Nonnegative ODF estimation via optimal constraint selection

We consider the problem of estimating a nonnegative orientation distribution function (ODF) from high angular resolution diffusion images. Since enforcing nonnegativity of the ODF for all directions on the sphere leads to an optimization problem with infinitely many constraints, prior work cannot guarantee the nonnegativity of the estimated ODF. The first contribution of this paper is to show that, under certain conditions, a single constraint is sufficient to guarantee the nonnegativity of the estimated ODF in all directions. Otherwise, when these conditions are violated, we propose an iterative algorithm that enforces one constraint at a time and is guaranteed to converge to the optimal nonnegative ODF. Experiments on synthetic and real data show that our methods produce more accurate solutions than prior work at a reduced runtime.