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

.. only:: html

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

        New to DeepInverse? Get started with the basics with the
        :ref:`5 minute quickstart tutorial <sphx_glr_auto_examples_basics_demo_quickstart.py>`.

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

.. _sphx_glr_auto_examples_physics_demo_lidar.py:


Single photon lidar operator for depth ranging.
===================================================

In this example we show how to use the :class:`deepinv.physics.SinglePhotonLidar` forward model.

.. GENERATED FROM PYTHON SOURCE LINES 8-14

.. code-block:: Python


    import deepinv as dinv
    import torch
    import matplotlib.pyplot as plt









.. GENERATED FROM PYTHON SOURCE LINES 15-32

Create forward model
-----------------------------------------------

We create a lidar model with 100 bins per pixel and a Gaussian impulse response function
with a standard deviation of 2 bins.

The forward model for the case of a single depth per pixel is defined as (e.g. see :footcite:t:`rapp2020advances`):

.. math::

      y_{i,j,t} = \mathcal{P}(h(t-d_{i,j}) r_{i,j} + b_{i,j})

where :math:`\mathcal{P}` is the Poisson noise model, :math:`h(t)` is a Gaussian impulse response function at
time :math:`t`, :math:`d_{i,j}` is the depth of the scene at pixel :math:`(i,j)`,
:math:`r_{i,j}` is the intensity of the scene at pixel :math:`(i,j)` and :math:`b_{i,j}` is the background noise
at pixel :math:`(i,j)`.


.. GENERATED FROM PYTHON SOURCE LINES 32-38

.. code-block:: Python


    device = dinv.utils.get_freer_gpu() if torch.cuda.is_available() else "cpu"
    bins = 100
    irf_sigma = 2
    physics = dinv.physics.SinglePhotonLidar(bins=bins, sigma=irf_sigma, device=device)








.. GENERATED FROM PYTHON SOURCE LINES 39-50

Generate toy signal and measurement
-----------------------------------------------

We generate a toy signal with a single peak per pixel located around the 50th bin
and a signal-to-background ratio of 10%.

Signals should have size (B, 3, H, W) where the first channel contains the depth of the scene,
the second channel contains the intensity of the scene and the third channel contains the
per pixel background noise levels.

The measurement associated with a signal has size (B, bins, H, W).

.. GENERATED FROM PYTHON SOURCE LINES 50-68

.. code-block:: Python


    sbr = 0.1
    signal = 50
    bkg_level = signal / sbr / bins
    depth = bins / 2

    # depth
    d = torch.ones(1, 1, 2, 2, device=device) * depth
    # signal
    r = torch.ones_like(d) * signal
    # background
    b = torch.ones_like(d) * bkg_level

    x = torch.cat([d, r, b], dim=1)  # signal of size (B, 3, H, W)

    y = physics(x)  # measurement of size (B, bins, H, W)









.. GENERATED FROM PYTHON SOURCE LINES 69-76

Apply matched filtering to recover the signal and plot the results
-------------------------------------------------------------------------------

We apply matched filtering to recover the signal and plot the results.

The measurements are shown in blue and the depth and intensity of the
recovered signals are shown in red.

.. GENERATED FROM PYTHON SOURCE LINES 76-97

.. code-block:: Python



    xhat = physics.A_dagger(y)

    plt.figure()
    for i in range(2):
        for j in range(2):
            plt.subplot(2, 2, i * 2 + j + 1)
            plt.plot(y[0, :, i, j].detach().cpu().numpy())
            plt.stem(
                xhat[0, 0, i, j].detach().cpu().numpy(),
                xhat[0, 1, i, j].detach().cpu().numpy() / 4,
                linefmt="red",
                markerfmt="red",
            )
            plt.title(f"pixel ({i}, {j})")


    plt.tight_layout()
    plt.show()




.. image-sg:: /auto_examples/physics/images/sphx_glr_demo_lidar_001.png
   :alt: pixel (0, 0), pixel (0, 1), pixel (1, 0), pixel (1, 1)
   :srcset: /auto_examples/physics/images/sphx_glr_demo_lidar_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    /home/runner/work/deepinv/deepinv/deepinv/physics/lidar.py:83: UserWarning: Using padding='same' with even kernel lengths and odd dilation may require a zero-padded copy of the input be created (Triggered internally at ../aten/src/ATen/native/Convolution.cpp:1031.)
      x = torch.nn.functional.conv1d(y, self.irf, padding="same")




.. GENERATED FROM PYTHON SOURCE LINES 98-101

:References:

.. footbibliography::


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

   **Total running time of the script:** (0 minutes 0.273 seconds)


.. _sphx_glr_download_auto_examples_physics_demo_lidar.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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