"Recent Developments in Compressed Sensing"
Speaker: Dr. Mathukumalli Vidyasagar
Abstract: At the simplest level, compressed sensing refers to the problem of finding sparse solutions to large, under-determined linear equations. More generally, compressed sensing refers to finding sparse solutions to convex optimisation problems with nonunique solutions. A great deal of progress has been realised during the past dozen years, but a "second wave" of progress began about two years ago. Originally methods for compressed sensing were based on using randomly generated measurement matrices. However, these are now known to be extremely inefficient for realistic-sized problems. Methods based on deterministically constructed measurement matrices can be up to a thousand times faster. A recent trend is the use of methods from algebraic coding, specifically expander graphs, for this purpose. Current work by the speaker and one of his students has resulted in a new algorithm that is again one hundred times faster than the fastest existing method. In this talk, all of the major known methods will be reviewed along with their strengths and weaknesses, and some open problems for future research will be indicated.
Biography: M. Vidyasagar was born in Guntur, India on September 29, 1947. He received all of his degrees at the University of Wisconsin in Madison, including the Ph.D. in Electrical Engineering in 1969. He has taught at Marquette University (1969-70), Concordia University (1970-80), and the University of Waterloo (1989-89). In 1989 he returned to his native India to set up the Centre for Artificial Intelligence and Robotics under the Government of India, and held the post of Director until 2000. Then he joined Tata Consultancy Services, then and now India's largest software company, as an Executive Vice President in charge of Advanced Technology. He retired from TCS in 2009 and joined the University of Texas at Dallas, where he was the Founding Chair of the Bioengineering Department, a position he laid down in 2013. He has received a number of awards in recognition of his research, including the IEEE Technical Field Award, the ASME Rufus Oldenburger Medal, and Fellowship in The Royal Society of London, the world's oldest scientific society. His current research interests are in compressed sensing, and sparsity-based methods in control systems. He is the author of 11 books (with No. 12 almost complete), and about 150 journal articles.