A reconstruction approach for noisy compressive sensing via iterative support detection

In this paper, the major contribution is to combine Bayesian inference with iterative support detection (ISD) to solve noisy compressive sensing, which can be called Bayesian compressive sensing via iterative support detection (BCS_ISD). The method consists of two main parts: signal value estimation and signal support detection. ISD estimates a support set S from a current reconstruction and obtains a new reconstruction by MMSE estimator, and then it iterates these two steps for a small number of times. BCS_ISD converges fast and it reconstructs more exactly than other belief propagation (BP) approaches. Numerical experiments are provided to verify that BCS_ISD has significant advantages over those recent methods.