.. _sphx_glr_auto_examples_02_encoding:

## Encoding operators

Operators with explicit domain and codomain shapes.  Check the adjoint before
using an encoding inside a solver.



.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="To be written: sensitivities, a centred unitary FFT and sampling composed into one operator, checked against torch&#x27;s FFT and the complex adjoint identity.">

.. only:: html

  .. image:: /auto_examples/02_encoding/images/thumb/sphx_glr_plot_01_cartesian_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_02_encoding_plot_01_cartesian.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">A Cartesian encoding and its adjoint</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="To be written: a radial trajectory and linop.NUFFT, checked against the explicit Fourier sum.">

.. only:: html

  .. image:: /auto_examples/02_encoding/images/thumb/sphx_glr_optional_02_noncartesian_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_02_encoding_optional_02_noncartesian.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Radial encoding and a direct Fourier reference</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="To be written: known shot phases and interleaved phase-encode masks as BART operators, solved with optim.CG.">

.. only:: html

  .. image:: /auto_examples/02_encoding/images/thumb/sphx_glr_plot_03_epi_shots_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_02_encoding_plot_03_epi_shots.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">An idealized multi-shot EPI encoding</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="To be written: a hybrid-space wave model with readout padding and a temporal basis, assembled from operators.">

.. only:: html

  .. image:: /auto_examples/02_encoding/images/thumb/sphx_glr_plot_04_wave_subspace_thumb.png
    :alt:

  :ref:`sphx_glr_auto_examples_02_encoding_plot_04_wave_subspace.py`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Wave encoding and temporal subspaces</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/02_encoding/plot_01_cartesian
   /auto_examples/02_encoding/optional_02_noncartesian
   /auto_examples/02_encoding/plot_03_epi_shots
   /auto_examples/02_encoding/plot_04_wave_subspace