Side information-aided compressed sensing reconstruction via approximate message passing

In this paper, the side information (SI)-aided compressed sensing reconstruction is considered, where a sparse signal is observed via a noisy underdetermined linear system, and a SI is available during the reconstruction. We develop a SI-aided approximate message passing (SI-AMP) algorithm to solve the problem. Based on the corresponding state evolution formula, the asymptotic prediction performance and noise-sensitivity analysis of the scheme are derived. Simulation results are presented to verify the efficiency of the proposed method.