Bayesian hypothesis testing for one bit compressed sensing with sensing matrix perturbation

Bayesian hypothesis testing for one bit compressed sensing with sensing matrix perturbation H. Zayyani, M. Korki and F. Marvasti This letter proposes a low-computational Bayesian algorithm for noisy sparse recovery in the context of one bit compressed sensing with sensing matrix perturbation. The proposed algorithm which is called BHT -MLE comprises a sparse support detector and an amplitude estimator. The support detector utilizes Bayesian hypothesis test, while the amplitude estimator uses an ML estimator which is obtained by solving a convex optimization problem. Simulation results show that BHT -MLE algorithm offers more reconstruction accuracy than that of an ML estimator (MLE) at a low computational cost. Introduction: The one bit compressed sensing which is the extreme case of quantized compressed sensing [1] has been extensively investigated recently [2-9]. In the one bit compressed sensing framework, it is proved that accurate and stable recovery can be achieved by using only the sign of linear measurements [2].