Bayesian compressive sensing using reweighted laplace priors

Bayesian compressive sensing (BCS) plays an important role in signal processing for dealing with sparse representation related problems. BCS utilizes a Bayesian model to solve the compressing sensing (CS) problem, such as signal sampling processing and model parameters using the hierarchical Bayesian framework. The use of Gaussian and Laplace distribution priors on the basic coefficients has already been demonstrated in previous works. However, the two existing priors cannot more effectively encode sparsity representation for unknown signals. In this paper, a reweighted Laplace distribution prior is proposed for hierarchical Bayesian to fully exploit the sparsity of unknown signals. The proposed algorithm can automatically estimate all the coefficients of unknown signal, and the expected model parameters are solely gotten from observation by developing a fast greedy algorithm to solve the Bayesian maximum posterior and type-II maximum likelihood. Theoretical analysis on the sparsity of the proposed model is analyzed and compared with the Laplace priors model. Moreover, numerical experiments are conducted to prove that the proposed algorithm can achieve superior performance for reconstructing unknown sparse signal with low computational burden as well as high accuracy.