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Examples
========


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PET scanner and sinogram geometry examples
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    <div class="sphx-glr-thumbcontainer" tooltip="This example shows how to create and visualize PET scanners where the LOR endpoints can be modeled as a stack of regular polygons.">

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  .. image:: /auto_examples/01_pet_geometry/images/thumb/sphx_glr_01_run_regular_polygon_pet_scanner_thumb.png
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  :doc:`/auto_examples/01_pet_geometry/01_run_regular_polygon_pet_scanner`

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      <div class="sphx-glr-thumbnail-title">Regular polygon PET scanner geometry</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In a scanner with &quot;cylindrical symmetry&quot;, all possible lines of response (LORs) between two LOR endpoints can be sorted into a sinogram containing a radial, view and plane dimension. This example shows how this can be done using the .RegularPolygonPETLORDescriptor">

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  .. image:: /auto_examples/01_pet_geometry/images/thumb/sphx_glr_02_run_regular_polygon_pet_sino_thumb.png
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  :doc:`/auto_examples/01_pet_geometry/02_run_regular_polygon_pet_sino`

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      <div class="sphx-glr-thumbnail-title">LOR descriptors and sinogram definition</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we show how to setup a generic PET scanner consisting of multiple block modules where each block module consists of a regular grid of LOR endpoints. We also show how to define a LOR descriptor for this geometry using a description of which block pairs are in coincidence.">

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  .. image:: /auto_examples/01_pet_geometry/images/thumb/sphx_glr_03_run_block_scanner_thumb.png
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  :doc:`/auto_examples/01_pet_geometry/03_run_block_scanner`

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      <div class="sphx-glr-thumbnail-title">Modularized (block) PET scanner geometry</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="A Michelogram is a diagram of which ring pairs (s, e) form valid coincidences in a cylindrical PET scanner, and how they are grouped into sinogram planes under Siemens / STIR axial compression conventions.  Ring pairs are sorted by segment (a function of the ring difference rd = e - s) and, within each segment, by axial midpoint s + e.">

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  .. image:: /auto_examples/01_pet_geometry/images/thumb/sphx_glr_04_run_michelogram_and_compression_thumb.png
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  :doc:`/auto_examples/01_pet_geometry/04_run_michelogram_and_compression`

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      <div class="sphx-glr-thumbnail-title">Michelograms and axial sinogram compression</div>
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PET sinogram and listmode projector examples
--------------------------------------------


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    <div class="sphx-glr-thumbcontainer" tooltip="In this example we will show how to setup and use a PET sinogram projector consisting of a geometrical forward projector (Joseph&#x27;s method), a resolution model and a correction for attenuation.">

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  .. image:: /auto_examples/02_pet_sinogram_projections/images/thumb/sphx_glr_01_run_pet_non_tof_sinogram_projector_thumb.png
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  :doc:`/auto_examples/02_pet_sinogram_projections/01_run_pet_non_tof_sinogram_projector`

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      <div class="sphx-glr-thumbnail-title">PET non-TOF sinogram projector</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example we will show how to setup and use a TOF PET sinogram projector consisting of a geometrical TOF forward projector (Joseph&#x27;s method), a resolution model and a correction for attenuation.">

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  .. image:: /auto_examples/02_pet_sinogram_projections/images/thumb/sphx_glr_02_run_pet_tof_sinogram_projector_thumb.png
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  :doc:`/auto_examples/02_pet_sinogram_projections/02_run_pet_tof_sinogram_projector`

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      <div class="sphx-glr-thumbnail-title">PET TOF sinogram projector</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we show how to perform non-TOF and TOF projections using a PET scanner consisting of multiple block modules where each block module consists of a regular grid of LOR endpoints.">

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  .. image:: /auto_examples/02_pet_sinogram_projections/images/thumb/sphx_glr_03_run_equalblock_projector_thumb.png
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  :doc:`/auto_examples/02_pet_sinogram_projections/03_run_equalblock_projector`

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      <div class="sphx-glr-thumbnail-title">Non-TOF and TOF projections using a modularized (block) PET scanner geometry</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example we show how to setup and use a PET listmode projector for both non-TOF and TOF acquisitions, including geometrical forward projection in listmode, image-based resolution model, and a listmode attenuation model.">

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  .. image:: /auto_examples/02_pet_sinogram_projections/images/thumb/sphx_glr_04_run_pet_listmode_projector_thumb.png
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  :doc:`/auto_examples/02_pet_sinogram_projections/04_run_pet_listmode_projector`

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      <div class="sphx-glr-thumbnail-title">PET listmode projector (non-TOF and TOF)</div>
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Iterative algorithm examples
----------------------------


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    <div class="sphx-glr-thumbcontainer" tooltip="This example compares the convergence speed (per epoch) of three algorithms for minimising the negative Poisson log-likelihood">

