Speaker: Sunav Choudhary, PhD. student in the Communication Sciences Institute of the University of Southern California, Los Angeles
Bilinear inverse problems (like blind deconvolution, matrix factorization, etc.) are important ill-posed inverse problems in signal processing. The recovery of input signals from bilinear map outputs has renewed interest due to recent results in sparse approximation and matrix recovery; however, the investigation of identifiability is not as mature. We show that bilinear inverse problems can be posed as rank-1 matrix recovery problems subject to linear constraints and develop deterministic sufficient conditions for identifiability for the cases when rank-2 matrices are present in the null space of the linear operator. Furthermore, under general assumptions on the distribution of the input signals, we show that bilinear inverse problems are identifiable with probability close to 1 as long as the size of the rank-2 null space grows as o(mn).