Statistical Image Recovery: A Message-Passing Perspective

Abstract:We consider the problem of recovering an image from "corrupted" outputs of a linear measurement operator, where corruption may occur through additive noise or some component-wise non-linear operation like quantization or phase removal. We describe recent results on "approximate message passing" (AMP) solutions to this problem, which are motivated by the case that the measurement operator is a large random matrix. In particular, we discuss connections between AMP and contemporary convex optimization algorithms, convergence properties of AMP and methods to robustify AMP to non-random matrices, and recent methods to automatically tune the parameters underlying the assumed statistical model. Numerical results for cosparse-analysis compressive imaging and compressive phase retrieval are provided to illustrate the advantages of the AMP methods.Bio:Philip Schniter received B.S. and M.S. in Electrical Engr from the U of I at Urbana-Champaign in 1992 and 1993, respectively, and Ph.D. in Electrical Engr from Cornell in 2000. From 1993 to 1996 he was employed by Tektronix Inc. in Beaverton, OR as a systems engineer. After receiving the Ph.D. degree, he joined the Dept of Electrical/Computer Engr at The Ohio State Univ, Columbus, where he is currently a Professor. In 2008-9 he was a visiting professor at Eurecom, Sophia Antipolis, Fr, and Supélec, Gif-sur-Yvette, Fr. In 2003, Dr. Schniter received the NSF CAREER Award, and 2014 he was elevated to Fellow, IEEE.