The problem of sparse signal reconstruction from the well-known Compressed Sensing
measurement is considered in this paper. The measured signal is assumed to be corrupted with
additive white Gaussian noise with zero mean and known variance. Based on detection theory, two
iterative algorithms are developed for detection and estimation of nonzero elements of sparse
signal. The principle of the proposed methods is based on applying composite multiple hypothesis
test to the underlying problem at each iteration. Simulation results show the satisfactory
performance of the proposed algorithms in sparse signal recovery. The proposed approach has the
potential of being applied to other models for noise and signal.