The 1-bit compressed sensing framework enables the recovery of a sparse vector x from the sign information of each entry of its linear transformation. Discarding the amplitude information can significantly reduce the amount of data, which is highly b
eneficial in practical applications. In this paper, we present a Bayesian approach to signal reconstruction for 1-bit compressed sensing, and analyze its typical performance using statistical mechanics. Utilizing the replica method, we show that the Bayesian approach enables better reconstruction than the L1-norm minimization approach, asymptotically saturating the performance obtained when the non-zero entries positions of the signal are known. We also test a message passing algorithm for signal reconstruction on the basis of belief propagation. The results of numerical experiments are consistent with those of the theoretical analysis.
