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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.19064 |
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| _version_ | 1866909753547948032 |
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| author | Shi, Cong |
| author_facet | Shi, Cong |
| contents | In this paper, we derive explicit reconstruction formulas for two common measurement geometries: a plane and a sphere. The problem is formulated as inverting the forward operator $R^a$, which maps the initial source to the measured wave data. Our first result pertains to planar observation surfaces. By extending the domain of $R^a$ to tempered distributions, we provide a complete characterization of its range and establish that the inverse operator $(R^a)^{-1}$ is uniquely defined and "almost" continuous in the distributional topology. Our second result addresses the case of a spherical observation geometry. Here, with the operator acting on $L^2$ spaces, we derive a stable reconstruction formula of the filtered backprojection type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit Inversion of the Attenuated Photoacoustic Operator in General Observation Geometries Shi, Cong Analysis of PDEs Mathematical Physics In this paper, we derive explicit reconstruction formulas for two common measurement geometries: a plane and a sphere. The problem is formulated as inverting the forward operator $R^a$, which maps the initial source to the measured wave data. Our first result pertains to planar observation surfaces. By extending the domain of $R^a$ to tempered distributions, we provide a complete characterization of its range and establish that the inverse operator $(R^a)^{-1}$ is uniquely defined and "almost" continuous in the distributional topology. Our second result addresses the case of a spherical observation geometry. Here, with the operator acting on $L^2$ spaces, we derive a stable reconstruction formula of the filtered backprojection type. |
| title | Explicit Inversion of the Attenuated Photoacoustic Operator in General Observation Geometries |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2508.19064 |