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

TL;DR

This paper introduces BHT-MLE, a Bayesian algorithm for noisy one bit compressed sensing with matrix perturbation, improving reconstruction accuracy with low computational complexity.

Contribution

It presents a novel Bayesian hypothesis testing-based support detector combined with an ML amplitude estimator for efficient sparse recovery.

Findings

BHT-MLE outperforms traditional ML estimators in accuracy.

The algorithm achieves low computational cost.

Simulation results validate the effectiveness of BHT-MLE.

Abstract

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.