Harmonic Analysis and Signal Processing Seminar

Bilinear inverse problems: theory, algorithms, and applications in imaging science and signal processing

Shuyang Ling
Courant Institute

Tuesday, November 14, 2017, 11am, WWH 201


Bilinear inverse problem pervades many areas of science and technology, including signal processing, imaging processing, and wireless communications. However, they are notoriously ill-posed since they are often closely related to nonconvex optimization. Solving nonconvex optimization is not an easy task because one may easily get trapped in local minima. We will discuss several important examples of bilinear inverse problems which can be solved efficiently and reliably with both convex and nonconvex approaches. One example brings compressive sensing, self-calibration, and biconvex optimization together with applications in array self-calibration. We will propose a novel method called SparseLift to exploit the sparsity in this bilinear model and provide explicit theoretical guarantees; the other one focuses on the well-known blind deconvolution. We will present a nonconvex algorithm which guarantees the exact recovery with the advantage of robustness and being computationally efficient. Moreover, our framework is extended to solve a more intricate but related problem: the joint blind deconvolution and demixing problem. Several applications in imaging processing and wireless communication will be discussed.