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<ul>
<li><a class="reference internal" href="#">Image denoising using dictionary learning</a><ul>
<li><a class="reference internal" href="#generate-distorted-image">Generate distorted image</a></li>
<li><a class="reference internal" href="#display-the-distorted-image">Display the distorted image</a></li>
<li><a class="reference internal" href="#extract-reference-patches">Extract reference patches</a></li>
<li><a class="reference internal" href="#learn-the-dictionary-from-reference-patches">Learn the dictionary from reference patches</a></li>
<li><a class="reference internal" href="#extract-noisy-patches-and-reconstruct-them-using-the-dictionary">Extract noisy patches and reconstruct them using the dictionary</a></li>
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<p class="admonition-title">Note</p>
<p><a class="reference internal" href="#sphx-glr-download-auto-examples-decomposition-plot-image-denoising-py"><span class="std std-ref">Go to the end</span></a>
to download the full example code or to run this example in your browser via JupyterLite or Binder</p>
</div>
<section class="sphx-glr-example-title" id="image-denoising-using-dictionary-learning">
<span id="sphx-glr-auto-examples-decomposition-plot-image-denoising-py"></span><h1>Image denoising using dictionary learning<a class="headerlink" href="#image-denoising-using-dictionary-learning" title="Link to this heading">¶</a></h1>
<p>An example comparing the effect of reconstructing noisy fragments
of a raccoon face image using firstly online <a class="reference internal" href="../../modules/decomposition.html#dictionarylearning"><span class="std std-ref">Dictionary Learning</span></a> and
various transform methods.</p>
<p>The dictionary is fitted on the distorted left half of the image, and
subsequently used to reconstruct the right half. Note that even better
performance could be achieved by fitting to an undistorted (i.e.
noiseless) image, but here we start from the assumption that it is not
available.</p>
<p>A common practice for evaluating the results of image denoising is by looking
at the difference between the reconstruction and the original image. If the
reconstruction is perfect this will look like Gaussian noise.</p>
<p>It can be seen from the plots that the results of <a class="reference internal" href="../../modules/linear_model.html#omp"><span class="std std-ref">Orthogonal Matching Pursuit (OMP)</span></a> with two
non-zero coefficients is a bit less biased than when keeping only one
(the edges look less prominent). It is in addition closer from the ground
truth in Frobenius norm.</p>
<p>The result of <a class="reference internal" href="../../modules/linear_model.html#least-angle-regression"><span class="std std-ref">Least Angle Regression</span></a> is much more strongly biased: the
difference is reminiscent of the local intensity value of the original image.</p>
<p>Thresholding is clearly not useful for denoising, but it is here to show that
it can produce a suggestive output with very high speed, and thus be useful
for other tasks such as object classification, where performance is not
necessarily related to visualisation.</p>
<section id="generate-distorted-image">
<h2>Generate distorted image<a class="headerlink" href="#generate-distorted-image" title="Link to this heading">¶</a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="k">try</span><span class="p">:</span> <span class="c1"># Scipy >= 1.10</span>
<span class="kn">from</span> <span class="nn">scipy.datasets</span> <span class="kn">import</span> <a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.misc.face.html#scipy.misc.face" title="scipy.misc.face" class="sphx-glr-backref-module-scipy-misc sphx-glr-backref-type-py-function"><span class="n">face</span></a>
<span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">scipy.misc</span> <span class="kn">import</span> <a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.misc.face.html#scipy.misc.face" title="scipy.misc.face" class="sphx-glr-backref-module-scipy-misc sphx-glr-backref-type-py-function"><span class="n">face</span></a>
<span class="n">raccoon_face</span> <span class="o">=</span> <a href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.misc.face.html#scipy.misc.face" title="scipy.misc.face" class="sphx-glr-backref-module-scipy-misc sphx-glr-backref-type-py-function"><span class="n">face</span></a><span class="p">(</span><span class="n">gray</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="c1"># Convert from uint8 representation with values between 0 and 255 to</span>
<span class="c1"># a floating point representation with values between 0 and 1.</span>
