Basis pursuit based algorithm for intra-voxel recovering information in DW-MRI

In this work, we applied the basis pursuit (BP) methodology for recovering the intra-voxel information in diffusion weighted MR images (DW-MRI). We compare the proposed BP approach with the diffusion basis function estimation (DBFE) algorithm. DBFE approach was previously applied to recover intra-voxel diffusion information in brain DW-MRI. The intra-voxel information is recovered at voxels that contain axon fiber crosses or bifurcations by means of a linear combination of a known diffusion functions. We state the DBFE solution in the signal decomposition context, i.e., the measured DW-MRI signal is decomposed as a linear combination of signals that belongs to a base of diffusion functions (BDF). In such a BDF, each signal is an M-dimensional vector, where each component indicates the water diffusion coefficient in a known three-dimensional orientation. In this work, we analyze and compare the solution given by DBFE method with the BP methodology. The BP methodology is used in order to select the set of base signals (which are taken from a dictionary) that best explain a given arbitrary signal. Moreover, solution strategies used in the BP and DBFE algorithm are compared and discussed. Examples in synthetic and real images are shown in order to demonstrate the performance of the compared methods.