Jensen divergence based SPD matrix means and applications

Author

Nielsen, Frank and Liu, Meizhu and Ye, Xiaojing and Vemuri, Baba C.

Abstract

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.