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Bilinear Inverse Problems: How much does structure help? (Leverhulme Lecture)

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If you have a question about this talk, please contact Prof. Ramji Venkataramanan.

A number of important inverse problems in signal processing, such as blind deconvolution, matrix factorization, dictionary learning and blind source separation share the common characteristic of being bilinear inverse problems. In such problems, the observation model is a function of two inputs and conditioned on one input being known, the observation is a linear function of the other. We will review important applications and challenges. A key question is that of identifiability: can one unambiguously recover the pair of inputs from the output? We shall consider both deterministic conditions for identifiability as well as probabilistic statements that result in new scaling laws under cone constraints. We provide additional results specific to blind deconvolution and show, surprisingly, that adding the sparsity structural constraint is insufficient for signal identifiability suggesting that other strategies such as coding are necessary to achieve identifiability. However, there is hope that additional structure can help in certain cases. To this end, we discuss a novel strategy that exploits low rank matrix factorization to estimate parameters of a time-varying wireless channel.

BIO: Urbashi Mitra received the B.S. and the M.S. degrees from the University of California at Berkeley and her Ph.D. from Princeton University. She began her academic career at The Ohio State University. Dr. Mitra is currently a Dean’s Professor of Electrical Engineering at the University of Southern California with a courtesy appointment in Computer Science. She is the inaugural Editor-in-Chief for the IEEE Transactions on Molecular, Biological and Multi-scale Communications. She is a member of the IEEE Information Theory Society’s Board of Governors (2002-2007, 2012-2017) and the IEEE Signal Processing Society’s Technical Committee on Signal Processing for Communications and Networks (2012-2016). Dr. Mitra is a Fellow of the IEEE . She is the recipient of: a 2015 UK Royal Academy of Engineering Distinguished Visiting Professorship, a 2015 US Fulbright Scholar Award, a 2015-2016 UK Leverhulme Trust Visiting Professorship, IEEE Communications Society Distinguished Lecturer, 2012 Globecom Signal Processing for Communications Symposium Best Paper Award, 2012 US National Academy of Engineering Lillian Gilbreth Lectureship, the 2009 DCOSS Applications & Systems Best Paper Award, Texas Instruments Visiting Professor (Fall 2002, Rice University), 2001 Okawa Foundation Award, 2000 OSU College of Engineering Lumley Award for Research, 1997 OSU College of Engineering MacQuigg Award for Teaching, and a 1996 National Science Foundation CAREER Award. She has been an Associate Editor for the following IEEE publications: Transactions on Signal Processing, Transactions on Information Theory, Journal of Oceanic Engineering, and Transactions on Communications. She has co-chaired: (technical program) 2014 IEEE International Symposium on Information Theory in Honolulu, HI, 2014 IEEE Information Theory Workshop in Hobart, Tasmania, IEEE 2012 International Conference on Signal Processing and Communications, Bangalore India, and the IEEE Communication Theory Symposium at ICC 2003 in Anchorage, AK; and general co-chair for the first ACM Workshop on Underwater Networks at Mobicom 2006, Los Angeles, CA. Dr. Mitra has held visiting appointments at: King’s College, London, Imperial College, the Delft University of Technology, Stanford University, Rice University, and the Eurecom Institute. Her research interests are in: wireless communications, communication and sensor networks, biological communication systems, detection and estimation and the interface of communication, sensing and control.

This talk is part of the Signal Processing and Communications Lab Seminars series.

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