Lipschitz stability at the boundary for time-harmonic diffuse optical tomography

Abstract

We study the inverse problem in Optical Tomography of determining the optical properties of a medium $\Omega \subset {\mathbb{R}}^n$, with $n\ge 3$, 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. We prove a result of Lipschitz stability of the absorption coefficient ${\mu }_a$ at the boundary $\partial \Omega$ in terms of the measurements in the case when the scattering coefficient ${\mu }_s$ is assumed to be known and $k$ belongs to certain intervals depending on some a-priori bounds on ${\mu }_a$, ${\mu }_s$.

22 pages