UNO: Unlimited Sampling Meets One-Bit Quantization

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 unlimited one-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 Σ∆ sampling.

Generalized Probability Density Function Estimation via Convex Optimization

“…The first step of the update process (56), Z i+1 = KA r (X i ), can be also replaced with Z i+1 = KA p (X i ) or Z i+1 = KA b (X i ) to be consistent with the updates of PrSKM and Block SKM, respectively. The convergence guarantee of SVP-ORKA is concluded according to the following lemma:…”

“…In [54], the authors provide a comprehensive investigation of estimating the covariance matrix from one-bit measurements using Uniform dithering. Dithered One-bit quantization has also been applied to various problems, such as sparse parameter estimation [35,49,55], phase retrieval [22], and sampling theory [56] as discussed in contemporary literature. The study presented in [53] demonstrates that one-bit signal parameter estimation with time-varying thresholds yields notably superior results compared to using constant thresholds.…”

L${}_{\text{2}}$min${}^{\text{2/2s}}$: Efficient Linear Reconstruction Filter for Incremental Delta-Sigma ADCs

“…In pursuit of this goal, various new quantization schemes have been reported. The recent pioneers in this field include unlimited sampling [2], [3] and one-bit quantization [3], [4], [5], [6], [7], [8], [9], which utilize advanced signal processing theories and powerful signal processing tools for signal Bo Wang and Jens Schneider are with the College of Science and Engineering, Hamad Bin Khalifa University, Doha 34110, Qatar (e-mail: bwang@hbku.edu.qa).…”

“…However, its signal reconstruction process is more hardware-friendly to be integrated into standalone ADC chips. Meanwhile, compared to the emerging one-bit quantization scheme using time-varying thresholds drawn from a predefined distribution [3], [4], [5], [6], [7], [8], [9], the loop filter in a ΔΣ ADC can effectively generate uniform distancing time-varying thresholds, which recursively makes the threshold closer to the input signal, thus accurate signal recovery becomes possible using simple digital processing.…”

One-Bit Matrix Completion With Time-Varying Sampling Thresholds

“…This process results in utilizing exclusively one-bit data for the subsequent reconstruction algorithm. It has been demonstrated that when the scalar parameter of uniform dithers is designed to dominate the dynamic range of measurements, multi-bit scalar quantization simplifies to a one-bit comparator [22,23]. Leveraging this observation along with the properties of uniform dithering, particularly in canceling quantization effects in the expectation, we aim to establish theoretical guarantees for quantized matrix completion.…”