# Line Spectral Estimation with Unlimited Sensing

arXiv: https://arxiv.org/abs/2408.06597 · HTML: https://mlsanity.com/paper/2408.06597/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 36 references that are in the map.
- First posted on arXiv 13 Aug 2024.

## Builds on (most cited first, 3 of 3)

- [Unlimited Sampling from Theory to Practice: Fourier-Prony Recovery and Prototype ADC](https://mlsanity.com/paper/2105.05818/) (2021)
- [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)

## Abstract (arXiv)

In the paper, we consider the line spectral estimation problem in an unlimited sensing framework (USF), where a modulo analog-to-digital converter (ADC) is employed to fold the input signal back into a bounded interval before quantization. Such an operation is mathematically equivalent to taking the modulo of the input signal with respect to the interval. To overcome the noise sensitivity of higher-order difference-based methods, we explore the properties of the first-order difference of modulo samples, and develop two line spectral estimation algorithms based on first-order difference, which are robust against noise. Specifically, we show that, with a high probability, the first-order difference of the original samples is equivalent to that of the modulo samples. By utilizing this property, line spectral estimation is solved via a robust sparse signal recovery approach. The second algorithms is built on our finding that, with a sufficiently high sampling rate, the first-order difference of the original samples can be decomposed as a sum of the first-order difference of the modulo samples and a sequence whose elements are confined to be three possible values. This decomposition enables us to formulate the line spectral estimation problem as a mixed integer linear program that can be efficiently solved. Simulation results show that both proposed methods are robust against noise and achieve a significant performance improvement over the higher-order difference-based method.