ML-EM algorithm with known continuous movement model
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.
Cite
@article{arxiv.2004.02444,
title = {ML-EM algorithm with known continuous movement model},
author = {Camille Pouchol and Olivier Verdier},
journal= {arXiv preprint arXiv:2004.02444},
year = {2021}
}