## File: plot_image_denoising.py

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scikit-learn 0.18-5
 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173` ``````""" ========================================= 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. """ print(__doc__) from time import time import matplotlib.pyplot as plt import numpy as np import scipy as sp from sklearn.decomposition import MiniBatchDictionaryLearning from sklearn.feature_extraction.image import extract_patches_2d from sklearn.feature_extraction.image import reconstruct_from_patches_2d from sklearn.utils.testing import SkipTest from sklearn.utils.fixes import sp_version if sp_version < (0, 12): raise SkipTest("Skipping because SciPy version earlier than 0.12.0 and " "thus does not include the scipy.misc.face() image.") ############################################################################### try: from scipy import misc face = misc.face(gray=True) except AttributeError: # Old versions of scipy have face in the top level package 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 # downsample for higher speed face = face[::2, ::2] + face[1::2, ::2] + face[::2, 1::2] + face[1::2, 1::2] 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) # 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('done in %.2fs.' % (time() - t0)) ############################################################################### # Learn the dictionary from reference patches print('Learning the dictionary...') t0 = time() dico = MiniBatchDictionaryLearning(n_components=100, alpha=1, n_iter=500) V = dico.fit(data).components_ dt = time() - t0 print('done in %.2fs.' % dt) 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) ############################################################################### # Display the distorted image 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') ############################################################################### # Extract noisy patches and reconstruct them using the dictionary 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\n5 atoms', 'lars', {'transform_n_nonzero_coefs': 5}), ('Thresholding\n alpha=0.1', 'threshold', {'transform_alpha': .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() ``````