A stable, accurate and robust-to-noise general framework for the estimation of the intra-voxel axial and radial diffusivity parameters for diffusion-weighted magnetic resonance imaging is presented. The method estimates the diffusion profiles at multi-fiber voxels, improving the estimation of the intra-voxel geometry at challenging microstructure configurations. It naturally constrains the sparsity on the recovered solutions and exploits the spatial redundancy of the axon packs. A useful evaluation metric is proposed: it combines the information of the success rate of the number of bundles and their angular error. A new evaluation method for the in-vivo estimations on large datasets is also proposed.