Recovery methods for 1-bit compressed sensing based on Hamming distance

Hamming distance denotes the amount of the positions' difference between two bit strings. In the 1-bit compressed sensing (CS) technology, the Hamming distance between the measurement vector and the certain column of the measurement matrix can be calculated. We show the relationship between this Hamming distance and the corresponding entry of the signal. By exploiting this relationship, this paper proposes a recovery algorithm for 1-bit CS. Furthermore, we extend the algorithm to the joint sparse model, where multiple correlated signals are considered. The simulation results show that the proposed algorithms enjoy better performance when compared with the existing algorithms.