ROCS: Robust One-Bit Compressed Sensing With Application to Direction of Arrival

One-bit compressed sensing (1-bit CS) inherits the merits of traditional CS and further reduces the cost and burden on the hardware device via employing the 1-bit analog-to-digital converter. When the measurements do not involve sign flips caused by additive noise, most contemporary algorithms can attain excellent signal restoration. However, their recovery performance might significantly degrade if there is even a small portion of sign flips. In order to increase the estimation accuracy in noisy scenarios, we devise a new signal model for 1-bit CS to attain robustness against sign flips. Then, we give a double-sparsity optimization formulation of the restoration problem. Subsequently, we combine proximal alternating minimization and projected gradient descent to tackle the problem. Different from existing robust methodologies, our approach, referred to as robust one-bit CS (ROCS), does not require the number of sign flips. Furthermore, we analyze the convergence behavior of ROCS and show that the objective value and variable sequences converge. Numerical results using synthetic data demonstrate that ROCS is superior to the competing methods in terms of reconstruction error in noisy environments. ROCS is also applied to direction-of-arrival estimation and outperforms state-of-the-art approaches.