UNO: Unlimited Sampling Meets One-Bit Quantization

TL;DR

This paper introduces UNO, a novel sampling method combining unlimited sampling and one-bit quantization, enabling high-resolution signal reconstruction with low-cost, low-power hardware, and demonstrates its effectiveness through numerical experiments.

Contribution

The paper proposes the UNO sampling approach that integrates unlimited sampling with one-bit quantization, utilizing the randomized Kaczmarz algorithm and PnP-ADMM for improved reconstruction.

Findings

UNO outperforms one-bit Sigma-Delta sampling in experiments.

Reconstruction accuracy is enhanced using RKA and PnP-ADMM techniques.

The method effectively handles noise in signal reconstruction.

Abstract

Recent results in one-bit sampling provide a framework for a relatively low-cost, low-power sampling, at a high rate by employing time-varying sampling threshold sequences. Another recent development in sampling theory is unlimited sampling, which is a high-resolution technique that relies on self-reset ADCs to yield an unlimited dynamic range. In this paper, we leverage the appealing attributes of the two aforementioned techniques to propose a novel \emph{un}limited \emph{o}ne-bit (UNO) sampling approach. In this framework, the information on the distance between the input signal value and the threshold are stored and utilized to accurately reconstruct the one-bit sampled signal. We then utilize this information to accurately reconstruct the signal from its one-bit samples via the randomized Kaczmarz algorithm (RKA); a strong linear feasibility solver that selects a random linear equation at each iteration. In the presence of noise, we employ the recent plug-and-play (PnP) priors technique with alternating direction method of multipliers (ADMM) to exploit integration of state-of-the-art regularizers in the reconstruction process. Numerical experiments with RKA and PnP-ADMM-based reconstruction illustrate the effectiveness of our proposed UNO, including its superior performance compared to the one-bit Sigma-Delta sampling.