.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <sphx_glr_download_auto_examples_decomposition_plot_image_denoising.py>` to download the full example code
.. 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.




.. code-block:: python

    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


    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.

    # 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()

**Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_decomposition_plot_image_denoising.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_image_denoising.py <plot_image_denoising.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_image_denoising.ipynb <plot_image_denoising.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_
