# UNO: Unlimited Sampling Meets One-Bit Quantization

arXiv: https://arxiv.org/abs/2301.10155 · HTML: https://mlsanity.com/paper/2301.10155/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 108 references that are in the map.
- First posted on arXiv 10 Dec 2022.

## Builds on (most cited first, 17 of 17)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [On Unlimited Sampling and Reconstruction](https://mlsanity.com/paper/1905.03901/) (2019)
- [Sparse Regularization via Convex Analysis](https://mlsanity.com/paper/1803.06765/) (2018)
- [Unlimited Sampling from Theory to Practice: Fourier-Prony Recovery and Prototype ADC](https://mlsanity.com/paper/2105.05818/) (2021)
- [One-bit compressive sensing with norm estimation](https://mlsanity.com/paper/1404.6853/) (2014)
- [The Generalized Lasso for Sub-gaussian Measurements with Dithered Quantization](https://mlsanity.com/paper/1807.06976/) (2018)
- [Above the Nyquist Rate, Modulo Folding Does Not Hurt](https://mlsanity.com/paper/1903.12289/) (2019)
- [Generalized Approximate Message Passing for Unlimited Sampling of Sparse Signals](https://mlsanity.com/paper/1807.03182/) (2018)
- [One-Bit Phase Retrieval: More Samples Means Less Complexity?](https://mlsanity.com/paper/2203.08982/) (2022)
- [On the Randomized Kaczmarz Algorithm](https://mlsanity.com/paper/1402.2863/) (2014)
- [Signal Recovery From 1-Bit Quantized Noisy Samples via Adaptive Thresholding](https://mlsanity.com/paper/1812.03977/) (2018)
- [Gridless Parameter Estimation for One-Bit MIMO Radar with Time-Varying Thresholds](https://mlsanity.com/paper/1908.10487/) (2019)
- [λ-MIMO: Massive MIMO via Modulo Sampling](https://mlsanity.com/paper/2210.10193/) (2022)
- [Blind Modulo Analog-to-Digital Conversion](https://mlsanity.com/paper/2108.08937/) (2021)
- [Time Encoding via Unlimited Sampling: Theory, Algorithms and Hardware Validation](https://mlsanity.com/paper/2208.10234/) (2022)
- [Localization with One-Bit Passive Radars in Narrowband Internet-of-Things using Multivariate Polynomial Optimization](https://mlsanity.com/paper/2007.15108/) (2020)

## Built on by (most cited first, 11 of 11)

- [Plug-in Channel Estimation with Dithered Quantized Signals in Spatially Non-Stationary Massive MIMO Systems](https://mlsanity.com/paper/2301.04641/) (2023)
- [Compressed Sensing Based Residual Recovery Algorithms and Hardware for Modulo Sampling](https://mlsanity.com/paper/2412.12724/) (2024)
- [One-Bit Quadratic Compressed Sensing: From Sample Abundance to Linear Feasibility](https://mlsanity.com/paper/2303.09594/) (2023)
- [Collaborative Automotive Radar Sensing via Mixed-Precision Distributed Array Completion](https://mlsanity.com/paper/2403.08168/) (2024)
- [Modulo Sampling: Performance Guarantees in The Presence of Quantization](https://mlsanity.com/paper/2501.01506/) (2025)
- [HDR Imaging With One-Bit Quantization](https://mlsanity.com/paper/2309.03982/) (2023)
- [One-Bit-Aided Modulo Sampling for DOA Estimation](https://mlsanity.com/paper/2309.04901/) (2023)
- [Matrix Completion from One-Bit Dither Samples](https://mlsanity.com/paper/2310.03224/) (2023)
- [MCRB for Parameter Estimation from One-Bit Quantized and Oversampled Measurements](https://mlsanity.com/paper/2503.22860/) (2025)
- [1-Bit Unlimited Sampling Beyond Fourier Domain: Low-Resolution Sampling of Quantization Noise](https://mlsanity.com/paper/2508.19408/) (2025)
- [Joint Extremum Compression and Detection of a Time-Delayed Signal for Distributed Sensing](https://mlsanity.com/paper/2607.10874/) (2026)

## Abstract (arXiv)

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 Sigma-Delta sampling.