Majorization-Minimization Algorithms for Maximum Likelihood Estimation of Magnetic Resonance Images

This paper addresses maximum likelihood estimation of images corrupted by a Rician noise, with the aim to propose an efficient optimization method. The application example is the restoration of magnetic resonance images. Starting from the fact that the criterion to minimize is non-convex but unimodal, the main contribution of this work is to propose an optimization scheme based on the majorization-minimization framework after introducing a variable change allowing to get a strictly convex criterion. The resulting descent algorithm is compared to the classical MM descent algorithm and its performances are assessed using synthetic and real MR images. Finally, by combining these two MM algorithms, two optimization strategies are proposed to improve the numerical efficiency of the image restoration for any signal-to-noise ratio.