Convergence Analysis of Reshaped Wirtinger Flow with Random Initialization for Phase Retrieval
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909697949302784 |
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| author | Li, Linbin Peng, Haiyang Xia, Yong Huang, Meng |
| author_facet | Li, Linbin Peng, Haiyang Xia, Yong Huang, Meng |
| contents | This paper investigates phase retrieval using the Reshaped Wirtinger Flow (RWF) algorithm, focusing on recovering target vector $\vx \in \R^n$ from magnitude measurements \(y_i = \left| \langle \va_i, \vx \rangle \right|, \; i = 1, \ldots, m,\) under random initialization, where $\va_i \in \R^n$ are measurement vectors. For Gaussian measurement designs, we prove that when $m\ge O(n \log^2 n\log^3 m)$, the RWF algorithm with random initialization achieves $ε$-accuracy within \(O\big(\log n + \log(1/ε)\big)\) iterations, thereby attaining nearly optimal sample and computational complexities comparable to those previously established for spectrally initialized methods. Numerical experiments demonstrate that the convergence rate is robust to initialization randomness and remains stable even with larger step sizes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence Analysis of Reshaped Wirtinger Flow with Random Initialization for Phase Retrieval Li, Linbin Peng, Haiyang Xia, Yong Huang, Meng Optimization and Control This paper investigates phase retrieval using the Reshaped Wirtinger Flow (RWF) algorithm, focusing on recovering target vector $\vx \in \R^n$ from magnitude measurements \(y_i = \left| \langle \va_i, \vx \rangle \right|, \; i = 1, \ldots, m,\) under random initialization, where $\va_i \in \R^n$ are measurement vectors. For Gaussian measurement designs, we prove that when $m\ge O(n \log^2 n\log^3 m)$, the RWF algorithm with random initialization achieves $ε$-accuracy within \(O\big(\log n + \log(1/ε)\big)\) iterations, thereby attaining nearly optimal sample and computational complexities comparable to those previously established for spectrally initialized methods. Numerical experiments demonstrate that the convergence rate is robust to initialization randomness and remains stable even with larger step sizes. |
| title | Convergence Analysis of Reshaped Wirtinger Flow with Random Initialization for Phase Retrieval |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.15684 |