Simultaneous uniqueness and numerical inversion for an inverse problem in a coupled diffusion system

In this work, we investigate an inverse problem in determining multiple coefficients in a coupled diffusion system arising from the time-domain diffuse optical tomography with fluorescence. We simultaneously recover the distribution of the background absorption coefficient, photon diffusion coefficient, and fluorescence absorption in biological tissue by time-dependent boundary measurements. We build the uniqueness theorem for this multiple coefficients simultaneous inverse problem. After that, the numerical inversions for non-smooth absorption featuring various shaped inclusions are considered.