<span class="n">raccoon_face</span> <span class="o">=</span> <span class="n">raccoon_face</span> <span class="o">/</span> <span class="mf">255.0</span>
<span class="c1"># downsample for higher speed</span>
<span class="n">raccoon_face</span> <span class="o">=</span> <span class="p">(</span>
<span class="n">raccoon_face</span><span class="p">[::</span><span class="mi">4</span><span class="p">,</span> <span class="p">::</span><span class="mi">4</span><span class="p">]</span>
<span class="o">+</span> <span class="n">raccoon_face</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">4</span><span class="p">,</span> <span class="p">::</span><span class="mi">4</span><span class="p">]</span>
<span class="o">+</span> <span class="n">raccoon_face</span><span class="p">[::</span><span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">::</span><span class="mi">4</span><span class="p">]</span>
<span class="o">+</span> <span class="n">raccoon_face</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">4</span><span class="p">,</span> <span class="mi">1</span><span class="p">::</span><span class="mi">4</span><span class="p">]</span>
<span class="p">)</span>
<span class="n">raccoon_face</span> <span class="o">/=</span> <span class="mf">4.0</span>
<span class="n">height</span><span class="p">,</span> <span class="n">width</span> <span class="o">=</span> <span class="n">raccoon_face</span><span class="o">.</span><span class="n">shape</span>
<span class="c1"># Distort the right half of the image</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Distorting image..."</span><span class="p">)</span>
<span class="n">distorted</span> <span class="o">=</span> <span class="n">raccoon_face</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="n">distorted</span><span class="p">[:,</span> <span class="n">width</span> <span class="o">//</span> <span class="mi">2</span> <span class="p">:]</span> <span class="o">+=</span> <span class="mf">0.075</span> <span class="o">*</span> <a href="https://numpy.org/doc/stable/reference/random/generated/numpy.random.randn.html#numpy.random.randn" title="numpy.random.randn" class="sphx-glr-backref-module-numpy-random sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span></a><span class="p">(</span><span class="n">height</span><span class="p">,</span> <span class="n">width</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Distorting image...
</pre></div>
</div>
</section>
<section id="display-the-distorted-image">
<h2>Display the distorted image<a class="headerlink" href="#display-the-distorted-image" title="Link to this heading">¶</a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="k">def</span> <span class="nf">show_with_diff</span><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="n">reference</span><span class="p">,</span> <span class="n">title</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Helper function to display denoising"""</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mf">3.3</span><span class="p">))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Image"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">image</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">gray</span><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="n">difference</span> <span class="o">=</span> <span class="n">image</span> <span class="o">-</span> <span class="n">reference</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html#matplotlib.pyplot.title" title="matplotlib.pyplot.title" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">title</span></a><span class="p">(</span><span class="s2">"Difference (norm: </span><span class="si">%.2f</span><span class="s2">)"</span> <span class="o">%</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.sqrt.html#numpy.sqrt" title="numpy.sqrt" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-data"><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span></a><span class="p">(</span><a href="https://numpy.org/doc/stable/reference/generated/numpy.sum.html#numpy.sum" title="numpy.sum" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">sum</span></a><span class="p">(</span><span class="n">difference</span><span class="o">**</span><span class="mi">2</span><span class="p">)))</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span>
