Convexification Numerical Method for Imaging of Moving Targets
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909972453916672 |
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| author | Klibanov, Michael V. Li, Jingzhi Romanov, Vladimir G. Yang, Zhipeng |
| author_facet | Klibanov, Michael V. Li, Jingzhi Romanov, Vladimir G. Yang, Zhipeng |
| contents | The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running along a straight line is used. Lateral Cauchy data are known for each position of the point source. A truncated Fourier series with respect to a special orthonormal basis is used. First, Lipschitz stability estimate is obtained. Next, a globally convergent numerical method, the so-called convexification method, is developed and its convergence analysis is carried out. The convexification method is based on a Carleman estimate. Results of numerical experiments are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convexification Numerical Method for Imaging of Moving Targets Klibanov, Michael V. Li, Jingzhi Romanov, Vladimir G. Yang, Zhipeng Numerical Analysis The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running along a straight line is used. Lateral Cauchy data are known for each position of the point source. A truncated Fourier series with respect to a special orthonormal basis is used. First, Lipschitz stability estimate is obtained. Next, a globally convergent numerical method, the so-called convexification method, is developed and its convergence analysis is carried out. The convexification method is based on a Carleman estimate. Results of numerical experiments are presented. |
| title | Convexification Numerical Method for Imaging of Moving Targets |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2512.18361 |