Jensen divergence based SPD matrix means and applications

Finding mean of matrices becomes increasingly important in modern signal processing problems that involve matrix-valued images. In this paper, we define the mean for a set of symmetric positive definite (SPD) matrices based on information-theoretic divergences as the unique minimizer of the averaged divergences, and compare it with the means computed using the Rieman-nian and Log-Euclidean metrics. For the class of divergences induced by the convexity gap of a matrix functional, we present a fast iterative concave-convex optimization scheme with guaranteed convergence to efficiently approximate those divergence-based means.