.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "tutorials/datafidelity_L1_vs_L2.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_tutorials_datafidelity_L1_vs_L2.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_tutorials_datafidelity_L1_vs_L2.py:


06. L1 vs. L2 Fidelity-Term
===========================
This tutorial shows the difference between
two fidelity norms with different underlying noise types.
Here using the example of Salt-And-Pepper and Gaussian noise.

.. GENERATED FROM PYTHON SOURCE LINES 9-23

.. code-block:: default

    import numpy as np
    from scipy import misc
    import matplotlib.pyplot as plt

    from recon.utils.utils import psnr
    from recon.interfaces import Smoothing

    img = misc.face(gray=True)[256:768,256:768]
    img = img/np.max(img)
    gt = img

    vmin, vmax = 0, 1
    sigma = 0.2 * vmax








.. GENERATED FROM PYTHON SOURCE LINES 24-26

Create two noisy images.


.. GENERATED FROM PYTHON SOURCE LINES 26-49

.. code-block:: default


    def sp_noise(image):
        """Add salt and pepper noise to image."""
        s_vs_p = 0.5
        amount = 0.1
        out = np.copy(image)
        # Salt mode
        num_salt = np.ceil(amount * image.size * s_vs_p)
        coords = [np.random.randint(0, i - 1, int(num_salt))
                  for i in image.shape]
        out[coords] = 1

        # Pepper mode
        num_pepper = np.ceil(amount * image.size * (1. - s_vs_p))
        coords = [np.random.randint(0, i - 1, int(num_pepper))
                  for i in image.shape]
        out[coords] = 0
        return out


    noise_img_sp = sp_noise(gt)
    noise_img_white = gt + np.random.normal(0, sigma, size=gt.shape)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    /Users/lucasplagwitz/git_projects/recon/tutorials/datafidelity_L1_vs_L2.py:36: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
      out[coords] = 1
    /Users/lucasplagwitz/git_projects/recon/tutorials/datafidelity_L1_vs_L2.py:42: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.
      out[coords] = 0




.. GENERATED FROM PYTHON SOURCE LINES 50-52

Application of the various fidelity norms.


.. GENERATED FROM PYTHON SOURCE LINES 52-109

.. code-block:: default


    # L1-fidelity
    tv_smoothing = Smoothing(domain_shape=gt.shape, reg_mode='tv', norm='L1', alpha=1, lam=1, tau='calc')
    u_L1_sp = tv_smoothing.solve(data=noise_img_sp, max_iter=2000, tol=1e-4)

    tv_smoothing = Smoothing(domain_shape=gt.shape, reg_mode='tv', norm='L1', alpha=0.8, lam=1, tau='calc')
    u_L1_white = tv_smoothing.solve(data=noise_img_white, max_iter=2000, tol=1e-4)


    # L2-fidelity
    tv_smoothing = Smoothing(domain_shape=gt.shape, reg_mode='tv', norm='L2', alpha=0.1, lam=0.5, tau='calc')
    u_L2_sp = tv_smoothing.solve(data=noise_img_sp, max_iter=2000, tol=1e-4)

    tv_smoothing = Smoothing(domain_shape=gt.shape, reg_mode='tv', norm='L2', alpha=0.1, lam=0.6, tau='calc')
    u_L2_white = tv_smoothing.solve(data=noise_img_white, max_iter=2000, tol=1e-4)

    # plot
    f = plt.figure(figsize=(9, 6))
    # Salt-And-Pepper
    f.add_subplot(2, 3, 1)
    plt.axis('off')
    plt.gray()
    plt.imshow(noise_img_sp, vmin=vmin, vmax=vmax)
    plt.title("S&P-Noise-PSNR: "+str(psnr(gt, noise_img_sp)))

    f.add_subplot(2, 3, 2)
    plt.imshow(u_L1_sp, vmin=vmin, vmax=vmax)
    plt.title("L1 - PSNR: "+str(psnr(gt, u_L1_sp)))
    plt.axis('off')
    plt.gray()

    f.add_subplot(2, 3, 3)
    plt.imshow(u_L2_sp, vmin=vmin, vmax=vmax)
    plt.title("L2 - PSNR: "+str(psnr(gt, u_L2_sp)))
    plt.axis('off')
    plt.gray()

    # Gaussian
    f.add_subplot(2, 3, 4)
    plt.axis('off')
    plt.gray()
    plt.imshow(noise_img_white, vmin=vmin, vmax=vmax)
    plt.title("White-Noise - PSNR: "+str(psnr(gt, noise_img_white)))

    f.add_subplot(2, 3, 5)
    plt.imshow(u_L1_white, vmin=vmin, vmax=vmax)
    plt.title("L1 - PSNR: "+str(psnr(gt, u_L1_white)))
    plt.axis('off')
    plt.gray()

    f.add_subplot(2, 3, 6)
    plt.imshow(u_L2_white, vmin=vmin, vmax=vmax)
    plt.title("L2 - PSNR: "+str(psnr(gt, u_L2_white)))
    plt.axis('off')
    plt.gray()

    plt.show(block=False)



.. image:: /tutorials/images/sphx_glr_datafidelity_L1_vs_L2_001.png
    :alt: S&P-Noise-PSNR: 15.31, L1 - PSNR: 28.53, L2 - PSNR: 22.75, White-Noise - PSNR: 13.97, L1 - PSNR: 23.94, L2 - PSNR: 24.72
    :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

     Early stopping.
     Early stopping.
     Early stopping.
     Early stopping.





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 2 minutes  27.311 seconds)


.. _sphx_glr_download_tutorials_datafidelity_L1_vs_L2.py:


.. only :: html

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



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: datafidelity_L1_vs_L2.py <datafidelity_L1_vs_L2.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: datafidelity_L1_vs_L2.ipynb <datafidelity_L1_vs_L2.ipynb>`


.. only:: html

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

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