Compressed sensing refers to the reconstruction of high-dimensional but low-complexity objects from a limited number of measurements. Examples include the recovery of high-dimensional but sparse vectors, and the recovery of high-dimensional but low-rank matrices, which includes the so-called partial realization problem in linear control theory. Much of the work to date focuses on probabilistic methods, which are CPU-intensive and have high computational complexity. In contrast, deterministic methods are far faster in execution and more efficient in terms of storage. Moreover, deterministic methods draw from many branches of mathematics, including graph theory and algebraic coding theory. In this talk a brief overview will be given of such recent developments.
Mathukumalli Vidyasagar received his B.S., M.S. and Ph.D. degrees from the University of Wisconsin in 1965, 1967, and 1969. During his nearly fifty-year career, he has worked in a number of research areas including control theory, robotics, statistical learning theory, computational cancer biology, and most recently, compressed sensing. He has received a number of awards in recognition of his research contributions, including the IEEE Technical Field Award in Control Systems, and Fellowship of The Royal Society, the world's oldest scientific society.