Direct inversion scheme of time-domain fluorescence diffuse optical tomography by asymptotic analysis of peak time

This paper proposes a direct inversion scheme for fluorescence diffuse optical tomography (FDOT) to reconstruct the location of a point target using the measured peak times of the temporal response functions. We show that the peak time approximately determines the radius of a sphere with the target lying on its surface. Then, we reconstruct the location of the target as a vertex of the tetrahedron, whose edges are determined by the radii. In other words, we derive an asymptotic relationship between the radius of the sphere and the peak time in the case of single point target. Multiple point targets case is also considered. We conduct several numerical tests to demonstrate the accuracy and performance of the asymptotic relationship and the inversion scheme.