<span class="n">difference</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=-</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">PuOr</span><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.suptitle.html#matplotlib.pyplot.suptitle" title="matplotlib.pyplot.suptitle" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span></a><span class="p">(</span><span class="n">title</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="mi">16</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots_adjust.html#matplotlib.pyplot.subplots_adjust" title="matplotlib.pyplot.subplots_adjust" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span></a><span class="p">(</span><span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.98</span><span class="p">,</span> <span class="mf">0.79</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">)</span>
<span class="n">show_with_diff</span><span class="p">(</span><span class="n">distorted</span><span class="p">,</span> <span class="n">raccoon_face</span><span class="p">,</span> <span class="s2">"Distorted image"</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_image_denoising_001.png" srcset="../../_images/sphx_glr_plot_image_denoising_001.png" alt="Distorted image, Image, Difference (norm: 11.71)" class = "sphx-glr-single-img"/></section>
<section id="extract-reference-patches">
<h2>Extract reference patches<a class="headerlink" href="#extract-reference-patches" title="Link to this heading">¶</a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a>
<span class="kn">from</span> <span class="nn">sklearn.feature_extraction.image</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.feature_extraction.image.extract_patches_2d.html#sklearn.feature_extraction.image.extract_patches_2d" title="sklearn.feature_extraction.image.extract_patches_2d" class="sphx-glr-backref-module-sklearn-feature_extraction-image sphx-glr-backref-type-py-function"><span class="n">extract_patches_2d</span></a>
<span class="c1"># Extract all reference patches from the left half of the image</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Extracting reference patches..."</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">patch_size</span> <span class="o">=</span> <span class="p">(</span><span class="mi">7</span><span class="p">,</span> <span class="mi">7</span><span class="p">)</span>
<span class="n">data</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.feature_extraction.image.extract_patches_2d.html#sklearn.feature_extraction.image.extract_patches_2d" title="sklearn.feature_extraction.image.extract_patches_2d" class="sphx-glr-backref-module-sklearn-feature_extraction-image sphx-glr-backref-type-py-function"><span class="n">extract_patches_2d</span></a><span class="p">(</span><span class="n">distorted</span><span class="p">[:,</span> <span class="p">:</span> <span class="n">width</span> <span class="o">//</span> <span class="mi">2</span><span class="p">],</span> <span class="n">patch_size</span><span class="p">)</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">data</span> <span class="o">-=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.mean.html#numpy.mean" title="numpy.mean" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">mean</span></a><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">data</span> <span class="o">/=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.std.html#numpy.std" title="numpy.std" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">std</span></a><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="si">}</span><span class="s2"> patches extracted in %.2fs."</span> <span class="o">%</span> <span class="p">(</span><a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
</pre></div>
</div>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Extracting reference patches...
22692 patches extracted in 0.01s.
</pre></div>
</div>
</section>
<section id="learn-the-dictionary-from-reference-patches">
<h2>Learn the dictionary from reference patches<a class="headerlink" href="#learn-the-dictionary-from-reference-patches" title="Link to this heading">¶</a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.decomposition</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.decomposition.MiniBatchDictionaryLearning.html#sklearn.decomposition.MiniBatchDictionaryLearning" title="sklearn.decomposition.MiniBatchDictionaryLearning" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">MiniBatchDictionaryLearning</span></a>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Learning the dictionary..."</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">dico</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.MiniBatchDictionaryLearning.html#sklearn.decomposition.MiniBatchDictionaryLearning" title="sklearn.decomposition.MiniBatchDictionaryLearning" class="sphx-glr-backref-module-sklearn-decomposition sphx-glr-backref-type-py-class sphx-glr-backref-instance"><span class="n">MiniBatchDictionaryLearning</span></a><span class="p">(</span>
<span class="c1"># increase to 300 for higher quality results at the cost of slower</span>
