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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.17102 |
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| _version_ | 1866914967747297280 |
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| author | Ueda, Hajime Katakami, Shun Okada, Masato |
| author_facet | Ueda, Hajime Katakami, Shun Okada, Masato |
| contents | Phase retrieval refers to the problem of recovering a high-dimensional vector $\boldsymbol{x} \in \mathbb{C}^N$ from the magnitude of its linear transform $\boldsymbol{z} = A \boldsymbol{x}$, observed through a noisy channel. To improve the ill-posed nature of the inverse problem, it is a common practice to observe the magnitude of linear measurements $\boldsymbol{z}^{(1)} = A^{(1)} \boldsymbol{x},..., \boldsymbol{z}^{(L)} = A^{(L)}\boldsymbol{x}$ using multiple sensing matrices $A^{(1)},..., A^{(L)}$, with ptychographic imaging being a remarkable example of such strategies. Inspired by existing algorithms for ptychographic reconstruction, we introduce stochasticity to Vector Approximate Message Passing (VAMP), a computationally efficient algorithm applicable to a wide range of Bayesian inverse problems. By testing our approach in the setup of phase retrieval, we show the superior convergence speed of the proposed algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Vector Approximate Message Passing with applications to phase retrieval Ueda, Hajime Katakami, Shun Okada, Masato Computation Phase retrieval refers to the problem of recovering a high-dimensional vector $\boldsymbol{x} \in \mathbb{C}^N$ from the magnitude of its linear transform $\boldsymbol{z} = A \boldsymbol{x}$, observed through a noisy channel. To improve the ill-posed nature of the inverse problem, it is a common practice to observe the magnitude of linear measurements $\boldsymbol{z}^{(1)} = A^{(1)} \boldsymbol{x},..., \boldsymbol{z}^{(L)} = A^{(L)}\boldsymbol{x}$ using multiple sensing matrices $A^{(1)},..., A^{(L)}$, with ptychographic imaging being a remarkable example of such strategies. Inspired by existing algorithms for ptychographic reconstruction, we introduce stochasticity to Vector Approximate Message Passing (VAMP), a computationally efficient algorithm applicable to a wide range of Bayesian inverse problems. By testing our approach in the setup of phase retrieval, we show the superior convergence speed of the proposed algorithm. |
| title | Stochastic Vector Approximate Message Passing with applications to phase retrieval |
| topic | Computation |
| url | https://arxiv.org/abs/2408.17102 |