Time-harmonic diffuse optical tomography: H\'older stability of the derivatives of the optical properties of a medium at the boundary
| Autor: | Curran, Jason, Gaburro, Romina, Nolan, Clifford J., Somersalo, Erkki |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study the inverse problem in Optical Tomography of determining the optical properties of a medium $\Omega\subset\mathbb{R}^n$, with $n\geq 3$, under the so-called diffusion approximation. We consider the time-harmonic case where $\Omega$ is probed with an input field that is modulated with a fixed harmonic frequency $\omega=\frac{k}{c}$, where $c$ is the speed of light and $k$ is the wave number. Under suitable conditions that include a range of variability for $k$, we prove a result of H\"older stability of the derivatives of the absorption coefficient $\mu_a$ of any order at the boundary $\partial\Omega$ in terms of the measurements, in the case when the scattering coefficient $\mu_s$ is assumed to be known. The stability estimates rely on the construction of singular solutions of the underlying forward elliptic system, which extend results obtained in J. Differential Equations 84 (2): 252-272 for the single elliptic equation. Comment: arXiv admin note: substantial text overlap with arXiv:2002.01828 |
| Databáze: | arXiv |
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