Full Field Inversion of the Attenuated Wave Equation: Theory and Numerical Inversion
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917687331913728 |
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| author | Do, Ngoc Haltmeier, Markus Kowar, Richard Nguyen, Linh V. Nuster, Robert |
| author_facet | Do, Ngoc Haltmeier, Markus Kowar, Richard Nguyen, Linh V. Nuster, Robert |
| contents | Standard photoacoustic tomography (PAT) provides data that consist of time-dependent signals governed by the wave equation, which are measured on an observation surface. In contrast, the measured data from the recently invented full-field PAT is the Radon transform of the solution of the wave equation on a spatial domain at a single instant in time. While reconstruction using classical PAT data has been extensively studied, not much is known about the full-field PAT problem. In this paper, we study full-field photoacoustic tomography with spatially variable sound speed and spatially variable damping. In particular, we prove the uniqueness and stability of the associated single-time full-field wave inversion problem and develop algorithms for its numerical inversion using iterative and variational regularization methods. Numerical simulations are presented for both full-angle and limited-angle data cases |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_18082 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Full Field Inversion of the Attenuated Wave Equation: Theory and Numerical Inversion Do, Ngoc Haltmeier, Markus Kowar, Richard Nguyen, Linh V. Nuster, Robert Numerical Analysis Analysis of PDEs Standard photoacoustic tomography (PAT) provides data that consist of time-dependent signals governed by the wave equation, which are measured on an observation surface. In contrast, the measured data from the recently invented full-field PAT is the Radon transform of the solution of the wave equation on a spatial domain at a single instant in time. While reconstruction using classical PAT data has been extensively studied, not much is known about the full-field PAT problem. In this paper, we study full-field photoacoustic tomography with spatially variable sound speed and spatially variable damping. In particular, we prove the uniqueness and stability of the associated single-time full-field wave inversion problem and develop algorithms for its numerical inversion using iterative and variational regularization methods. Numerical simulations are presented for both full-angle and limited-angle data cases |
| title | Full Field Inversion of the Attenuated Wave Equation: Theory and Numerical Inversion |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2405.18082 |