.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/decomposition/plot_image_denoising.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_decomposition_plot_image_denoising.py: ========================================= Image denoising using dictionary learning ========================================= An example comparing the effect of reconstructing noisy fragments of a raccoon face image using firstly online :ref:`DictionaryLearning` and various transform methods. 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. 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. It can be seen from the plots that the results of :ref:`omp` 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. The result of :ref:`least_angle_regression` is much more strongly biased: the difference is reminiscent of the local intensity value of the original image. 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. .. GENERATED FROM PYTHON SOURCE LINES 36-38 Generate distorted image ------------------------ .. GENERATED FROM PYTHON SOURCE LINES 38-64 .. code-block:: default import numpy as np import scipy as sp try: # SciPy >= 0.16 have face in misc from scipy.misc import face face = face(gray=True) except ImportError: face = sp.face(gray=True) # Convert from uint8 representation with values between 0 and 255 to # a floating point representation with values between 0 and 1. face = face / 255.0 # downsample for higher speed face = face[::4, ::4] + face[1::4, ::4] + face[::4, 1::4] + face[1::4, 1::4] face /= 4.0 height, width = face.shape # Distort the right half of the image print("Distorting image...") distorted = face.copy() distorted[:, width // 2 :] += 0.075 * np.random.randn(height, width // 2) .. rst-class:: sphx-glr-script-out .. code-block:: none Distorting image... .. GENERATED FROM PYTHON SOURCE LINES 65-67 Display the distorted image --------------------------- .. GENERATED FROM PYTHON SOURCE LINES 67-94 .. code-block:: default import matplotlib.pyplot as plt def show_with_diff(image, reference, title): """Helper function to display denoising""" plt.figure(figsize=(5, 3.3)) plt.subplot(1, 2, 1) plt.title("Image") plt.imshow(image, vmin=0, vmax=1, cmap=plt.cm.gray, interpolation="nearest") plt.xticks(()) plt.yticks(()) plt.subplot(1, 2, 2) difference = image - reference plt.title("Difference (norm: %.2f)" % np.sqrt(np.sum(difference**2))) plt.imshow( difference, vmin=-0.5, vmax=0.5, cmap=plt.cm.PuOr, interpolation="nearest" ) plt.xticks(()) plt.yticks(()) plt.suptitle(title, size=16) plt.subplots_adjust(0.02, 0.02, 0.98, 0.79, 0.02, 0.2) show_with_diff(distorted, face, "Distorted image") .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_001.png :alt: Distorted image, Image, Difference (norm: 11.76) :srcset: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 95-97 Extract reference patches ---------------------------- .. GENERATED FROM PYTHON SOURCE LINES 97-112 .. code-block:: default from time import time from sklearn.feature_extraction.image import extract_patches_2d # Extract all reference patches from the left half of the image print("Extracting reference patches...") t0 = time() patch_size = (7, 7) data = extract_patches_2d(distorted[:, : width // 2], patch_size) data = data.reshape(data.shape[0], -1) data -= np.mean(data, axis=0) data /= np.std(data, axis=0) print(f"{data.shape[0]} patches extracted in %.2fs." % (time() - t0)) .. rst-class:: sphx-glr-script-out .. code-block:: none Extracting reference patches... 22692 patches extracted in 0.01s. .. GENERATED FROM PYTHON SOURCE LINES 113-115 Learn the dictionary from reference patches ------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 115-145 .. code-block:: default from sklearn.decomposition import MiniBatchDictionaryLearning print("Learning the dictionary...") t0 = time() dico = MiniBatchDictionaryLearning( # increase to 300 for higher quality results at the cost of slower # training times. n_components=50, batch_size=200, alpha=1.0, max_iter=10, ) V = dico.fit(data).components_ dt = time() - t0 print(f"{dico.n_iter_} iterations / {dico.n_steps_} steps in {dt:.2f}.") plt.figure(figsize=(4.2, 4)) for i, comp in enumerate(V[:100]): plt.subplot(10, 10, i + 1) plt.imshow(comp.reshape(patch_size), cmap=plt.cm.gray_r, interpolation="nearest") plt.xticks(()) plt.yticks(()) plt.suptitle( "Dictionary learned from face patches\n" + "Train time %.1fs on %d patches" % (dt, len(data)), fontsize=16, ) plt.subplots_adjust(0.08, 0.02, 0.92, 0.85, 0.08, 0.23) .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_002.png :alt: Dictionary learned from face patches Train time 14.2s on 22692 patches :srcset: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Learning the dictionary... 1.0 iterations / 114 steps in 14.16. .. GENERATED FROM PYTHON SOURCE LINES 146-148 Extract noisy patches and reconstruct them using the dictionary --------------------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 148-187 .. code-block:: default from sklearn.feature_extraction.image import reconstruct_from_patches_2d print("Extracting noisy patches... ") t0 = time() data = extract_patches_2d(distorted[:, width // 2 :], patch_size) data = data.reshape(data.shape[0], -1) intercept = np.mean(data, axis=0) data -= intercept print("done in %.2fs." % (time() - t0)) transform_algorithms = [ ("Orthogonal Matching Pursuit\n1 atom", "omp", {"transform_n_nonzero_coefs": 1}), ("Orthogonal Matching Pursuit\n2 atoms", "omp", {"transform_n_nonzero_coefs": 2}), ("Least-angle regression\n4 atoms", "lars", {"transform_n_nonzero_coefs": 4}), ("Thresholding\n alpha=0.1", "threshold", {"transform_alpha": 0.1}), ] reconstructions = {} for title, transform_algorithm, kwargs in transform_algorithms: print(title + "...") reconstructions[title] = face.copy() t0 = time() dico.set_params(transform_algorithm=transform_algorithm, **kwargs) code = dico.transform(data) patches = np.dot(code, V) patches += intercept patches = patches.reshape(len(data), *patch_size) if transform_algorithm == "threshold": patches -= patches.min() patches /= patches.max() reconstructions[title][:, width // 2 :] = reconstruct_from_patches_2d( patches, (height, width // 2) ) dt = time() - t0 print("done in %.2fs." % dt) show_with_diff(reconstructions[title], face, title + " (time: %.1fs)" % dt) plt.show() .. rst-class:: sphx-glr-horizontal * .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_003.png :alt: Orthogonal Matching Pursuit 1 atom (time: 0.5s), Image, Difference (norm: 10.69) :srcset: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_003.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_004.png :alt: Orthogonal Matching Pursuit 2 atoms (time: 1.1s), Image, Difference (norm: 9.32) :srcset: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_004.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_005.png :alt: Least-angle regression 4 atoms (time: 8.3s), Image, Difference (norm: 13.45) :srcset: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_005.png :class: sphx-glr-multi-img * .. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_006.png :alt: Thresholding alpha=0.1 (time: 0.1s), Image, Difference (norm: 14.40) :srcset: /auto_examples/decomposition/images/sphx_glr_plot_image_denoising_006.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none Extracting noisy patches... done in 0.00s. Orthogonal Matching Pursuit 1 atom... done in 0.54s. Orthogonal Matching Pursuit 2 atoms... done in 1.09s. Least-angle regression 4 atoms... done in 8.29s. Thresholding alpha=0.1... done in 0.09s. .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 25.422 seconds) .. _sphx_glr_download_auto_examples_decomposition_plot_image_denoising.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.1.X?urlpath=lab/tree/notebooks/auto_examples/decomposition/plot_image_denoising.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_image_denoising.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_image_denoising.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_