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 proposed 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 unknown model parameters. The performance of the proposed hierarchical Bayesian approach is illustrated on the reconstruction 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.