Tomographic reconstruction from Poisson distributed data: a fast and convergent EM-TV dual approach

This paper focuses on tomographic reconstruction for nuclear medicine imaging, where the classical approach consists to maximize the likelihood of Poisson distributed data using the iterative Expectation Maximization algorithm. In this context and when the quantity of acquired data is low and produces low signal-to-noise ratio in the images, a step forward consists to incorporate a total variation a priori on the solution into a MAP-EM formulation. The novelty of this paper is to propose a convergent and efficient numerical scheme to compute the MAP-EM optimizer, based on a splitting approach which alternates an EM step and a dual-TV-minimization step. The main theoretical result is the proof of stability and convergence of this scheme. Moreover, we also present some numerical experiments in which our algorithm appears at least as efficient and accurate as some other reference algorithms from the literature