Robust One-Bit Bayesian Compressed Sensing with Sign-Flip Errors

We consider the problem of sparse signal recovery from one-bit measurements. Due to the noise present in the acquisition and transmission process, some quantized bits may be flipped to their opposite states. These bit-flip errors, also referred to as the sign-flip errors, may result in severe performance degradation. To address this issue, we introduce a robust Bayesian compressed sensing framework to account for sign flip errors. Specifically, sign-flip errors are considered as a result of a sparse noise-corrupted model in which original (unquantized) observations are corrupted by sparse (impulse) noise. A Gaussian-inverse Gamma hierarchical prior is assigned to the noise vector to promote sparsity. Based on the modified hierarchical model, we develop a variational expectation-maximization (EM) algorithm to identify the sign-flip errors and recover the sparse signal simultaneously. Numerical results are provided to illustrate the effectiveness and superiority of the proposed method.