Frequency-Domain Entropy-Based Blind Support Recovery from Multiple Measurement Vectors

Support recovery from multiple measurement vectors has been regarded as a critical aspect of compressive sensing. Most existing recovery algorithms require the prior knowledge of the sparsity or the noise power, which are unknown or even time-varying in actual applications, to determine the termination condition of the iterative recovery process. Motivated by the entropy concept from information theory, a frequency-domain entropy (FDE)-based blind support recovery algorithm is proposed, where the FDE is employed as the test statistic to determine whether there is a sparse signal remains in the residual signal. Specifically, the statistical distribution of the residual signal is proved to be Gaussian when the recovery iterations are adequately satisfied. Then, the cumulative distribution function of the test statistic and the closed-form expressions of the stop threshold are derived. Our proposed algorithm exploits the merit that the FDE is uncorrelated with the noise power, thus the estimation of the noise power is not required. Simulation results illustrate that the proposed algorithm is robust to different signal-to-noise ratios.