Robust 1-bit compressive sensing against sign flips

In this paper, we introduce a new robust 1-bit compressive sensing reconstruction algorithm in the noisy environment, where a lot of signs are flipped. By calculating the number of inconsistencies, this algorithm can adaptively detect the positions where sign flips occur. Subsequently, the sparse signals can be recovered by using "corrected" measurements without a priori knowledge of the noise level. Numerical experiments show the high performance of signal recovery for the proposed algorithm in the presence of both measurement noise and transmission noise.