Signal Recovery on Algebraic Varieties Using Linear Samples
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915359860195328 |
|---|---|
| author | Xu, Zhiqiang |
| author_facet | Xu, Zhiqiang |
| contents | The recovery of an unknown signal from its linear measurements is a fundamental problem spanning numerous scientific and engineering disciplines. Commonly, prior knowledge suggests that the underlying signal resides within a known algebraic variety. This context naturally leads to a question: what is the minimum number of measurements required to uniquely recover any signal belonging to such an algebraic variety? In this survey paper, we introduce a method that leverages tools from algebraic geometry to address this question. We then demonstrate the utility of this approach by applying it to two problems: phase retrieval and low-rank matrix recovery. We also highlight several open problems, which could serve as a basis for future investigations in this field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17572 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Signal Recovery on Algebraic Varieties Using Linear Samples Xu, Zhiqiang Information Theory Algebraic Geometry The recovery of an unknown signal from its linear measurements is a fundamental problem spanning numerous scientific and engineering disciplines. Commonly, prior knowledge suggests that the underlying signal resides within a known algebraic variety. This context naturally leads to a question: what is the minimum number of measurements required to uniquely recover any signal belonging to such an algebraic variety? In this survey paper, we introduce a method that leverages tools from algebraic geometry to address this question. We then demonstrate the utility of this approach by applying it to two problems: phase retrieval and low-rank matrix recovery. We also highlight several open problems, which could serve as a basis for future investigations in this field. |
| title | Signal Recovery on Algebraic Varieties Using Linear Samples |
| topic | Information Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2506.17572 |