Recent Advances on Compressed Sensing and Matrix Completion
Ming-Jun Lai, professor
Department of Mathematics, University of Georgia
This talk starts with a motivation on how to recover a low-rank matrix from a small number of its linear measurements, e.g., a subset of its entries. As such a problem shares many common features with the recent study of recovering sparse vectors in compressed sensing; Lai will give a quick review of some most updated research results on sparse vector recovery and matrix completion. The discussion will move on to an explanation of an unconstrained Lq minimization approach and an iteratively reweighted algorithm for recovering sparse vectors as well as for recovering low-rank matrices. A convergence analysis of these iterative algorithms will be given. The talk will end with a presentation of some numerical results for recovering images from their random sampling entries without and with noises.
Ming-Jun Lai is a full professor of Department of Mathematics at the University of Georgia. He received his B.S. from Hangzhou University, China, in 1982 and his Ph.D. from Texas A&M University in 1989. After his Ph.D., he was an instructor at University of Utah, Salt Lake City during 1989-1992. He became an assistant professor at University of Georgia in 1992. Then he was promoted to associate professor in 1995. He has been a full professor since 2000. He has several specializations: approximation theory, compressed sensing, mathematical image analysis, multivariate splines, numerical analysis, numerical solution of partial differential equations, wavelet and frame analysis. He published a monograph on spline functions over triangulations in 2007.
This invited talk is hosted by Jieping Ye.