.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_ch7\ch7_denoising.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_ch7_ch7_denoising.py>`
        to download the full example code.

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

.. _sphx_glr_auto_ch7_ch7_denoising.py:


====================================
7.02 Denoising
====================================
We reproduce here the figure 7.3 of the book.
Utilitary functions can be found next to this file. Here, we only define codpy-related functions.

.. GENERATED FROM PYTHON SOURCE LINES 10-12

Necessary Imports
------------------------

.. GENERATED FROM PYTHON SOURCE LINES 12-27

.. code-block:: Python

    import os 
    import sys 

    import matplotlib.pyplot as plt 

    try:
        CURRENT_DIR = os.path.dirname(os.path.abspath(__file__))
    except NameError:
        CURRENT_DIR = os.getcwd()
    data_path = os.path.join(CURRENT_DIR, "data")
    PARENT_DIR = os.path.abspath(os.path.join(CURRENT_DIR, ".."))
    sys.path.insert(0, PARENT_DIR)

    from utils.ch7.ch7_utils import Denoising








.. GENERATED FROM PYTHON SOURCE LINES 28-33

Problem statement
------------------------
We consider the denoiser procedure introduced in the book, which aims to solve: 
$$\inf_{G \in \mathcal{H}_k} \|G-F\|_{L^2}^2 + \epsilon \|\nabla G\|_{L^2}^2.$$
The noisy signal (left image) is given by $F_\eta(x) = F(x) + \eta$, where $\eta$ is a white noise, and $f$ is a cosine function. The regularized solution is plotted on the right.

.. GENERATED FROM PYTHON SOURCE LINES 33-36

.. code-block:: Python


    Denoising() 
    plt.show()



.. image-sg:: /auto_ch7/images/sphx_glr_ch7_denoising_001.png
   :alt: Noisy signal, Denoised signal
   :srcset: /auto_ch7/images/sphx_glr_ch7_denoising_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.185 seconds)


.. _sphx_glr_download_auto_ch7_ch7_denoising.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: ch7_denoising.ipynb <ch7_denoising.ipynb>`

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

      :download:`Download Python source code: ch7_denoising.py <ch7_denoising.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: ch7_denoising.zip <ch7_denoising.zip>`


.. only:: html

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

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