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.

翻译：本文开发了一种新的经验性贝叶斯推论算法, 用于解决线性反问题, 给出了抽样不足和吵闹的可观测数据的多度测量矢量( MMV ) 。 具体地说, 我们通过在基本信号或图像的稀疏领域利用多度测量的共聚性, 构建了一种新的支持支持性、 知情的宽度, 从而提前推广。 一些应用可以使用这个框架建模, 并且作为一个原始例子, 我们考虑利用附近方位角从合成孔径雷达(SAR)观测中重建图像。 我们的数字实验表明, 使用这个新先期不仅提高了恢复的准确性, 而且还降低了远地点的不确定性, 与生成前题的标准宽度相比 。