Compressed sensing of correlated signals using belief propagation

Compressed Sensing (CS) has developed rapidly as an innovation in signal processing domain. Considering the situation that there are multiple sparse signals with redundancy, the correlation between them need to be properly utilized for further compression. To this end, a CS scheme based on Belief Propagation (BP) algorithm is proposed to compress correlated sparse (compressible) signals in this paper. The BP algorithm is a kind of solution of Bayesian CS by considering CS problem as an analogy of channel coding. Inspired by this, we modify the original BP algorithm by the side information available only at the decoder to obtain better recovery performance with the same sensing rate. The simulation results show that the proposed scheme is superior to the separate BP scheme and the joint L1 scheme for the correlated sparse signals.