
Sparse Representation in Highly Coherent Dictionary by Minimizing Difference of L1 and L2
Tue, Mar 25, 2014 @ 03:00 PM  04:00 PM
Ming Hsieh Department of Electrical Engineering
Conferences, Lectures, & Seminars
Speaker: Prof. Jack Xin, University of California, Irvine
Talk Title: Sparse Representation in Highly Coherent Dictionary by Minimizing Difference of L1 and L2
Series: Medical Imaging Seminar Series
Abstract: Overcomplete bases appear in human visual and auditory systems and related mathematical constructions such as Gabor frames and Gammatone filters. Though one gains robustness and resolution, finding an optimal compact representation requires minimization of sparsity or L0. The L1 norm is an effective convex proxy that works very well when dictionary elements (basis vectors) are incoherent enough. However, it may fail when some of the basis vectors are nearly aligned or degeneracy appears (loss of uniqueness of minimizer). We introduce a Lipschitz continuous nonconvex alternative, the difference of L1 and L2 norms, and show its analytical and numerical properties for sparse recovery in highly coherent dictionaries. We present the difference of convex algorithms, their convergence and enhancement by sparsity driven simulated annealing strategies. Applications include oversampled discrete cosine transform, optical spectroscopy, image denoising and reconstruction.
Biography: ack Xin received his B.S in computational mathematics at Peking University in 1985, and Ph.D. in applied mathematics at New York University in 1990. He was a postdoctoral fellow at Berkeley and Princeton in 1991 and 1992. He was assistant and associate professor of mathematics at the University of Arizona from 1991 to 1999. He was a professor of mathematics from 1999 to 2005 at the University of Texas at Austin. He has been a professor of mathematics in the Department of Mathematics, Center for Hearing Research, Institute for Mathematical Behavioral Sciences, and Center for Mathematical and Computational Biology at UC Irvine since 2005. He is a fellow of the Guggenheim Foundation and the American Mathematical Society. His research interests include applied analysis and computation in nonlinear and multiscale problems, mathematical modeling and signal processing. He authored two Springer books and is involved in undergraduate research training and mentoring such as the iCAMP funded by the NSF.
Host: Hosted By Dr. Angel Pineda
Location: Hughes Aircraft Electrical Engineering Center (EEB)  132
Audiences: Everyone Is Invited
Posted By: Talyia Veal