Title: Linear Inverse Problems: From Model Based to Data Driven Solutions 
Speaker: Bhaskar Rao, Professor at the University of California, San Diego
Date: Friday, March 6, 2026
Time: 3:00 p.m.
Location: CSIP Library (Centergy One Building, Room 5126)

Abstract: Given a matrix X, nonnegative matrix factorization (NMF) aims to find the smallest nonnegative matrices U and V such that X=UV'. The nonnegative rank of X is the number of columns in U (and V). Surprisingly, nobody knows how to find this number! One of the main reasons is that NMF is ill-posed with infinitely many feasible solutions. In this talk, I will introduce what we call nonnegative canonical edges (NCEs), which reveal the optimal (maximal volume) solution to NMF. This is analogous to the Moore-Penrose pseudo-inverse, which selects the optimal (minimum-norm) solution to ill-posed least-squares problems. We conjecture that NCEs hold the key to determining the nonnegative rank, and I will discuss our ideas to determine this number exactly and finally give a definitive answer to NMF.

Bio: Bhaskar D. Rao is a pioneer in sparsity‑based signal processing, known for co‑authoring the seminal 1992 FOCUSS algorithm and helping launch the field through early leadership such as co‑organizing the first ICASSP special session on sparsity in 1998. He has been a faculty member at UC San Diego since 1983, serving as Professor Emeritus and Distinguished Professor of the Graduate Division, as well as holding the Ericsson Endowed Chair in Wireless Access Networks and directing the Center for Wireless Communications (2008–2011). His research spans digital signal processing, estimation, and optimization with impactful applications in communications, speech, and biomedical systems. Rao’s acclaimed contributions have earned multiple honors, including the 2012 IEEE SPS Best Paper Award, the Stephen O. Rice Prize, the 2016 IEEE SPS Technical Achievement Award, election as an IEEE Fellow in 2000, and the 2023 IEEE SPS Norbert Wiener Society Award.