# Compressed Sensing Based Residual Recovery Algorithms and Hardware for Modulo Sampling

arXiv: https://arxiv.org/abs/2412.12724 · HTML: https://mlsanity.com/paper/2412.12724/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 48 references that are in the map.
- First posted on arXiv 17 Dec 2024.

## Builds on (most cited first, 11 of 11)

- [On Unlimited Sampling and Reconstruction](https://mlsanity.com/paper/1905.03901/) (2019)
- [Unlimited Sampling from Theory to Practice: Fourier-Prony Recovery and Prototype ADC](https://mlsanity.com/paper/2105.05818/) (2021)
- [UNO: Unlimited Sampling Meets One-Bit Quantization](https://mlsanity.com/paper/2301.10155/) (2022)
- [Above the Nyquist Rate, Modulo Folding Does Not Hurt](https://mlsanity.com/paper/1903.12289/) (2019)
- [Back in the US-SR: Unlimited Sampling and Sparse Super-Resolution with its Hardware Validation](https://mlsanity.com/paper/2207.13230/) (2022)
- [Generalized Approximate Message Passing for Unlimited Sampling of Sparse Signals](https://mlsanity.com/paper/1807.03182/) (2018)
- [Residual Recovery Algorithm For Modulo Sampling](https://mlsanity.com/paper/2110.03335/) (2021)
- [Modulo Sampling of FRI Signals](https://mlsanity.com/paper/2207.08774/) (2022)
- [λ-MIMO: Massive MIMO via Modulo Sampling](https://mlsanity.com/paper/2210.10193/) (2022)
- [Unlimited Dynamic Range Analog-to-Digital Conversion](https://mlsanity.com/paper/1911.09371/) (2019)
- [Modulo Sampling in Shift-Invariant Spaces: Recovery and Stability Enhancement](https://mlsanity.com/paper/2406.10929/) (2024)

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

Analog-to-Digital Converters (ADCs) are essential components in modern data acquisition systems. A key design challenge is accommodating high dynamic range (DR) input signals without clipping. Existing solutions, such as oversampling, automatic gain control (AGC), and compander-based methods, have limitations in handling high-DR signals. Recently, the Unlimited Sampling Framework (USF) has emerged as a promising alternative. It uses a non-linear modulo operator to map high-DR signals within the ADC range. Existing recovery algorithms, such as higher-order differences (HODs), prediction-based methods, and beyond bandwidth residual recovery (B2R2), have shown potential but are either noise-sensitive, require high sampling rates, or are computationally intensive. To address these challenges, we propose LASSO-B2R2, a fast and robust recovery algorithm. Specifically, we demonstrate that the first-order difference of the residual (the difference between the folded and original samples) is sparse, and we derive an upper bound on its sparsity. This insight allows us to formulate the recovery as a sparse signal reconstruction problem using the least absolute shrinkage and selection operator (LASSO). Numerical simulations show that LASSO-B2R2 outperforms prior methods in terms of speed and robustness, though it requires a higher sampling rate at lower DR. To overcome this, we introduce the bits distribution mechanism, which allocates 1 bit from the total bit budget to identify modulo folding events. This reduces the recovery problem to a simple pseudo-inverse computation, significantly enhancing computational efficiency. Finally, we validate our approach through numerical simulations and a hardware prototype that captures 1-bit folding information, demonstrating its practical feasibility.