Noisy One-bit Compressed Sensing with Side-Information
Swatantra Kafle, Thakshila Wimalajeewa, and, Pramod K. Varshney

TL;DR
This paper introduces a generalized approximate message passing method for reconstructing sparse signals from noisy one-bit compressed measurements, leveraging side-information to significantly improve reconstruction accuracy.
Contribution
It develops novel algorithms that incorporate support and amplitude side-information, enhancing reconstruction performance in noisy one-bit compressed sensing scenarios.
Findings
Reconstruction performance improves with side-information.
The method effectively estimates noise parameters using EM algorithm.
Side-information reduces sensitivity to measurement noise.
Abstract
We consider the problem of sparse signal reconstruction from noisy one-bit compressed measurements when the receiver has access to side-information (SI). We assume that compressed measurements are corrupted by additive white Gaussian noise before quantization and sign-flip error after quantization. A generalized approximate message passing-based method for signal reconstruction from noisy one-bit compressed measurements is proposed, which is then extended for the case where the receiver has access to a signal that aids signal reconstruction, i.e., side-information. Two different scenarios of side-information are considered-a) side-information consisting of support information only, and b) side information consisting of support and amplitude information. SI is either a noisy version of the signal or a noisy estimate of the support of the signal. We develop reconstruction algorithms from…
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