SPARSE SIGNAL RECONSTRUCTION FROM COMPRESSED SENSING MEASUREMENTS BASED ON DETECTION THEORY

The problem of sparse signal reconstruction from the well-known Compressed Sensingmeasurement is considered in this paper. The measured signal is assumed to be corrupted withadditive white Gaussian noise with zero mean and known variance. Based on detection theory, twoiterative algorithms are developed for detection and estimation of nonzero elements of sparsesignal. The principle of the proposed methods is based on applying composite multiple hypothesistest to the underlying problem at each iteration. Simulation results show the satisfactoryperformance of the proposed algorithms in sparse signal recovery. The proposed approach has thepotential of being applied to other models for noise and signal.