  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.
