.. _sphx_glr_auto_examples_03_algorithms:

Emission tomography reconstruction algorithms (sinogram data)
-------------------------------------------------------------

A tour of reconstruction algorithms for the (regularised) Poisson problem,
all built on the data-fidelity and prior objects in ``parallelproj.functions``.
Start with the MLEM / OSEM / SVRG convergence comparison, then explore the
stochastic-gradient variants, PDHG / SPDHG with edge-preserving priors,
filtered back projection, De Pierro's MAP-EM, the effect of TOF on variance,
and out-of-core (memory-mapped) OSEM.


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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 logcosh 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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  .. image:: /auto_examples/03_algorithms/images/thumb/sphx_glr_05_run_tof_variance_thumb.png
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  :doc:`/auto_examples/03_algorithms/05_run_tof_variance`

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      <div class="sphx-glr-thumbnail-title">TOF vs non-TOF: variance reduction in a uniform cylinder</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Demonstrates a memory-efficient OSEM variant in which full TOF sinograms are never held in RAM simultaneously.  Instead they are stored on disk in a subset-contiguous binary layout via numpy.memmap, and only one subset&#x27;s data is loaded at a time during each OSEM update.">

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  .. image:: /auto_examples/03_algorithms/images/thumb/sphx_glr_06_run_osem_memmap_thumb.png
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  :doc:`/auto_examples/03_algorithms/06_run_osem_memmap`

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      <div class="sphx-glr-thumbnail-title">RAM-efficient OSEM with disk-backed TOF sinograms</div>
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    <div class="sphx-glr-thumbcontainer" tooltip=".NegPoissonLogL offers two evaluation modes:">

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  .. image:: /auto_examples/03_algorithms/images/thumb/sphx_glr_07_run_mlem_negpoissonlogl_modes_thumb.png
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  :doc:`/auto_examples/03_algorithms/07_run_mlem_negpoissonlogl_modes`

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      <div class="sphx-glr-thumbnail-title">Exact vs. "safe epsilon" mode of the negative Poisson log-likelihood</div>
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.. toctree::
   :hidden:

   /auto_examples/03_algorithms/00_run_mlem_osem_svrg
   /auto_examples/03_algorithms/01_run_sgd_svrg
   /auto_examples/03_algorithms/02_run_pdhg_spdhg_dtv
   /auto_examples/03_algorithms/03_run_fbp
   /auto_examples/03_algorithms/04_run_depierro
   /auto_examples/03_algorithms/05_run_tof_variance
   /auto_examples/03_algorithms/06_run_osem_memmap
   /auto_examples/03_algorithms/07_run_mlem_negpoissonlogl_modes