Truncated Newton's optimization scheme for absorption and fluorescence optical tomography: Part I theory and formulation

The development of non-invasive, biomedical optical imaging from time-dependent measurements of near-infrared (NIR) light propagation in tissues depends upon two crucial advances: (i) the instrumental tools to enable photon "time-of-flight" measurement within rapid and clinically realistic times, and (ii) the computational tools enabling the reconstruction of interior tissue optical property maps from exterior measurements of photon "time-of-flight" or photon migration. In this contribution, the image reconstruction algorithm is formulated as an optimization problem in which an interior map of tissue optical properties of absorption and fluorescence lifetime is reconstructed from synthetically generated exterior measurements of frequency-domain photon migration (FDPM). The inverse solution is accomplished using a truncated Newton's method with trust region to match synthetic fluorescence FDPM measurements with that predicted by the finite element prediction. The computational overhead and error associated with computing the gradient numerically is minimized upon using modified techniques of reverse automatic differentiation. (C) 1999 Optical Society of America.