Empirical Bayesian Inference Using a Support Informed Prior

Abstract

This paper develops a new empirical Bayesian inference algorithm for solving a linear inverse problem given multiple measurement vectors 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. Several applications can be modeled using this framework, including synthetic aperture radar observations using nearby azimuth angles and parallel magnetic resonance imaging. Our numerical experiments suggest that using the support informed prior usually improves accuracy of the recovery in the form of the sampled posterior mean and reduces its uncertainty when compared to posteriors constructed using some more standard priors.