Abstract. This paper proposes a new adaptive wavelet-based Magnetic Resonance images denoising algorithm. A Rician distribution for background-noise modelling is introduced and a Maximum-Likelihood method for the parameter estimation procedure is used. Further discrimination between edge- and noise-related coefficients is achieved by updating the shrinkage function along consecutive scales and applying spatial constraints. The efficacy of the algorithm is demonstrated on both simulated and real Magnetic Resonance images. The results is shown to be promising and outperform other denoising approaches.