Studies On Reconstruction Algorithm For Optical Tomography Under Robin Boundary Condition

In recent years, time-resolved Optical Tomography (OT), which is a new technique for biomedical research, has attracted much attention because of its non-invasiveness, real time and non-destructiveness, which are impossible for other imaging techniques, to biological and medical problem.There are two kinds of boundary conditions for diffusion equation, which are the Robin Boundary Condition (RBC) and the Dirichlet Boundary Condition (DBC). Although it is quite complex, RBC is much closer to the actual physical application and hence it is selected for image reconstruction in this thesis.In this thesis, the forward simulation method for solving the Diffusion Equation is firstly studied with FEM, from which the integral photon density of the tissue and some data type needed for the image reconstruction are obtained. Comparison between the results of the DBC and those of the RBC are performed for the placement of the sources and set the detectors. Secondly, the formation of the Jacobian matrix is analyzed with the forward model and, meanwhile, the impacts of the perturbation on the Jacobian Matrix are also analyzed. Finally, the image reconstruction algorithm is proposed under RBC, which actually uses iterative procedure to solve least squares problem. Experimental resultsof image reconstruction under RBC exhibit excellent performance of proposed method in this thesis, which also can be a reference for further study.