论文标题
在边界处的Lipschitz稳定性，以进行时间谐波弥漫性光学断层扫描
Lipschitz stability at the boundary for time-harmonic diffuse optical tomography
论文作者
论文摘要
我们研究了在所谓的扩散近似下，确定介质$ω\ subset \ mathbb {r}^n $的光学特性的逆问题，该特性具有$ n \ geq 3 $。我们考虑使用固定谐波频率$ω= \ frac {k} {c} $调制的输入字段探测$ω$的时间谐波案例，其中$ c $是光的速度，$ k $是波浪号。我们证明，在尺寸$ \\partialΩ$的Lipschitz稳定性在测量方面的稳定性$ \\partialΩ$，当时假定散射系数$μ_s$已知，并且根据$μ_A$ $μ__s$ $ $μ_s的某些A PRIORI范围，$ k $属于$ k $。
We study the inverse problem in Optical Tomography of determining the optical properties of a medium $Ω\subset\mathbb{R}^n$, with $n\geq 3$, under the so-called diffusion approximation. We consider the time-harmonic case where $Ω$ is probed with an input field that is modulated with a fixed harmonic frequency $ω=\frac{k}{c}$, where $c$ is the speed of light and $k$ is the wave number. We prove a result of Lipschitz stability of the absorption coefficient $μ_a$ at the boundary $\partialΩ$ in terms of the measurements in the case when the scattering coefficient $μ_s$ is assumed to be known and $k$ belongs to certain intervals depending on some a-priori bounds on $μ_a$, $μ_s$.
