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

This paper 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 obtained by solving a convex optimization problem. Simulation results show that Bayesian hypothesis testing in combination with the ML estimator has more reconstruction accuracy than that of only an ML estimator and also has less computational complexity.