Automated Recovery of Compressedly Observed Sparse Signals From Smooth Background

We propose a Bayesian based algorithm to recover sparse signals from compressed noisy measurements in the presence of a smooth background component. This problem is closely related to robust principal component analysis and compressive sensing, and is found in a number of practical areas. The proposed algorithm adopts a hierarchical Bayesian framework for modeling, and employs approximate inference to estimate the unknowns. Numerical examples demonstrate the effectiveness of the proposed algorithm and its advantage over the current state-of-the-art solutions.