<span class="c1"># training times.</span>
<span class="n">n_components</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
<span class="n">batch_size</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span>
<span class="n">alpha</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span>
<span class="n">max_iter</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span>
<span class="p">)</span>
<span class="n">V</span> <span class="o">=</span> <span class="n">dico</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">data</span><span class="p">)</span><span class="o">.</span><span class="n">components_</span>
<span class="n">dt</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span>
<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">dico</span><span class="o">.</span><span class="n">n_iter_</span><span class="si">}</span><span class="s2"> iterations / </span><span class="si">{</span><span class="n">dico</span><span class="o">.</span><span class="n">n_steps_</span><span class="si">}</span><span class="s2"> steps in </span><span class="si">{</span><span class="n">dt</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2">."</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.figure.html#matplotlib.pyplot.figure" title="matplotlib.pyplot.figure" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mf">4.2</span><span class="p">,</span> <span class="mi">4</span><span class="p">))</span>
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">comp</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">V</span><span class="p">[:</span><span class="mi">100</span><span class="p">]):</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="matplotlib.pyplot.subplot" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html#matplotlib.pyplot.imshow" title="matplotlib.pyplot.imshow" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">imshow</span></a><span class="p">(</span><span class="n">comp</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">patch_size</span><span class="p">),</span> <span class="n">cmap</span><span class="o">=</span><span class="n">plt</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">gray_r</span><span class="p">,</span> <span class="n">interpolation</span><span class="o">=</span><span class="s2">"nearest"</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xticks.html#matplotlib.pyplot.xticks" title="matplotlib.pyplot.xticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">xticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.yticks.html#matplotlib.pyplot.yticks" title="matplotlib.pyplot.yticks" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">yticks</span></a><span class="p">(())</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.suptitle.html#matplotlib.pyplot.suptitle" title="matplotlib.pyplot.suptitle" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span></a><span class="p">(</span>
<span class="s2">"Dictionary learned from face patches</span><span class="se">\n</span><span class="s2">"</span>
<span class="o">+</span> <span class="s2">"Train time </span><span class="si">%.1f</span><span class="s2">s on </span><span class="si">%d</span><span class="s2"> patches"</span> <span class="o">%</span> <span class="p">(</span><span class="n">dt</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">)),</span>
<span class="n">fontsize</span><span class="o">=</span><span class="mi">16</span><span class="p">,</span>
<span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots_adjust.html#matplotlib.pyplot.subplots_adjust" title="matplotlib.pyplot.subplots_adjust" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span></a><span class="p">(</span><span class="mf">0.08</span><span class="p">,</span> <span class="mf">0.02</span><span class="p">,</span> <span class="mf">0.92</span><span class="p">,</span> <span class="mf">0.85</span><span class="p">,</span> <span class="mf">0.08</span><span class="p">,</span> <span class="mf">0.23</span><span class="p">)</span>
</pre></div>
</div>
<img src="../../_images/sphx_glr_plot_image_denoising_002.png" srcset="../../_images/sphx_glr_plot_image_denoising_002.png" alt="Dictionary learned from face patches Train time 15.8s on 22692 patches" class = "sphx-glr-single-img"/><div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Learning the dictionary...
2.0 iterations / 125 steps in 15.84.
</pre></div>
</div>
</section>
<section id="extract-noisy-patches-and-reconstruct-them-using-the-dictionary">
<h2>Extract noisy patches and reconstruct them using the dictionary<a class="headerlink" href="#extract-noisy-patches-and-reconstruct-them-using-the-dictionary" title="Link to this heading">¶</a></h2>
