Blind deconvolution by Optimizing over a Quotient Manifold

4:30PM at UNIV 103
Dr. Wen Huang, Rice University.
Blind deconvolution by Optimizing over a Quotient Manifold

Blind deconvolution is to recover two unknown signals from their convolution. We formulate this problem as a nonconvex optimization problem on a quotient manifold and propose Riemannian optimization algorithms for solving the problem. The proposed algorithm is proven to recover the exact solution with high probability when the number of measurements is (up to log-factors) slightly larger than the information-theoretical minimum, which is the same as the state-of-the-art results. The quotient structure in our formulation yields a simpler penalty term in the cost function when compared to the state-of-the-art nonconvex method. This simplifies the convergence analysis to some extent and yields a natural implementation. Empirically, the algorithm has the best performance in the sense that compared to state-of-the-art methods, i) it needs least number of various operations, such as DFT, to reach a similar accuracy, and ii) it has the highest probability of successful recovery. This is joint work with Paul Hand at Rice university.