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Spatiotemporal Reconstruction of PET Data

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Spatiotemporal Reconstruction of PET Data. Andrew McLennan. Professor Sir Mike Brady FRS FREng ... Prior: A Spatiotemporal Regularise. Implementation. We ... – PowerPoint PPT presentation

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Title: Spatiotemporal Reconstruction of PET Data


1
Spatiotemporal Reconstruction of PET Data
  • Andrew McLennan

Professor Sir Mike Brady FRS FREng Professor Nick
Trefethen FRS David Schottlander, Siemens
Molecular Imaging
2
What is PET?
  • Positron Emission Tomography (PET) enables
    doctors to look and study non-invasively inside
    the body
  • Detects areas of heightened metabolic activity

3
Positron Emission Tomography
  • Positron emitting tracer compound injected into
    patient
  • Radionuclide decays emitting a high energy
    positron
  • Positron is annihilated by an electron, producing
    two 511 keV photons travelling in opposite
    directions
  • Signal noise caused by
  • Compton scattering
  • Random observations

4
PET Image Reconstruction
  • The 3 main Static PET algorithms
  • Filtered Back Projection (FBP)
  • Maximum a Posteriori (MAP)
  • Ordered Subset Expectation Maximisation (OSEM)
  • Current Dynamic PET ideas arebased around Static
    PET

Wait 45-60mins
20 mins acquisition
Start acquisition immediately
Combine acquisitions
5
Dynamic List-Mode PET
  • We would like to combine the spatial resolution
    of Static PET and temporal resolution of Dynamic
    PET
  • List-mode data records both the detector pair and
    the time of acquisition, avoidingthe need to use
    Sinograms

6
Dynamic List-Mode Reconstruction
  • We assume that both the observed detection data,
    and each voxels emission rate, can be modelled
    using inhomogeneous Poisson process (i.e. Rate
    functions dependent on time)
  • The rate functions of the observed data are then
    linear combinations of the dynamic voxel tracer
    densities
  • Rate functions are parameterise by Cubic B-Spline
    Basis

7
Calculation of each w i j
  • Account for Randoms and Scatter
  • Likelihood function of an inhomogeneous Poisson
    process is
  • Taking Logs and using Bayes Theorem, we penalize
    our objective function so that it includes 3
    smoothing terms
  • Temporal roughness
  • Spatial roughness
  • Penalizes negativity of the rate function

Bayesian Prior A Spatiotemporal Regularise
8
Implementation
  • We choose the B-Spline knotlocations to be
    equally spreadalong the head curve, to
    accountfor the early high concentrations
  • The objective function is strictly concave with a
    global maximum, hence can befound using a
    preconditionedPolak-Ribiere ConjugateGradient
    search method

9
Project Aims
  • Implement the model in a modular fashion
  • Run the program on provided List-Mode data
  • Determine the Phantoms list-mode geometry
  • Analyse the variance and bias for Phantom PET
    data
  • Improving the implementation There is always a
    trade off between accuracy/stability biological
    meaning of the model
  • Implement different basis functions
  • Use more accurate spatial temporal regularizes
  • Compare different optimisation methods
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