Statistical mechanics analysis of 1-bit compressed sensing
by
Yingying Xu(Tokyo Institute of Technology)
→
Europe/Stockholm
122:026
122:026
Description
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 beneficial in practical applications. We present a L1-norm minimization approach and a Bayesian approach to the signal reconstruction for 1-bit compressed sensing, and analyze their 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.
