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

HISTORY: An Efficient and Robust Algorithm for Noisy 1-bit Compressed Sensing