Noisy 1-Bit Compressed Sensing with Heterogeneous Side-information

Abstract

We consider the problem of sparse signal reconstruction from noisy 1-bit compressed measurements using a statistically dependent signal, as an aid. We assume that this signal does not share joint sparse representation with the sparse signal and call it a heterogeneous side-information. We assume that compressed measurements are corrupted by additive white Gaussian noise before quantization and sign-flip errors after quantization. We propose a generalized approximate message passing-based algorithm for signal reconstruction from noisy 1-bit compressed measurements which leverages the dependence between the signal and the heterogeneous side-information. We model the dependence between signal and heterogeneous side-information using copula functions and show, through numerical experiments, that the proposed algorithm yields a better reconstruction performance than 1-bit CS-based recovery algorithms that do not exploit the side-information.