# On Unlimited Sampling and Reconstruction

arXiv: https://arxiv.org/abs/1905.03901 · HTML: https://mlsanity.com/paper/1905.03901/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2019.

## Built on by (most cited first, 22 of 22)

- [UNO: Unlimited Sampling Meets One-Bit Quantization](https://mlsanity.com/paper/2301.10155/) (2022)
- [MantissaCam: Learning Snapshot High-dynamic-range Imaging with Perceptually-based In-pixel Irradiance Encoding](https://mlsanity.com/paper/2112.05221/) (2021)
- [Physics vs. Learned Priors: Rethinking Camera and Algorithm Design for Task-Specific Imaging](https://mlsanity.com/paper/2204.09871/) (2022)
- [Compressed Sensing Based Residual Recovery Algorithms and Hardware for Modulo Sampling](https://mlsanity.com/paper/2412.12724/) (2024)
- [Autoregressive High-Order Finite Difference Modulo Imaging: High-Dynamic Range for Computer Vision Applications](https://mlsanity.com/paper/2504.04228/) (2025)
- [The Modulo Radon Transform: Theory, Algorithms and Applications](https://mlsanity.com/paper/2105.04194/) (2021)
- [Spiked Covariance Estimation from Modulo-Reduced Measurements](https://mlsanity.com/paper/2110.01150/) (2021)
- [ORKA: Accelerated Kaczmarz Algorithms for Signal Recovery from One-Bit Samples](https://mlsanity.com/paper/2301.03467/) (2022)
- [One-Bit Quadratic Compressed Sensing: From Sample Abundance to Linear Feasibility](https://mlsanity.com/paper/2303.09594/) (2023)
- [Blind-Adaptive Quantizers](https://mlsanity.com/paper/2409.04077/) (2024)
- [Blind Time-of-Flight Imaging: Sparse Deconvolution on the Continuum with Unknown Kernels](https://mlsanity.com/paper/2411.00893/) (2024)
- [Modulo Sampling: Performance Guarantees in The Presence of Quantization](https://mlsanity.com/paper/2501.01506/) (2025)
- [mSQUID: Model-Based Leanred Modulo Recovery at Low Sampling Rates](https://mlsanity.com/paper/2510.18729/) (2025)
- [Recovering H"older smooth functions from noisy modulo samples](https://mlsanity.com/paper/2112.01610/) (2021)
- [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)
- [1-Bit Unlimited Sampling Beyond Fourier Domain: Low-Resolution Sampling of Quantization Noise](https://mlsanity.com/paper/2508.19408/) (2025)
- [Unlocking Off-the-Grid Sparse Recovery with Unlimited Sensing: Simultaneous Super-Resolution in Time and Amplitude](https://mlsanity.com/paper/2510.16948/) (2025)
- [Modulo Video Recovery via Selective Spatiotemporal Vision Transformer](https://mlsanity.com/paper/2511.07479/) (2025)
- [Deep Lightweight Unrolled Network for High Dynamic Range Modulo Imaging](https://mlsanity.com/paper/2601.12526/) (2026)
- [Scale Equivariance Regularization and Feature Lifting in High Dynamic Range Modulo Imaging](https://mlsanity.com/paper/2601.23037/) (2026)
- [Lattice Modulo Sampling](https://mlsanity.com/paper/2605.24974/) (2026)

## Abstract (arXiv)

Shannon's sampling theorem is one of the cornerstone topics that is well understood and explored, both mathematically and algorithmically. That said, practical realization of this theorem still suffers from a severe bottleneck due to the fundamental assumption that the samples can span an arbitrary range of amplitudes. In practice, the theorem is realized using so-called analog-to-digital converters (ADCs) which clip or saturate whenever the signal amplitude exceeds the maximum recordable ADC voltage thus leading to a significant information loss. In this paper, we develop an alternative paradigm for sensing and recovery, called the Unlimited Sampling Framework. It is based on the observation that when a signal is mapped to an appropriate bounded interval via a modulo operation before entering the ADC, the saturation problem no longer exists, but one rather encounters a different type of information loss due to the modulo operation. Such an alternative setup can be implemented, for example, via so-called folding or self-reset ADCs, as they have been proposed in various contexts in the circuit design literature. The key task that we need to accomplish in order to cope with this new type of information loss is to recover a bandlimited signal from its modulo samples. In this paper we derive conditions when perfect recovery is possible and complement them with a stable recovery algorithm. The sampling density required to guarantee recovery is independent of the maximum recordable ADC voltage and depends on the signal bandwidth only. Our recovery guarantees extend to measurements affected by bounded noise, which includes the case of round-off quantization. Numerical experiments validate our approach. Applications of the unlimited sampling paradigm can be found in a number of fields such as signal processing, communication and imaging.