The forward and inverse models in time-resolved optical tomography imaging and their finite-element method solutions

Abstract

Time-resolved optical computerized tomographic imaging has gained widespread attention in biomedical research recently because of its non-invasiveness and non-destructiveness to biological and several attempts, aimed at implementing a practical system, have been made for eliminating the obstacles arising from multiple light scattering of biological tissue. In this paper the basic principle of time-resolved optical absorption and scattering tomography is first presented. The diffusion approximation-based photon transport model in a highly scattering tissue, which offers an advantage in speed in comparison vath other stochastic models, and the procedure for solving this forward model by using the finite-element method (FEM) are then accessed. Theoretically, a commonly used iterative steepest descent algorithm for solving the inverse problem is introduced based on the FEM solution of Jacobian of the forward operator. Owing to the ill-posed Jacobian matrix of the forward operator caused by scatter-dominated photon propagation and unavoidable influence of the noise from the measurement process, a Tikhonov–Miller regularization method is applied to the inverse problem in order to provide an acceptable approximation to its solution. A universal strategy for the FEM solution to the optical tomography problem several numerically simulated images of absorbers and scatters embedded in a homogeneous tissue sample are reconstructed from either mean-time-of-flight or integrated intensity data for the verification of the approach.