A numerical algorithm for the diffusion equation using 3D FEM and the Arnoldi method [human tissue cells detection]

We introduce a computational method for solving the photon diffusion equation in an unusual human cells detection problem. In particular, we construct a "generalized" state-space system and compute the impulse response of an equivalent truncated state-space system. We use a 3D finite element method (FEM) to obtain the state space system. Secondly, we use the Arnoldi iteration to approximate the state impulse response by projecting on the dominant controllable subspace. The idea exploited here is the approximation of the impulse response of the linear system. The homogeneous and heterogeneous cases are studied and the approximation error is discussed. Finally, we compare our computational results to our experimental set up.