Sparse Bayesian Learning for non-Gaussian sources

In this paper, we show that in the multiple measurement vector model we can take advantage of having multiple samples to learn the properties of the distributions of the sources as part of the recovery process and demonstrate that this improves the recovery performance. We propose a method to solve the simultaneous sparse approximation problem using a mixture of Gaussians prior, inspired by existing Sparse Bayesian Learning approaches. We justify our proposed prior by showing that there are a number of signals modelled better by a mixture of Gaussians prior than the standard zero-mean Gaussian prior, such as communications signals which often have a multimodal distribution. We further show that this method can be applied to data distributed according to an alpha-stable distribution. We also show that our proposed method can be applied to compressed sensing of ultrasound images and demonstrate an improvement over existing methods.