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Diffusion weighted magnetic resonance images allows one to infer white matter axon fiber orientations. Nowadays it is possible to estimate intra-voxel orientations at voxels where fibers cross or split. Though, the recovered orientations could be prone to error because of low signal to noise ratio, the complex fiber structure and/or reduced number of measurements. Spatial regularization can improve the estimations but it must be done carefully such that real information is not removed and false orientations are not introduced. In this work we propose a robust method for regularizing local multi-fiber estimations given by the Diffusion Basis Function method. Our method is based on a robust outlier rejection framework which integrates data while preserves important local information. Additionally, our method constrains the solution orientation-space within a voxel by using the diffusion tensor diffusivity profile as prior information. Our experiments using both in vivo and realistic synthetic data demonstrate the advantage of using the proposed approach.