<div class="highlight-Python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.feature_extraction.image</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.feature_extraction.image.reconstruct_from_patches_2d.html#sklearn.feature_extraction.image.reconstruct_from_patches_2d" title="sklearn.feature_extraction.image.reconstruct_from_patches_2d" class="sphx-glr-backref-module-sklearn-feature_extraction-image sphx-glr-backref-type-py-function"><span class="n">reconstruct_from_patches_2d</span></a>
<span class="nb">print</span><span class="p">(</span><span class="s2">"Extracting noisy patches... "</span><span class="p">)</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">data</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.feature_extraction.image.extract_patches_2d.html#sklearn.feature_extraction.image.extract_patches_2d" title="sklearn.feature_extraction.image.extract_patches_2d" class="sphx-glr-backref-module-sklearn-feature_extraction-image sphx-glr-backref-type-py-function"><span class="n">extract_patches_2d</span></a><span class="p">(</span><span class="n">distorted</span><span class="p">[:,</span> <span class="n">width</span> <span class="o">//</span> <span class="mi">2</span> <span class="p">:],</span> <span class="n">patch_size</span><span class="p">)</span>
<span class="n">data</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">intercept</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.mean.html#numpy.mean" title="numpy.mean" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">mean</span></a><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">data</span> <span class="o">-=</span> <span class="n">intercept</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"done in </span><span class="si">%.2f</span><span class="s2">s."</span> <span class="o">%</span> <span class="p">(</span><a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span><span class="p">))</span>
<span class="n">transform_algorithms</span> <span class="o">=</span> <span class="p">[</span>
<span class="p">(</span><span class="s2">"Orthogonal Matching Pursuit</span><span class="se">\n</span><span class="s2">1 atom"</span><span class="p">,</span> <span class="s2">"omp"</span><span class="p">,</span> <span class="p">{</span><span class="s2">"transform_n_nonzero_coefs"</span><span class="p">:</span> <span class="mi">1</span><span class="p">}),</span>
<span class="p">(</span><span class="s2">"Orthogonal Matching Pursuit</span><span class="se">\n</span><span class="s2">2 atoms"</span><span class="p">,</span> <span class="s2">"omp"</span><span class="p">,</span> <span class="p">{</span><span class="s2">"transform_n_nonzero_coefs"</span><span class="p">:</span> <span class="mi">2</span><span class="p">}),</span>
<span class="p">(</span><span class="s2">"Least-angle regression</span><span class="se">\n</span><span class="s2">4 atoms"</span><span class="p">,</span> <span class="s2">"lars"</span><span class="p">,</span> <span class="p">{</span><span class="s2">"transform_n_nonzero_coefs"</span><span class="p">:</span> <span class="mi">4</span><span class="p">}),</span>
<span class="p">(</span><span class="s2">"Thresholding</span><span class="se">\n</span><span class="s2"> alpha=0.1"</span><span class="p">,</span> <span class="s2">"threshold"</span><span class="p">,</span> <span class="p">{</span><span class="s2">"transform_alpha"</span><span class="p">:</span> <span class="mf">0.1</span><span class="p">}),</span>
<span class="p">]</span>
<span class="n">reconstructions</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">for</span> <span class="n">title</span><span class="p">,</span> <span class="n">transform_algorithm</span><span class="p">,</span> <span class="n">kwargs</span> <span class="ow">in</span> <span class="n">transform_algorithms</span><span class="p">:</span>
<span class="nb">print</span><span class="p">(</span><span class="n">title</span> <span class="o">+</span> <span class="s2">"..."</span><span class="p">)</span>
<span class="n">reconstructions</span><span class="p">[</span><span class="n">title</span><span class="p">]</span> <span class="o">=</span> <span class="n">raccoon_face</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
<span class="n">t0</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span>
<span class="n">dico</span><span class="o">.</span><span class="n">set_params</span><span class="p">(</span><span class="n">transform_algorithm</span><span class="o">=</span><span class="n">transform_algorithm</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="n">code</span> <span class="o">=</span> <span class="n">dico</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
