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In Positron Emission Tomography, movement leads to blurry reconstructionswhen not accounted for. Whether known a priori or estimated jointly toreconstruction, motion models are increasingly defined in continuum rather thatin discrete, for example by means of diffeomorphisms. The present work providesboth a statistical and functional analytic framework suitable for handling suchmodels. It is based on time-space Poisson point processes as well as regardingimages as measures, and allows to compute the maximum likelihood problem forline-of-response data with a known movement model. Solving the resultingoptimisation problem, we derive an Maximum Likelihood Expectation Maximisation(ML-EM) type algorithm which recovers the classical ML-EM algorithm as aparticular case for a static phantom. The algorithm is proved to be monotoneand convergent in the low-noise regime. Simulations confirm that it correctlyremoves the blur that would have occurred if movement were neglected.

ML-EM algorithm with known continuous movement model