Bayesian compressive sensing using wavelet based Markov random fields

Abstract

Compressive sensing (CS) is a novel method for acquisition of signals below the Nyquist sampling rate. Many signals and images are sparse in the wavelet domain. Therefore, in CS reconstruction algorithms, in addition to the sparsity, tree-structure of wavelet coefficients can be used as a knowledge of the signal. Also, the probability of each element of the sparse vector to be negligible depends on the value of its neighbors. So in this paper, we propose a model which exploits both the tree structure and the neighborhood relation of the coefficients, named wavelet-based Markov random fields (WMRF), and we use Bayesian method for signal reconstruction. Variational Bayesian expectation maximization (VBEM) inference procedure is used to acquire posterior distributions of the model. Also, SESOP algorithm, which is based on MPL estimation, is employed to estimate model parameters. Simulation results demonstrate that the reconstruction error of the proposed algorithm is lower than that of the state-of-the-art algorithms.