<span class="n">patches</span> <span class="o">=</span> <a href="https://numpy.org/doc/stable/reference/generated/numpy.dot.html#numpy.dot" title="numpy.dot" class="sphx-glr-backref-module-numpy sphx-glr-backref-type-py-function"><span class="n">np</span><span class="o">.</span><span class="n">dot</span></a><span class="p">(</span><span class="n">code</span><span class="p">,</span> <span class="n">V</span><span class="p">)</span>
<span class="n">patches</span> <span class="o">+=</span> <span class="n">intercept</span>
<span class="n">patches</span> <span class="o">=</span> <span class="n">patches</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">),</span> <span class="o">*</span><span class="n">patch_size</span><span class="p">)</span>
<span class="k">if</span> <span class="n">transform_algorithm</span> <span class="o">==</span> <span class="s2">"threshold"</span><span class="p">:</span>
<span class="n">patches</span> <span class="o">-=</span> <span class="n">patches</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
<span class="n">patches</span> <span class="o">/=</span> <span class="n">patches</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
<span class="n">reconstructions</span><span class="p">[</span><span class="n">title</span><span class="p">][:,</span> <span class="n">width</span> <span class="o">//</span> <span class="mi">2</span> <span class="p">:]</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.feature_extraction.image.reconstruct_from_patches_2d.html#sklearn.feature_extraction.image.reconstruct_from_patches_2d" title="sklearn.feature_extraction.image.reconstruct_from_patches_2d" class="sphx-glr-backref-module-sklearn-feature_extraction-image sphx-glr-backref-type-py-function"><span class="n">reconstruct_from_patches_2d</span></a><span class="p">(</span>
<span class="n">patches</span><span class="p">,</span> <span class="p">(</span><span class="n">height</span><span class="p">,</span> <span class="n">width</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
<span class="p">)</span>
<span class="n">dt</span> <span class="o">=</span> <a href="https://docs.python.org/3/library/time.html#time.time" title="time.time" class="sphx-glr-backref-module-time sphx-glr-backref-type-py-function"><span class="n">time</span></a><span class="p">()</span> <span class="o">-</span> <span class="n">t0</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">"done in </span><span class="si">%.2f</span><span class="s2">s."</span> <span class="o">%</span> <span class="n">dt</span><span class="p">)</span>
<span class="n">show_with_diff</span><span class="p">(</span><span class="n">reconstructions</span><span class="p">[</span><span class="n">title</span><span class="p">],</span> <span class="n">raccoon_face</span><span class="p">,</span> <span class="n">title</span> <span class="o">+</span> <span class="s2">" (time: </span><span class="si">%.1f</span><span class="s2">s)"</span> <span class="o">%</span> <span class="n">dt</span><span class="p">)</span>
<a href="https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="matplotlib.pyplot.show" class="sphx-glr-backref-module-matplotlib-pyplot sphx-glr-backref-type-py-function"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
</pre></div>
</div>
<ul class="sphx-glr-horizontal">
<li><img src="../../_images/sphx_glr_plot_image_denoising_003.png" srcset="../../_images/sphx_glr_plot_image_denoising_003.png" alt="Orthogonal Matching Pursuit 1 atom (time: 0.6s), Image, Difference (norm: 10.70)" class = "sphx-glr-multi-img"/></li>
<li><img src="../../_images/sphx_glr_plot_image_denoising_004.png" srcset="../../_images/sphx_glr_plot_image_denoising_004.png" alt="Orthogonal Matching Pursuit 2 atoms (time: 1.1s), Image, Difference (norm: 9.37)" class = "sphx-glr-multi-img"/></li>
<li><img src="../../_images/sphx_glr_plot_image_denoising_005.png" srcset="../../_images/sphx_glr_plot_image_denoising_005.png" alt="Least-angle regression 4 atoms (time: 9.1s), Image, Difference (norm: 13.35)" class = "sphx-glr-multi-img"/></li>
<li><img src="../../_images/sphx_glr_plot_image_denoising_006.png" srcset="../../_images/sphx_glr_plot_image_denoising_006.png" alt="Thresholding alpha=0.1 (time: 0.1s), Image, Difference (norm: 14.26)" class = "sphx-glr-multi-img"/></li>
</ul>
<div class="sphx-glr-script-out highlight-none notranslate"><div class="highlight"><pre><span></span>Extracting noisy patches...
done in 0.00s.
Orthogonal Matching Pursuit
1 atom...
done in 0.55s.
Orthogonal Matching Pursuit
2 atoms...
done in 1.12s.
Least-angle regression
4 atoms...
done in 9.07s.
Thresholding
alpha=0.1...
done in 0.09s.
</pre></div>
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