Inverse acoustic scattering for random obstacles with multi-frequency data

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Hauptverfasser: Sun, Zhiqi, Xu, Xiang, Lin, Yiwen
Format: Preprint
Veröffentlicht: 2026
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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