Speaker: Anne Gelb (John G. Kemeny Parents Professor, Department of Mathematics, Dartmouth College)

Title: Empirical Bayesian Inference using Joint Sparsity

We develop a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of under-sampled and noisy observable data. Specifically, by exploiting the joint sparsity across the multiple measurements in the sparse domain of the underlying signal or image, we construct a new support informed sparsity promoting prior. Several applications can be modeled using this framework. Our numerical experiments demonstrate that using this new prior not only improves accuracy of the recovery, but also reduces the uncertainty in the posterior when compared to standard sparsity producing priors.

This is joint work with Theresa Scarnati at the Air Force Research Lab Wright Patterson and Jack Zhang, recent bachelor degree recipient at Dartmouth College and now enrolled at University of Minnesota’s PhD program in mathematics.