A deconvolution approach is presented to solve fiber crossing in diffusion magnetic resonance imaging. In order to provide a direct physical interpretation of the signal generation process, we started from the classical multicompartment model and rewrote this in terms of a convolution process, identifying a significant scalar parameter alpha to characterize the physical system response. Deconvolution is performed by a modified version of the Richardson-Lucy algorithm. Simulations show the ability of this method to correctly separate fiber crossing, even in the presence of noisy data, with lower signal-to-noise ratio, and imprecision in the impulse response function imposed during deconvolution. The in vivo data confirms the efficacy of this method to resolve fiber crossing in real complex brain structures. These results suggest the usefulness of our approach in fiber tracking or connectivity studies