Fiber orientation distribution from non-negative sparse recovery

We revisit the theory of spherical deconvolution and propose a new fiber orientation distribution (FOD) model that can efficiently reconstruct extremely narrow fiber-crossings from limited number of acquisitions. First, we show how to physically model fiber-orientations as rank-1 tensors. Then, we parameterize the FODs with tensors that are decomposable into non-negative sums of rank-1 tensors and finally, we propose a non-negative sparse recovery scheme to estimate FODs of any tensor order from limited acquisitions. Our method features three important advantages: (1) it estimates non-negative FODs, (2) it estimates the number of fiber-compartments, which need not be predefined and (3) it computes the fiber-directions directly, rendering maxima detection superfluous. We test for various SNRs on synthetic, phantom and real data and find our method accurate and robust to signal-noise: fibers crossing up to 23° are recovered from just 21 acquisitions. This opens new and exciting perspectives in diffusion MRI (dMRI), where our improved characterization of the FOD can be of great help for applications such as tractography.