# Signal Reconstruction from Modulo Observations

arXiv: https://arxiv.org/abs/1812.00557 · HTML: https://mlsanity.com/paper/1812.00557/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2018.

## Built on by (most cited first, 3 of 3)

- [MantissaCam: Learning Snapshot High-dynamic-range Imaging with Perceptually-based In-pixel Irradiance Encoding](https://mlsanity.com/paper/2112.05221/) (2021)
- [Asymmetric compressive learning guarantees with applications to quantized sketches](https://mlsanity.com/paper/2104.10061/) (2021)
- [Modulo Video Recovery via Selective Spatiotemporal Vision Transformer](https://mlsanity.com/paper/2511.07479/) (2025)

## Abstract (arXiv)

We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a (relatively) less well-known imaging mechanism called modulo imaging, which can be used to extend the dynamic range of imaging systems; variations of this model have also been studied under the category of phase unwrapping. Signal reconstruction in the under-determined regime with modulo observations is a challenging ill-posed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to solving the inverse problem limited to two modulo periods, inspired by recent advances in algorithms for phase retrieval under sparsity constraints. We show that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal and provides improved performance over other existing algorithms. We also provide experiments validating our approach on both synthetic and real data to depict its superior performance.