A Semi-blind Greedy Support Recovery Algorithm with Adjustable Stop Threshold

Greedy algorithm is an important class of sparse recovery algorithm of compressive sensing. Most existing greedy recovery algorithms need the prior knowledge of the signal’s sparsity, which is unknown or even time-varying in actual applications, to determine the stop threshold of the iterative recovery process. Recently, the power of the residual signal is used to compare with the noise power to determine whether there is some sparse signal remaining. In this paper, the statistical property of the residual signal power is proved to follow the chi square distribution with parameter L(M-k), where L and M and the size of the observation matrix, and k is the recovery iteration times. Then, a semi-blind greedy algorithm is proposed, in which the stop threshold is adjust according to the recovery times. Simulation results illustrate that the proposed algorithm is more effective than the existing energy-based support recovery algorithm.