Abstract: We develop a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors (MMV) of  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 prior. While a variety of applications can be modeled using this framework, our prototypical example comes from synthetic aperture radar (SAR) data, from which data are acquired from neighboring aperture windows. Hence a good test case is to consider the observations modeled as noisy Fourier samples. Our numerical experiments demonstrate that using the support informed 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 formerly of the Air Force Research Lab Wright Patterson and now working at Qualis Corporation in Huntsville, AL, and Jack Zhang, a 2020 bachelor degree recipient at Dartmouth College now enrolled in the University of Minnesota’s PhD program in mathematics.