featuring Ming-Jun Lai, Professor, Department of Mathematics at University of Georgia
hosted by Jieping Ye
Monday, February 4th 2013, 10:30-11:30am
“Some Recent Advances on Compressed Sensing and Matrix Completion”
Abstract: I will start 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; I shall give a quick review of some most updated research results on sparse vector recovery and matrix completion. Then I will explain 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. Finally, I shall present some numerical results for recovering images from their random sampling entries without and with noises.
Bio: Ming-Jun Lai is a full professor of Department of mathematics, University of Georgia, Athens, GA 30602. 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.