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

Article; Early Access

关键词: IMAGE-RECONSTRUCTION;    EMISSION TOMOGRAPHY;    MAXIMUM-LIKELIHOOD;    ORDERED SUBSETS;    ALGORITHM;    NOISE;   

DOI  :  10.1007/s11075-023-01517-w

来源: SCIE

【 摘 要 】

This paper focuses on tomographic reconstruction for nuclear medicine imaging, where a 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 prior on the solution into a MAP-EM formulation. This prior is not differentiable. The novelty of the paper is to propose a convergent and efficient numerical scheme to compute the MAP-EM optimizer, alternating regular maximum likelihood maximization steps and TV-denoising solved using the convex-duality principle of Fenchel-Rockafellar. The main theoretical result is the proof of stability and convergence of this scheme. We also present some numerical experiments where we compare the proposed algorithm with some other algorithms from the literature.

【 授权许可】

Free