In this paper, we present a new formulation for recovering the fiber tract geometry within a voxel from diffusion weighted MRI data, in the presence of single or multiple neuronal fibers. To this end, we define a discrete set of Diffusion Basis Functions. The intra-voxel information is recovered at voxels containing fiber crossings or bifurcations via the use of a linear combination of the above mentioned base functions. Then, the parametric representation of the intra-voxel fiber geometry is a discrete mixture of Gaussians. Our synthetic experiments depict several advantages by using this discrete schema: the approach uses a small number of diffusion weighted images (23) and relatively small b values (1250 s/mm 2), i.e., the intra-voxel information can be inferred at a fraction of the acquisition time required for datasets involving a large number of diffusion gradient orientations. Moreover our method is robust in the presence of more than 2 fibers within a voxel, improving the stateof-the-art of such parametric models. We present two algorithmic solutions to our formulation: by solving a linear program or by minimizing a quadratic cost function (both with non-negativity constraints). Such minimizations are efficiently achieved with standard iterative deterministic algorithms. Finally, we present results of applying the algorithms to synthetic as well as real data.