Holographic Phase Retrieval via Wirtinger Flow: Cartesian Form with Auxiliary Amplitude
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910453522759680 |
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| author | Uchiyama, Ittetsu Tsutake, Chihiro Takahashi, Keita Fujii, Toshiaki |
| author_facet | Uchiyama, Ittetsu Tsutake, Chihiro Takahashi, Keita Fujii, Toshiaki |
| contents | We propose a new gradient method for holography, where a phase-only hologram is parameterized by not only the phase but also amplitude. The key idea of our approach is the formulation of a phase-only hologram using an auxiliary amplitude. We optimize the parameters using the so-called Wirtinger flow algorithm in the Cartesian domain, which is a gradient method defined on the basis of the Wirtinger calculus. At the early stage of optimization, each element of the hologram exists inside a complex circle, and it can take a large gradient while diverging from the origin. This characteristic contributes to accelerating the gradient descent. Meanwhile, at the final stage of optimization, each element evolves along a complex circle, similar to previous state-of-the-art gradient methods. The experimental results demonstrate that our method outperforms previous methods, primarily due to the optimization of the amplitude. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holographic Phase Retrieval via Wirtinger Flow: Cartesian Form with Auxiliary Amplitude Uchiyama, Ittetsu Tsutake, Chihiro Takahashi, Keita Fujii, Toshiaki Information Theory Graphics Numerical Analysis Image and Video Processing We propose a new gradient method for holography, where a phase-only hologram is parameterized by not only the phase but also amplitude. The key idea of our approach is the formulation of a phase-only hologram using an auxiliary amplitude. We optimize the parameters using the so-called Wirtinger flow algorithm in the Cartesian domain, which is a gradient method defined on the basis of the Wirtinger calculus. At the early stage of optimization, each element of the hologram exists inside a complex circle, and it can take a large gradient while diverging from the origin. This characteristic contributes to accelerating the gradient descent. Meanwhile, at the final stage of optimization, each element evolves along a complex circle, similar to previous state-of-the-art gradient methods. The experimental results demonstrate that our method outperforms previous methods, primarily due to the optimization of the amplitude. |
| title | Holographic Phase Retrieval via Wirtinger Flow: Cartesian Form with Auxiliary Amplitude |
| topic | Information Theory Graphics Numerical Analysis Image and Video Processing |
| url | https://arxiv.org/abs/2403.10560 |