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  .. image:: /auto_examples/03_algorithms/images/thumb/sphx_glr_00_run_mlem_osem_svrg_thumb.png
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  :doc:`/auto_examples/03_algorithms/00_run_mlem_osem_svrg`

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      <div class="sphx-glr-thumbnail-title">Convergence comparison: MLEM vs OSEM vs SVRG</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example compares the convergence speed (per epoch) of two algorithms for minimising the regularised negative Poisson log-likelihood">

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  .. image:: /auto_examples/03_algorithms/images/thumb/sphx_glr_01_run_sgd_svrg_thumb.png
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  :doc:`/auto_examples/03_algorithms/01_run_sgd_svrg`

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      <div class="sphx-glr-thumbnail-title">Convergence comparison: SGD vs SVRG with quadratic regularization</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the primal-dual hybrid gradient (PDHG) algorithm and its stochastic variant (SPDHG) applied to the regularized PET reconstruction problem">

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  .. image:: /auto_examples/03_algorithms/images/thumb/sphx_glr_02_run_pdhg_spdhg_dtv_thumb.png
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  :doc:`/auto_examples/03_algorithms/02_run_pdhg_spdhg_dtv`

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      <div class="sphx-glr-thumbnail-title">PDHG and SPDHG for PET reconstruction with a directional TV prior</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the run 2D filtered back projection (FBP) on pre-corrected Poisson emission data.">

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  .. image:: /auto_examples/03_algorithms/images/thumb/sphx_glr_03_run_fbp_thumb.png
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  :doc:`/auto_examples/03_algorithms/03_run_fbp`

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      <div class="sphx-glr-thumbnail-title">2D non-TOF filtered back projection (FBP) of Poisson data</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the use of DePierro&#x27;s algorithm to minimize the negative Poisson log-likelihood function combined with a quadratic intensity prior:">

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  .. image:: /auto_examples/03_algorithms/images/thumb/sphx_glr_04_run_depierro_thumb.png
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  :doc:`/auto_examples/03_algorithms/04_run_depierro`

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      <div class="sphx-glr-thumbnail-title">DePierro's algorithm to optimize the Poisson logL with quadratic intensity prior</div>
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Iterative listmode algorithm examples
-------------------------------------


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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how to run MLEM, OSEM, and SVRG using listmode (event-by-event) data, and compares all algorithms with their sinogram equivalents via a convergence plot of the negative Poisson log-likelihood.">

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  .. image:: /auto_examples/04_listmode_algorithms/images/thumb/sphx_glr_00_run_listmode_mlem_osem_svrg_thumb.png
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  :doc:`/auto_examples/04_listmode_algorithms/00_run_listmode_mlem_osem_svrg`

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      <div class="sphx-glr-thumbnail-title">Listmode MLEM, OSEM, and SVRG</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example compares sinogram and listmode variants of SGD and SVRG for minimising the regularised negative Poisson log-likelihood">

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  .. image:: /auto_examples/04_listmode_algorithms/images/thumb/sphx_glr_01_run_listmode_sgd_svrg_thumb.png
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  :doc:`/auto_examples/04_listmode_algorithms/01_run_listmode_sgd_svrg`

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      <div class="sphx-glr-thumbnail-title">Convergence comparison: SGD vs SVRG with regularization (sinogram and listmode)</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates the use of the primal dual hybrid gradient (PDHG) algorithm, the listmode stochastic PDHG (LM-SPDHG) to minimize the negative Poisson log-likelihood function combined with a total variation regularizer:">

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  .. image:: /auto_examples/04_listmode_algorithms/images/thumb/sphx_glr_03_lm_spdhg_thumb.png
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  :doc:`/auto_examples/04_listmode_algorithms/03_lm_spdhg`

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      <div class="sphx-glr-thumbnail-title">PDHG and LM-SPHG to optimize the Poisson logL and total variation</div>
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Custom parallelproj pytorch layer examples
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    <div class="sphx-glr-thumbcontainer" tooltip="In this example, we show how to define a custom pytorch layer that can be used to define a feed forward neural network that includes a parallelproj forward and back backward projections (or any .LinearOperator) that can be used with pytorch&#x27;s autograd engine.">

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  .. image:: /auto_examples/05_torch/images/thumb/sphx_glr_01_run_projection_layer_thumb.png
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  :doc:`/auto_examples/05_torch/01_run_projection_layer`

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      <div class="sphx-glr-thumbnail-title">pytorch parallelproj projection layer</div>
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.. toctree::
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   :includehidden:


   /auto_examples/01_pet_geometry/index.rst
   /auto_examples/02_pet_sinogram_projections/index.rst
   /auto_examples/03_algorithms/index.rst
   /auto_examples/04_listmode_algorithms/index.rst
   /auto_examples/05_torch/index.rst


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      :download:`Download all examples in Python source code: auto_examples_python.zip </auto_examples/auto_examples_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </auto_examples/auto_examples_jupyter.zip>`


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