This paper deals with the denoising of SAR images. We draw our inspiration from the modeling of multiplicative speckle noise. By using a MAP estimator, we propose a functional whose minimizer corresponds to the denoised image we want to recover. Although the functional is not convex, we prove the existence of a minimizer. Then we study a semi-discrete version of the associated evolution problem, for which we derive existence and uniqueness results for the solution. We prove the convergence of this semi-discrete scheme. We conclude with some numerical results.