Spherical finite rate of innovation theory for the recovery of fiber orientations

In this paper, we investigate the reconstruction of a signal defined as the sum of orientations from samples taken with a kernel defined on the 3D rotation group. A potential application is the recovery of fiber orientations in diffusion magnetic resonance imaging. We propose an exact reconstruction algorithm based on the finite rate of innovation theory that makes use of the spherical harmonics representation of the signal. The number of measurements needed for perfect recovery, which may be as low as 3K, depends only on the number of orientations and the bandwidth of the kernel used. Furthermore, the angular resolution of our method does not depend on the number of available measurements. We illustrate the performance of the algorithm using several simulations.