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

.. only:: html

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

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

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

.. _sphx_glr_tutorials_radon.py:


02. Reconstruction I
====================
This tutorial demonstrates the reconstruction of a
measurement obtained in computerized tomography.
As mathematical construct the radon transform is obtained.
The implementation of the Astra-Toolbox is used.

.. GENERATED FROM PYTHON SOURCE LINES 12-14

We create a scenario with a 180 equal distributed angles.


.. GENERATED FROM PYTHON SOURCE LINES 14-54

.. code-block:: default


    import numpy as np
    import matplotlib.pyplot as plt

    from recon.utils import psnr
    from recon.operator.ct_radon import CtRt
    from recon.interfaces import Recon, Smoothing

    from matplotlib import image

    # load image as pixel array
    gt = image.imread("../data/phantom.png")
    gt = gt/np.max(gt)

    ntheta = 180
    theta = np.linspace(0, 180, ntheta, endpoint=False)
    sigma = 0.01
    R = CtRt(gt.shape, center=[gt.shape[0]//2, gt.shape[1]//2], theta=theta)

    y = R*gt.ravel()
    y_max = np.max(y)

    n = np.random.normal(0, sigma*y_max, size=y.shape)
    y = y + n

    x_rec = np.reshape(R.inv*y.ravel(), gt.shape)

    fig, axs = plt.subplots(1, 3, figsize=(14, 5))
    axs[0].imshow(gt, vmin=0, vmax=1)
    axs[0].set_title('Model')
    axs[0].axis('tight')
    axs[1].imshow(np.reshape(y, R.image_dim).T)
    axs[1].set_title('Data')
    axs[1].axis('tight')
    axs[2].imshow(x_rec, vmin=0, vmax=1)
    axs[2].set_title("FBP - PSNR: "+str(psnr(gt, x_rec)))
    axs[2].axis('tight')
    fig.tight_layout()
    plt.show(block=False)




.. image:: /tutorials/images/sphx_glr_radon_001.png
    :alt: Model, Data, FBP - PSNR: 18.53
    :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 55-58

Now we solve the problem using the optimization problem.
A comparison to the denoising of the FBP solution is shown.


.. GENERATED FROM PYTHON SOURCE LINES 58-79

.. code-block:: default


    lam = 15
    rec = Recon(operator=R, domain_shape=gt.shape, reg_mode='tv', alpha=1, lam=lam, extend_pdhgm=True)
    x_tv = rec.solve(data=y.ravel(), max_iter=1000, tol=1e-4)

    tv_smoothing = Smoothing(domain_shape=gt.shape, reg_mode='tv', lam=10, tau='calc')
    fbp_smooth = tv_smoothing.solve(data=x_rec, max_iter=1000, tol=1e-4)


    fig, axs = plt.subplots(1, 3, figsize=(14, 5))
    axs[0].imshow(gt, vmin=0, vmax=1)
    axs[0].set_title('Model')
    axs[0].axis('tight')
    axs[1].imshow(x_tv, vmin=0, vmax=1)
    axs[1].set_title("TV-Recon - PSNR: "+str(psnr(gt, x_tv)))
    axs[1].axis('tight')
    axs[2].imshow(fbp_smooth, vmin=0, vmax=1)
    axs[2].set_title("FBP-Smooth - PSNR: "+str(psnr(gt, fbp_smooth)))
    axs[2].axis('tight')
    fig.tight_layout()
    plt.show(block=False)



.. image:: /tutorials/images/sphx_glr_radon_002.png
    :alt: Model, TV-Recon - PSNR: 25.96, FBP-Smooth - PSNR: 20.75
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    /Users/lucasplagwitz/git_projects/recon/recon/solver/pd_hgm_extend.py:137: RuntimeWarning: divide by zero encountered in double_scalars
      self.sens = np.linalg.norm(p_gap)/np.linalg.norm(p_old)
    inf
    0.0575879430761
    0.0250657895096
    0.0123394724924
    0.00698178486739
    0.00383661007699
    0.00223954403196
    0.00136202788
    0.000839463622562
    0.000535423830805
    0.000357559031815
    0.000246971744871
    0.000188842471093
    0.000151375819315
    0.000126698668617
    0.000109222033788
    9.76307796608e-05
     Early stopping.
     Early stopping.





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

   **Total running time of the script:** ( 3 minutes  32.760 seconds)


.. _sphx_glr_download_tutorials_radon.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: radon.py <radon.py>`



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

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


.. only:: html

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

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