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 $n\geq 3$, 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. 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 $\mu_a$, $\mu_s$.