Statistical Model and ML-EM Algorithm for Emission Tomography with Known Movement

Abstract

In positron emission tomography, movement leads to blurry reconstructions when not accounted for. Whether known a priori or estimated jointly to reconstruction, motion models are increasingly defined in continuum rather that in discrete, for example by means of diffeomorphisms. The present work provides both a statistical and functional analytic framework suitable for handling such models. It is based on time-space Poisson point processes as well as regarding images as measures, and allows to compute the maximum likelihood problem for line-of-response data with a known movement model. Solving the resulting optimisation problem, we derive an maximum likelihood expectation maximisation (ML-EM)-type algorithm which recovers the classical ML-EM algorithm as a particular case for a static phantom. The algorithm is proved to be monotone and convergent in the low-noise regime. Simulations confirm that it correctly removes the blur that would have occurred if movement were neglected.

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Correspondence to Camille Pouchol.

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Pouchol, C., Verdier, O. Statistical Model and ML-EM Algorithm for Emission Tomography with Known Movement. J Math Imaging Vis (2021). https://doi.org/10.1007/s10851-021-01021-7

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Keywords

  • Maximum likelihood expectation maximisation
  • Positron emission tomography
  • Diffeomorphism
  • Poisson point process