Speaker: Yoram Bresler, University of Illinois at Urbana-Champaign
Abstract: With the increasing amounts and diversity of data, calibrated or theory-driven models for the data acquisition process are often unavailable. This gives rise to so-called blind signal recovery problems in applications such channel equalization, speech dereverberation, seismic data analysis, computer vision, and large-scale radio telescope arrays. These are instances of bilinear inverse problems (BIPs). However, while the solution of linear inverse problems under both classical signal models and modern sparsity models has been studied extensively and is well understood, relatively little is known about the solution of BIPs.
We give an overview of several such problems and of recent results determining the conditions for unique and stable solution. We also describe a practical recovery algorithm for blind deconvolution that achieves guaranteed essentially optimal scaling of the amount of data needed with the number of degrees of freedom in the problem.