Denoising diffusion-weighted MR magnitude image sequences using low rank and edge constraints

This paper addresses the denoising problem associated with diffusion MR imaging. Building on previous approaches to this problem, this paper presents a new method for joint denoising of a sequence of diffusion-weighted (DW) magnitude images. The proposed method uses a maximum a posteriori (MAP) estimation formulation to incorporate a Rician likelihood (for modeling the noisy magnitude data), a low rank model (for the DW image sequences) and a spatial prior (for imposing joint edge constraints). An efficient algorithm to solve the associated optimization problem is also described. The proposed method has been evaluated using both simulated and experimental diffusion tensor imaging (DTI) data, which yields very encouraging results both qualitatively and quantitatively.