  This paper develops 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, and
as a prototypical example we consider reconstructing an image from synthetic
aperture radar (SAR) observations using nearby azimuth angles. 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.
