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.