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 MMdescent algorithm and its performances are assessed using synthetic and real MR images.