On the Remarkable Efficiency of SMART

Max Kahl, Stefania Petra, Christoph Schnörr, Gabriele Steidl, Matthias Zisler

Abstract: We consider the problem of minimizing the Kullback-Leibler divergence between two unnormalised positive measures, where the first measure lies in a finitely generated convex cone. We identify SMART (simultaneous multiplicative algebraic reconstruction technique) as a Riemannian gradient descent on the parameter manifold of the Poisson distribution. By comparing SMART to recent acceleration techniques from convex optimization that rely on Bregman geometry and first-order information, we demonstrate that it solves this problem very efficiently.