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A highly efficient iterative approach for inverse acoustic obstacle scattering problems in three dimensions
Abstract
This paper concerns a three-dimensional inverse acoustic obstacle scattering problem from scattered field or phased/phaseless far-field data. Based on the boundary integral defined on a homothetic surface, we propose a highly efficient iterative approach for obstacle reconstruction that completely avoids dealing with any singularity. Here, the injectivity and dense-range property of the Fréchet derivative have been proved to ensure the solvability of the linearized equivalent data equation. We also prove that the scattered field generated by the homothetic surface can arbitrarily approximate the exact one. Numerical experiments are presented to verify the superiority and robustness of the proposed approach.
Versions
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BibTeX
@misc{cheng2026highly,
title = {{A highly efficient iterative approach for inverse acoustic obstacle scattering problems in three dimensions}},
author = {Zhiyong Cheng and Heping Dong and Lu Zhao},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2607.02180},
eprint = {2607.02180},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.02180},
}
RIS
TY - UNPB
TI - A highly efficient iterative approach for inverse acoustic obstacle scattering problems in three dimensions
AU - Zhiyong Cheng
AU - Heping Dong
AU - Lu Zhao
PY - 2026
DA - 2026/07/02
PB - arXiv
DO - 10.48550/arxiv.2607.02180
UR - https://arxiv.org/abs/2607.02180
AB - This paper concerns a three-dimensional inverse acoustic obstacle scattering problem from scattered field or phased/phaseless far-field data. Based on the boundary integral defined on a homothetic surface, we propose a highly efficient iterative approach for obstacle reconstruction that completely avoids dealing with any singularity. Here, the injectivity and dense-range property of the Fréchet derivative have been proved to ensure the solvability of the linearized equivalent data equation. We also prove that the scattered field generated by the homothetic surface can arbitrarily approximate the exact one. Numerical experiments are presented to verify the superiority and robustness of the proposed approach.
ER -