A variational bayesian approach to compressive sensing based on Double Lomax priors

Automatic Relevance Determination (ARD) priors have been widely used to induce sparse reconstructions in Bayesian compressive sensing approaches. In this paper, we propose a new sparsity-promoting prior coined as Double Lomax prior. Its connection with the generalized inverse Gaussian distribution and Rayleigh distribution leads to a tractable full Variational Bayesian (VB) inference procedure here. It is shown that the proposed update procedure includes the canonical ARD update procedure as a special case, but provides a better global convergence performance and results in improved signal reconstructions.