Insights into the Stable Recovery of Sparse Solutions

Free and open to the public



Abstract:

The problem of sparse signal recovery has received much attention recently with the development of compressed sensing. In this talk, we will examine the problem of stable recovery of sparse solutions in noisy environments. irst we will briefly review algorithms for sparse signal recovery and discuss the connection between l1 minimization and support recovery of sparse signals to provide context. We then establish a connection between the sparse signal recovery problem and wireless communication models in network information theory. We will show that the stable recovery of a sparse solution with a single measurement vector (SMV) can be viewed as decoding competing users simultaneously transmitting messages through a Multiple Access Channel (MAC) at the same rate. With multiple measurement vectors (MMV), we relate the inverse problem to the wireless communication scenario with a Multiple-Input Multiple Output (MIMO) channel. In each case, based on the connection established between the two domains, we will leverage channel capacity results to shed light on the fundamental limits of any algorithm to stably recover sparse solutions in the presence of noise.



About the Speaker:

Bhaskar D. Rao received the B.Tech. degree in electronics and electrical communication engineering from the Indian Institute of Technology, Kharagpur, India, and the M.S. and Ph.D. degrees from the University of Southern California, Los Angeles, in 1981 and 1983, respectively. Since 1983, he has been with the University of California at San Diego, La Jolla, where he is currently a professor with the Electrical and Computer Engineering Department. His interests are in the areas of digital signal processing, estimation theory, and optimization theory, with applications to digital communications, speech signal processing, and human-computer interactions.He is the holder of the Ericsson endowed chair in Wireless Access Networks and is the director of the Center for Wireless Communications. His research group has received several paper awards. Recently, a paper he co-authored with B. Song and R. Cruz received the 2008 Stephen O. Rice Prize Paper Award in the Field of Communications Systems and a paper he co-authored with S. Shivappa and M. Trivedi received the best paper award at AVSS 2008. He was elected to the fellow grade in 2000 for his contributions in high resolution spectral estimation.