Title: Identifiability Results for Bilinear Inverse Problems: With Applications to Blind Deconvolution and Matrix Factorization
Abstract: A number of difficult nonlinear inverse problems in signal processing, like blind deconvolution, matrix factorization, dictionary learning and blind source separation share the common characteristic of being bilinear inverse problems. A key concern for these inverse problems in applications like blind equalization in wireless communications and data mining in machine learning is that of identifiability of the generative models/signals. In this talk, we take an optimization theory motivated approach to develop a flexible and unifying framework for the analysis of identifiability in general bilinear inverse problems subject to conic constraints. In particular, we show that bilinear inverse problems can be characterized as low-rank matrix recovery problems and exploiting this connection enables us to develop sufficient conditions for identifiability. We further characterize identifiability as a function of problem size through scaling laws. Our approach is also algorithmically significant since low-rank matrix recovery problems admit well known tractable convex relaxations, but exploiting multiple sources of structure still remains a major challenge.
This is joint work with Prof. Urbashi Mitra at USC.
Bio: Sunav Choudhary received his Bachelor of Technology degree in Electronics and Communication from the Indian Institute of Technology, Kharagpur, India, in 2010. He joined the Communication Sciences Institute of the University of Southern California in 2010 where he is currently a doctoral student. He is a recepient of the USC Annenberg Graduate Fellowship. His present research interests are in the field of sparse signal approximation and low rank matrix recovery with applications to underwater acoustic communications. He is advised by Prof. Urbashi Mitra.