.. _sphx_glr_auto_examples_05_transmission:

Transmission and joint activity/attenuation (MLAA) examples
-----------------------------------------------------------

Reconstruction of the attenuation image from transmission data using the exact
Poisson model (no log-linearisation) with a strictly positive scatter
background: MLTR and separable paraboloidal surrogates (SPS), their
ordered-subset and SVRG variants, and penalised transmission reconstruction
(MAPTR) with an edge-preserving prior.  The final example extends these ideas to
joint activity-and-attenuation estimation (MLAA) from a single TOF emission scan.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

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

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example reconstructs a linear attenuation image \mu from transmission data using the exact Poisson model (no log-linearisation into a weighted least squares problem) including a strictly positive, smooth scatter background s with known mean:">

.. only:: html

  .. image:: /auto_examples/05_transmission/images/thumb/sphx_glr_00_mltr_sps_thumb.png
    :alt:

  :doc:`/auto_examples/05_transmission/00_mltr_sps`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Transmission reconstruction: MLTR, SPS and L-BFGS-B</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example accelerates the transmission MLTR reconstruction of 00_mltr_sps.py with subset-based algorithms.  The model is the exact transmission Poisson likelihood with a strictly positive, smooth scatter background s of known mean,">

.. only:: html

  .. image:: /auto_examples/05_transmission/images/thumb/sphx_glr_01_os_mltr_svrg_thumb.png
    :alt:

  :doc:`/auto_examples/05_transmission/01_os_mltr_svrg`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Accelerating MLTR with ordered subsets (OS-MLTR) and SVRG</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="This example adds an edge-preserving smoothing prior to the ordered-subset transmission reconstruction of 01_os_mltr_svrg.py (MAPTR -- maximum a posteriori transmission reconstruction).  We now minimise the penalised objective">

.. only:: html

  .. image:: /auto_examples/05_transmission/images/thumb/sphx_glr_02_run_maptr_thumb.png
    :alt:

  :doc:`/auto_examples/05_transmission/02_run_maptr`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Penalised transmission reconstruction (MAPTR) with an edge-preserving prior</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Maximum Likelihood Activity and Attenuation (MLAA) jointly estimates the activity image \lambda and the attenuation image \mu from a single (TOF) emission scan, without a separate transmission/CT measurement.  The TOF emission model is">

.. only:: html

  .. image:: /auto_examples/05_transmission/images/thumb/sphx_glr_03_mlaa_thumb.png
    :alt:

  :doc:`/auto_examples/05_transmission/03_mlaa`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Joint activity and attenuation reconstruction (MLAA) for TOF PET</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /auto_examples/05_transmission/00_mltr_sps
   /auto_examples/05_transmission/01_os_mltr_svrg
   /auto_examples/05_transmission/02_run_maptr
   /auto_examples/05_transmission/03_mlaa