Department of Computational and Applied Mathematics
"Blind deconvolution by Optimizing over a Quotient Manifold"
Riemannian optimization, also called optimization on Riemannian manifolds, considers finding an optimum of a real-valued function defined on a Riemannian manifold. In this presentation, we consider the problem of separating two unknown signals given their circular convolution. We formulate this problem as a nonconvex optimization problem on a quotient manifold and propose Riemannian optimization algorithms for solving the problem. Empirically, the proposed algorithm has better performance than the Wirtinger gradient descent algorithm and an alternating minimization algorithm in the sense that i) it needs fewer operations, such as DFTs and matrix-vector multiplications, to reach a similar accuracy, and ii) it has a higher probability of successful recovery in synthetic tests.
This is joint work with Paul Hand at Rice university