Jensen divergence-based means of SPD matrices

Author

Nielsen, Frank and Liu, Meizhu and Vemuri, Baba C

Abstract

Computing matrix means is becoming more and more important in modern signal processing involving processing of matrix-valued images. In this communication, we define the mean for a set of symmetric positive definite (SPD) matrices with respect to information-theoretic divergences as the unique minimizer of the average divergence, and compare it with the means computed using the Riemannian and Log-Euclidean metrics respectively. 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.