Adaptive finite element methods for distributed parameter system identification: applications in fluorescence enhanced frequency domain optical tomography

This article addresses the distributed parameter system identification problem encountered in fluorescence enhanced optical tomography. Adaptive mesh refinement techniques can increase the efficiency of estimation algorithms by reducing the computational storage as well as tailoring the solution strategy to the problem structure. An adaptive refinement based Galerkin finite element scheme for coupled photon diffusion equations is implemented with a simply bound limited memory quasi-Newton algorithm, which is suitable for large scale nonlinear optimization. The efficacy of the proposed scheme is demonstrated on two dimensional test cases.