Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.06402 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913644091015168 |
|---|---|
| author | Gao, Bing Gu, Ran Ma, Shigui |
| author_facet | Gao, Bing Gu, Ran Ma, Shigui |
| contents | This paper presents a rigorous theoretical convergence analysis of the Wirtinger Flow (WF) algorithm for Poisson phase retrieval, a fundamental problem in imaging applications. Unlike prior analyses that rely on truncation or additional adjustments to handle outliers, our framework avoids eliminating measurements or introducing extra computational steps, thereby reducing overall complexity. We prove that WF achieves linear convergence to the true signal under noiseless conditions and remains robust and stable in the presence of bounded noise for Poisson phase retrieval. Additionally, we propose an incremental variant of WF, which significantly improves computational efficiency and guarantees convergence to the true signal with high probability under suitable conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of Wirtinger Flow for Poisson phase retrieval Gao, Bing Gu, Ran Ma, Shigui Numerical Analysis 94A12 This paper presents a rigorous theoretical convergence analysis of the Wirtinger Flow (WF) algorithm for Poisson phase retrieval, a fundamental problem in imaging applications. Unlike prior analyses that rely on truncation or additional adjustments to handle outliers, our framework avoids eliminating measurements or introducing extra computational steps, thereby reducing overall complexity. We prove that WF achieves linear convergence to the true signal under noiseless conditions and remains robust and stable in the presence of bounded noise for Poisson phase retrieval. Additionally, we propose an incremental variant of WF, which significantly improves computational efficiency and guarantees convergence to the true signal with high probability under suitable conditions. |
| title | Convergence analysis of Wirtinger Flow for Poisson phase retrieval |
| topic | Numerical Analysis 94A12 |
| url | https://arxiv.org/abs/2501.06402 |