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Title: Compressive sensing of low-rank matrices

Speaker: Kiryung Lee

Abstract: Compressed sensing addresses the recovery of a sparse vector from a small number of linear measurements. The inverse problem that arises in compressed sensing is ill-posed, but with a sparse prior the solution can be unique and computed in polynomial time. Recently, the success in solving the problem for the vector case has been extended to the matrix case.

For the matrix problem, a low-rank prior plays a similar role to that of the sparse prior. Many applications in practice can be formulated as a linear inverse problem where the linear system is underdetermined but the solution has low-rank. These include the collaborative filtering, sensor network localization, and low-order system identification. In this survey, we study the analogy and difference between the vector problem and the matrix problem.

The inverse problem can be formulated as two different optimization problems and there are several efficient and/or guaranteed algorithms for their solution. The performance guarantees of the different algorithms will be investigated and compared. Finally, related problems such as robust principal component analysis and sparse principal component analysis will be mentioned.

Speaker Bio

Kiryung Lee received the B.S. degree in electrical engineering and the M.S. degree in electrical engineering and computer science from Seoul National University, Seoul, Korea, in 2000 and 2002, respectively. From 2002 to 2004, he was a member of engineering staff at the Electronic Telecommunications Research Institute, Daejeon, Korea. From 2004 to 2006, he was a research engineer at LG Electronics, Seoul, Korea. Currently, he is working toward the Ph.D. in electrical and computer engineering at University of Illinois at Urbana-Champaign. His advisor is Prof. Yoram Bresler and his main research interests are compressed sensing and matrix completion.