Abstract. This paper introduces an outlier rejection and signal reconstruction method for high angular resolution diffusion weighted imaging. The approach is based on the thresholding of Laplacian measurements over the sphere of the apparent diffusion coefficient profiles defined for a given set of gradient directions. Exemplary results are presented. 1 Motivation and Background Diffusion weighted imaging (DWI) has become an increasingly popular imaging technique in neuroscience as it provides insight into the architecture of brain white matter. The imaging technology is ever improving and high angular and spatial resolutions are now possible. However, acquiring many gradient directions and small voxel sizes requires fast imaging techniques such as Echo Planar Imaging (EPI), and these are usually prone to various artifacts and often have low signal to noise ratios. The most common artifacts associated with diffusion EPI are susceptibility artifacts and geometric distortions due to grad...