Quasi-Newton methods in optical tomographic image reconstruction

Optical tomography (OT) recovers the cross-sectional distribution of optical parameters inside a highly scattering medium from information contained in measurements that are performed on the boundaries of the medium. The image reconstruction problem in OT can be considered as a large-scale optimization problem, in which an appropriately defined objective function needs to be minimized. In the simplest case, the objective function is the least-square error norm between the measured and the predicted data. In biomedical applications that apply near-infrared light as the probing tool the predictions are obtained from a model of light propagation in tissue. Gradient techniques are commonly used as optimization methods, which employ the gradient of the objective function with respect to the optical parameters to find the minimum. Conjugate gradient (CG) techniques that use information about the first derivative of the objective function have shown some good results in the past. However, this approach is frequently characterized by low convergence rates. To alleviate this problem we have implemented and studied so-called quasi-Newton (QN) methods, which use approximations to the second derivative. The performance of the QN and CG methods are compared by utilizing both synthetic and experimental data.