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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/2410.05098 |
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| _version_ | 1866912062131666944 |
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| author | Ning, Jianfeng Zou, Jun |
| author_facet | Ning, Jianfeng Zou, Jun |
| contents | This work studies an inverse scattering problem when limited-aperture data are available that are from just one or a few incident fields. This inverse problem is highly ill-posed due to the limited receivers and a few incident fields employed. Solving inverse scattering problems with limited-aperture data is important in applications as collecting full data is often either unrealistic or too expensive. The direct sampling methods (DSMs) with full-aperture data can effectively and stably estimate the locations and geometric shapes of the unknown scatterers with a very limited number of incident waves. However, a direct application of DSMs to the case of limited receivers would face the resolution limit. To break this limitation, we propose a finite space framework with two specific schemes, and an unsupervised deep learning strategy to construct effective probing functions for the DSMs in the case with limited-aperture data. Several representative numerical experiments are carried out to illustrate and compare the performance of different proposed schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constructing probing functions for direct sampling methods for inverse scattering problems with limited-aperture data: finite space framework and deep probing network Ning, Jianfeng Zou, Jun Numerical Analysis This work studies an inverse scattering problem when limited-aperture data are available that are from just one or a few incident fields. This inverse problem is highly ill-posed due to the limited receivers and a few incident fields employed. Solving inverse scattering problems with limited-aperture data is important in applications as collecting full data is often either unrealistic or too expensive. The direct sampling methods (DSMs) with full-aperture data can effectively and stably estimate the locations and geometric shapes of the unknown scatterers with a very limited number of incident waves. However, a direct application of DSMs to the case of limited receivers would face the resolution limit. To break this limitation, we propose a finite space framework with two specific schemes, and an unsupervised deep learning strategy to construct effective probing functions for the DSMs in the case with limited-aperture data. Several representative numerical experiments are carried out to illustrate and compare the performance of different proposed schemes. |
| title | Constructing probing functions for direct sampling methods for inverse scattering problems with limited-aperture data: finite space framework and deep probing network |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2410.05098 |