A FAST ALGORITHM FOR THE BAYESIAN ADAPTIVE LASSO

This paper presents a novel hierarchical Bayesian model which allows to reconstruct sparse signals using a set of linear measurements corrupted by Gaussian noise. The pro-posed model can be considered as the Bayesian counterpart of the adaptive lasso criterion. A fast iterative algorithm, which is based on the type-II maximum likelihood methodology, is properly adjusted to conduct Bayesian inference on the un-known model parameters. The performance of the proposed hierarchical Bayesian approach is illustrated on the recon-struction of both sparse synthetic data, as well as real images. Experimental results show the improved performance of the proposed approach, when compared to state-of-the-art Bayesian compressive sensing algorithms. Index Terms — Bayesian compressive sensing, adaptive lasso, sparse linear regression, hierarchical Bayesian analysis