection" href="#RadonKA.filtered_backprojection"><code>RadonKA.filtered_backprojection</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">filtered_backprojection(sinogram, θs, backend=CPU())</code></pre><p>Calculates the simple Filtered Backprojection in CT with applying a ramp filter in Fourier space.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/roflmaostc/RadonKA.jl/blob/a98ae81981102d2a9063957c8ddacccf4572198b/src/iradon.jl#L3-L9">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« RadonKA.jl</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.0 on <span class="colophon-date" title="Sunday 3 December 2023 00:01">Sunday 3 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Function Docstrings · RadonKA.jl</title><meta name="title" content="Function Docstrings · RadonKA.jl"/><meta property="og:title" content="Function Docstrings · RadonKA.jl"/><meta property="twitter:title" content="Function Docstrings · RadonKA.jl"/><meta name="description" content="Documentation for RadonKA.jl."/><meta property="og:description" content="Documentation for RadonKA.jl."/><meta property="twitter:description" content="Documentation for RadonKA.jl."/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../">RadonKA.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">RadonKA.jl</a></li><li class="is-active"><a class="tocitem" href>Function Docstrings</a><ul class="internal"><li><a class="tocitem" href="#Radon"><span>Radon</span></a></li><li><a class="tocitem" href="#IRadon"><span>IRadon</span></a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Function Docstrings</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Function Docstrings</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/roflmaostc/RadonKA.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/roflmaostc/RadonKA.jl/blob/main/docs/src/functions.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h2 id="Radon"><a class="docs-heading-anchor" href="#Radon">Radon</a><a id="Radon-1"></a><a class="docs-heading-anchor-permalink" href="#Radon" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="RadonKA.radon" href="#RadonKA.radon"><code>RadonKA.radon</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">radon(I, θs; backend=CPU())</code></pre><p>Calculates the parallel Radon transform of the AbstractArray <code>I</code>. The first two dimensions are y and x. The third dimension is z, the rotational axis. <code>size(I, 1)</code> and <code>size(I, 2)</code> have to be equal and a even number. The Radon transform is rotated around the pixel <code>size(I, 1) ÷ 2 + 1</code>, so there is always a real center pixel! Works either with a <code>AbstractArray{T, 3}</code> or <code>AbstractArray{T, 2}</code>.</p><p><code>θs</code> is a vector or range storing the angles in radians.</p><p><code>backend</code> can be either <code>CPU()</code> for multithreaded CPU execution or <code>CUDABackend()</code> for CUDA execution. In principle, all backends of KernelAbstractions.jl should work but are not tested</p><p>Please note: the implementation is not quite optimized for cache efficiency and it is a very naive algorithm. But still, it is fast!</p><p>See also <a href="#RadonKA.iradon"><code>iradon</code></a>.</p><p><strong>Example</strong></p><p>The reason the sinogram has the value <code>1.41421</code> for the diagonal ray <code>π/4</code> is, that such a diagonal travels a longer distance through the pixel.</p><pre><code class="language-julia-repl hljs">julia&gt; arr = zeros((4,4)); arr[3,3] = 1;

julia&gt; radon(arr, [0, π/4, π/2])
3×3 view(::Array{Float64, 3}, :, :, 1) with eltype Float64:
0.0 0.0 0.0
1.0 1.41421 1.0
0.0 0.0 0.0</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/roflmaostc/RadonKA.jl/blob/b32dd9c93327dc7bb252c742b021065121edca66/src/radon.jl#L12-L46">source</a></section></article><h2 id="IRadon"><a class="docs-heading-anchor" href="#IRadon">IRadon</a><a id="IRadon-1"></a><a class="docs-heading-anchor-permalink" href="#IRadon" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="RadonKA.iradon" href="#RadonKA.iradon"><code>RadonKA.iradon</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">iradon(sinogram, θs; backend=CPU())</code></pre><p>Calculates the parallel inverse Radon transform of the <code>sinogram</code>. The first two dimensions are y and x. The third dimension is z, the rotational axis. Works either with a <code>AbstractArray{T, 3}</code> or <code>AbstractArray{T, 2}</code>. <code>size(sinogram, 1)</code> has to be a odd number. And <code>size(sinogram, 2)</code> has to be equal to <code>length(angles)</code>. The inverse Radon transform is rotated around the pixel <code>size(sinogram, 1) ÷ 2</code>, so there is always a real center pixel! Works either with a <code>AbstractArray{T, 3}</code> or <code>AbstractArray{T, 2}</code>.</p><p><code>θs</code> is a vector or range storing the angles in radians.</p><p><code>backend</code> can be either <code>CPU()</code> for multithreaded CPU execution or <code>CUDABackend()</code> for CUDA execution. In principle, all backends of KernelAbstractions.jl should work but are not tested.</p><p>See also <a href="#RadonKA.radon"><code>radon</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/roflmaostc/RadonKA.jl/blob/b32dd9c93327dc7bb252c742b021065121edca66/src/iradon.jl#L26-L45">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="RadonKA.filtered_backprojection" href="#RadonKA.filtered_backprojection"><code>RadonKA.filtered_backprojection</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">filtered_backprojection(sinogram, θs, backend=CPU())</code></pre><p>Calculates the simple Filtered Backprojection in CT with applying a ramp filter in Fourier space.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/roflmaostc/RadonKA.jl/blob/b32dd9c93327dc7bb252c742b021065121edca66/src/iradon.jl#L3-L9">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« RadonKA.jl</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="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.0 on <span class="colophon-date" title="Sunday 3 December 2023 15:24">Sunday 3 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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