Inverse acoustic scattering for random obstacles with multi-frequency data
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908799150850048 |
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| author | Sun, Zhiqi Xu, Xiang Lin, Yiwen |
| author_facet | Sun, Zhiqi Xu, Xiang Lin, Yiwen |
| contents | We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically well-defined and physically consistent, the Gaussian process admits a parameterization via Karhunen--Loève (KL) expansion. Based on observed multi-frequency data, we develop a two-stage inversion method: the first stage reconstructs the baseline shape of the random scatterer and the second stage estimates the statistical characteristics of the boundary fluctuations, including KL eigenvalues and covariance hyperparameters. We further provide theoretical justifications for the modeling and inversion pipeline, covering well-definedness of the Gaussian-process model, convergence for the two-stage procedure and a brief discussion on uniqueness. Numerical experiments demonstrate stable recovery of both geometric and statistical information for obstacles with simple and more complex shapes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22560 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inverse acoustic scattering for random obstacles with multi-frequency data Sun, Zhiqi Xu, Xiang Lin, Yiwen Numerical Analysis We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically well-defined and physically consistent, the Gaussian process admits a parameterization via Karhunen--Loève (KL) expansion. Based on observed multi-frequency data, we develop a two-stage inversion method: the first stage reconstructs the baseline shape of the random scatterer and the second stage estimates the statistical characteristics of the boundary fluctuations, including KL eigenvalues and covariance hyperparameters. We further provide theoretical justifications for the modeling and inversion pipeline, covering well-definedness of the Gaussian-process model, convergence for the two-stage procedure and a brief discussion on uniqueness. Numerical experiments demonstrate stable recovery of both geometric and statistical information for obstacles with simple and more complex shapes. |
| title | Inverse acoustic scattering for random obstacles with multi-frequency data |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.22560 |