UNO: Unlimited Sampling Meets One-Bit Quantization
Arian Eamaz, Kumar Vijay Mishra, Farhang Yeganegi, Mojtaba Soltanalian
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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">modulo ADCs</i> to yield an unlimited dynamic range. In this paper, we leverage the appealing attributes of the two aforementioned techniques to propose a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">un</i> limited <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</i> ne-bit (UNO) sampling approach. In this framework, the information on the distance between the input signal value and the threshold is 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). 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 ΣΔ sampling.