Bilinear Inverse Problems: How much does structure help?

ΟΜΙΛΗΤΗΣ<:  Prof. Urbashi Mitra, University of Southern California, U.S.A.

ΤΙΤΛΟΣ:   Bilinear Inverse Problems: How much does structure help?

ΧΡΟΝΟΣ:   Τρίτη, 4 April 2017, 12-13 μμ

ΑΙΘΟΥΣΑ:  Αίθουσα Συνεδριάσεων Α56 (1ος όροφος)

ΠΕΡΙΛΗΨΗ:

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.