System identification using the extended Kalman filter with applications to medical imaging

We first review the concept of computational tomography (CT) and a laser technique using the photon diffusion equation. The forward and the inverse problems are two key problems concerned with the photon 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 the inverse problem using state-space equations and use the extended Kalman filtering method to solve the inverse problem. The convergence property of the filter is analyzed and examples of using the extended Kalman filtering method to solve the inverse problem are also given