Estimation Under a Non-Convex Rank Constraint: A Signal and Image Processing Case Study

Date(s):

Location:
Jacobs Hall, Room 2515, Jacobs School of Engineering, 9500 Gilman Dr, La Jolla, San Diego, California 92093

Sponsored By:
Professor Piya Pal

Speaker(s):
Dr. Vishal Monga
Dr. Vishal Monga

Abstract:

This talk will cover two seemingly disparate problems under the umbrella of an exact rank constraint: one in statistical and radar signal processing focusing on the estimation of structured covariance matrices and the other a key image processing/vision task called robust alignment of images. In the first part, we look at the regularized maximum likelihood (ML) estimation of structured covariance matrices (SCM) that arise in radar space time adaptive processing. The underlying physical model enables knowledge of the rank of the semi-definite component of the SCM which is a key constraint to incorporate. We will show that despite the presence of the challenging non-convex rank constraint, a closed form result that achieves the global optima is indeed possible. We also investigate scenarios where the knowledge of the rank may be imprecise and use expected likelihood approaches to determine the rank and other constraints of interest. Several uniqueness results in determining imprecise constraints are provided in this context. The second part of the talk sets up a key open problem in computer vision and image processing – that of batch aligning images. Technically, we formulate the alignment problem as rank-1 and sparse matrix decomposition over transformed images, and develop an efficient algorithm for solving this challenging nonconvex optimization problem. The algorithm reduces to a sequence of sub-problems, where we analytically establish exact recovery conditions, provide convergence and optimality guarantees. From a practical viewpoint, we demonstrate via results that an exact vs. approximate capture of the rank helps improve results over state of the art image alignment approaches based on robust PCA and other competing methods.

Speaker Bio:
Prof. Vishal Monga has been on the EE faculty at Penn State since Fall 2009, where he is currently a tenured Associate Professor.
From Oct 2005-July 2009 he was an imaging scientist with Xerox Research Labs. He has also been a visiting researcher at Microsoft
Research in Redmond, WA and a visiting faculty at the University of Rochester. Prior to that, he received his PhDEE from the University
of Texas at Austin in August 2005. Prof. Monga is a recipient of the National Science Foundation CAREER award. For his educational
efforts, Dr. Monga received the 2016 Joel and Ruth Spira Teaching Excellence award. He is an Associate Editor for the IEEE Transactions
on Image Processing and IEEE Signal Processing Letters, as well as an elected member of the IEEE Image, Video and Multidimensional
Signal Processing (IVMSP) Technical Committee (2017-2019). Dr. Monga holds 45 granted US Patents.

Contact:
Bethany Carson
Email: bacarson@eng.ucsd.edu
Phone: 858-822-6347