Are the measurement data enough: an instability study for an inverse problem for the stationary radiative transport near the diffusion limit

Data Science Seminar

Hongkai Zhao (Duke University)

Abstract

Radiative transport equation is used widely to model propagation of particles through a scattering medium, such as photon transport in tissues in optical imaging. In this talk, I will present an instability study of an inverse problem of radiative transport equation with angularly independent source and angularly averaged measurement near the diffusion limit when the normalized mean free path is small. For the reconstruction of absorption coefficient, by analyzing the dimension mismatch between the measurement space and unknown space we show that the instability transition depends on the relative sizes between the mean free path and the perturbation in measurements.