The proposal attempts to model more properly the intra-voxel information from DW-MRI signals in order to obtain tissue diffusion properties in white matter. The method is based on Sparse and Adaptive Diffusion Dictionary (SADD) strategy that dynamically adapts a dictionary of diffusion functions by changing size and orientation of the diffusion tensors. In ISMRM2015, we demonstrated that our accelerated version (LASADD) reduces complexity and computational cost wrt SADD with similar quality results. This work extends the idea of LASADD to three compartments (intracellular, extracellular and cerebrospinal fluid) and presents experimental results depicting the computed properties about the diffusion structure.