Instability of an Inverse Problem for the Stationary Radiative Transport Near the Diffusion Limit

Source abstract

In this work, we study the instability of an inverse problem of radiative transport equation with angularly independent source and angularly averaged measurement near the diffusion limit, i.e., the normalized mean free path (the Knudsen number) $0 < \varepsilon \ll 1$. For the reconstruction of absorption coefficient, we show that instability depends on the relative sizes between $\varepsilon$ and the perturbation in measurements. When $\varepsilon$ is sufficiently small, we obtain exponential instability, which stands for the diffusion regime, and otherwise we obtain Hölder instability instead, which stands for the transport regime.