Simultaneous uniqueness and numerical inversion for an inverse problem in the time-domain diffuse optical tomography with fluorescence

In this work, an inverse problem on the determination of multiple coefficients arising from the time-domain diffuse optical tomography with fluorescence (DOT-FDOT) is investigated. We simultaneously recover the distribution of background absorption coefficient, photon diffusion coefficient as well as the fluorescence absorption in biological tissue by the time-dependent boundary measurements. We build the uniqueness theorem of this multiple coefficients simultaneous inverse problem. After that, the numerical inversions are considered. We introduce an accelerated Landweber iterative algorithm and give several numerical examples illustrating the performance of the proposed inversion schemes.