System identification using nonlinear filtering methods with applications to medical imaging

We first review the concept of computational tomography (CT) and laser technique using the photon diffusion equation. The forward and inverse problems are two key problems concerned with the diffusion equation, while the solution to the latter one is the goal of research in optical CT. The inverse problem can be stated as follows: given the photon density measured from the detectors outside the tissue, we need to find the anomalies (benign or malignant) inside the tissue. We model the forward and inverse problems using state-space equations and pose the inverse problem as a system identification problem. The nonlinear filtering techniques, namely the extended Kalman filter and the second order filter, are proposed to solve the inverse problem. Comparisons are made through an example of a medical imaging problem.