Enhanced multi-task compressive sensing using Laplace priors and MDL-based task classification

Abstract

In multi-task compressive sensing (MCS), the original signals of multiple compressive sensing (CS) tasks are assumed to be correlated. This is explored to recover signals in a joint manner to improve signal reconstruction performance. In this paper, we first develop an improved version of MCS that imposes sparseness over the original signals using Laplace priors. The newly proposed technique, termed as the Laplace prior-based MCS (LMCS), adopts a hierarchical prior model, and the MCS is shown analytically to be a special case of LMCS. This paper next considers the scenario where the CS tasks belong to different groups. In this case, the original signals from different task groups are not well correlated, which would degrade the signal recovery performance of both MCS and LMCS. We propose the use of the minimum description length (MDL) principle to enhance the MCS and LMCS techniques. New algorithms, referred to as MDL-MCS and MDL-LMCS, are developed. They first classify tasks into different groups and then reconstruct signals from each cluster jointly. Simulations demonstrate that the proposed algorithms have better performance over several state-of-art benchmark techniques.