Approximate peak time and a global reconstruction algorithm for time-domain fluorescence diffuse optical tomography

This paper concerns a global reconstruction method for fluorescence diffuse optical tomography (FDOT), reconstructing locations of multiple point targets from the measured temporal response functions. The targets are multiple fluorescent point objects with a nonzero fluorescence lifetime at unknown locations. Peak time, when the temporal response function of the fluorescence reaches its maximum, is a robust parameter of the temporal response function in FDOT. We derive an approximate peak time equation based on asymptotic analysis in an explicit way for the nonzero fluorescence lifetime when either single or multiple point targets exist. Then we develop a global bisection method to reconstruct the location of a single point target globally. Moreover, we adopt the global bisection method for the reconstruction of the locations of multiple point targets. Finally, several numerical experiments are implemented to show the efficiency and robustness of the addressed algorithms.