GraHTP: A Provable Newton-like Algorithm for Sparse Phase Retrieval
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916616257667072 |
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| author | Dai, Licheng Lu, Xiliang You, Juntao |
| author_facet | Dai, Licheng Lu, Xiliang You, Juntao |
| contents | This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit (GraHTP), for sparse phase retrieval with complex sensing vectors. GraHTP is theoretically provable and exhibits high efficiency, achieving a quadratic convergence rate after a finite number of iterations, while maintaining low computational complexity per iteration. Numerical experiments further demonstrate GraHTP's superior performance compared to state-of-the-art algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_04034 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | GraHTP: A Provable Newton-like Algorithm for Sparse Phase Retrieval Dai, Licheng Lu, Xiliang You, Juntao Numerical Analysis This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit (GraHTP), for sparse phase retrieval with complex sensing vectors. GraHTP is theoretically provable and exhibits high efficiency, achieving a quadratic convergence rate after a finite number of iterations, while maintaining low computational complexity per iteration. Numerical experiments further demonstrate GraHTP's superior performance compared to state-of-the-art algorithms. |
| title | GraHTP: A Provable Newton-like Algorithm for Sparse Phase Retrieval |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2410.04034 |