Compressive sensing (CS) shows that a sparse or compressible signal can be exactly recovered from its linear measurements at a rate significantly lower than the Nyquist rate. As an extreme case, 1-bit compressive sensing (1-bit CS) states that an original sparse signal can be recovered from the 1-bit measurements. In this paper, we intrduce a Fast and Accurate Two-Stage (FATS) algorithm for 1-bit compressive sensing. Simulations show that FATS not only significantly increases the signal reconstruction speed but also improves the reconstruction accuracy.

We consider the problem of sparse signal recovery from 1-bit measurements. Due to the noise present in the acquisition and transmission process, some quantized bits may be flipped to their opposite states. These sign flips may result in severe performance degradation. In this study, a novel algorithm, termed HISTORY, is proposed. It consists of Hamming support detection and coefficients recovery. The HISTORY algorithm has high recovery accuracy and is robust to strong measurement noise. Numerical results are provided to demonstrate the effectiveness and superiority of the proposed algorithm.