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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2510.26227 |
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| _version_ | 1866917050250690560 |
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| author | Pan, Guanyu Zhou, Jianing Liu, Xiaotong Huang, Yunqing Yi, Nianyu |
| author_facet | Pan, Guanyu Zhou, Jianing Liu, Xiaotong Huang, Yunqing Yi, Nianyu |
| contents | Inverse source localization from Helmholtz boundary data collected over a narrow aperture is highly ill-posed and severely undersampled, undermining classical solvers (e.g., the Direct Sampling Method). We present a modular framework that significantly improves multi-source localization from extremely sparse single-frequency measurements. First, we extend a uniqueness theorem for the inverse source problem, proving that a unique solution is guaranteed under limited viewing apertures. Second, we employ a Deep Operator Network (DeepONet) with a branch-trunk architecture to interpolate the sparse measurements, lifting six to ten samples within the narrow aperture to a sufficiently dense synthetic aperture. Third, the super-resolved field is fed into the Direct Sampling Method (DSM). For a single source, we derive an error estimate showing that sparse data alone can achieve grid-level precision. In two- and three-source trials, localization from raw sparse measurements is unreliable, whereas DeepONet-reconstructed data reduce localization error by about an order of magnitude and remain effective with apertures as small as $π/4$. By decoupling interpolation from inversion, the framework allows the interpolation and inversion modules to be swapped with neural operators and classical algorithms, respectively, providing a practical and flexible design that improves localization accuracy compared with standard baselines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26227 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Transcending Sparse Measurement Limits: Operator-Learning-Driven Data Super-Resolution for Inverse Source Problem Pan, Guanyu Zhou, Jianing Liu, Xiaotong Huang, Yunqing Yi, Nianyu Numerical Analysis Inverse source localization from Helmholtz boundary data collected over a narrow aperture is highly ill-posed and severely undersampled, undermining classical solvers (e.g., the Direct Sampling Method). We present a modular framework that significantly improves multi-source localization from extremely sparse single-frequency measurements. First, we extend a uniqueness theorem for the inverse source problem, proving that a unique solution is guaranteed under limited viewing apertures. Second, we employ a Deep Operator Network (DeepONet) with a branch-trunk architecture to interpolate the sparse measurements, lifting six to ten samples within the narrow aperture to a sufficiently dense synthetic aperture. Third, the super-resolved field is fed into the Direct Sampling Method (DSM). For a single source, we derive an error estimate showing that sparse data alone can achieve grid-level precision. In two- and three-source trials, localization from raw sparse measurements is unreliable, whereas DeepONet-reconstructed data reduce localization error by about an order of magnitude and remain effective with apertures as small as $π/4$. By decoupling interpolation from inversion, the framework allows the interpolation and inversion modules to be swapped with neural operators and classical algorithms, respectively, providing a practical and flexible design that improves localization accuracy compared with standard baselines. |
| title | Transcending Sparse Measurement Limits: Operator-Learning-Driven Data Super-Resolution for Inverse Source Problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.26227 |