Unknown functions estimation in a parabolic equation arises from Diffusion Tensor Magnetic Resonance Imaging

In this work, a general mathematical model of Diffusion Tensor Magnetic Resonance Imaging is formulated as an inverse problem. An effective numerical approach based on space marching method and mollifcation scheme is established to solve this problem. Convergence and stability of proposed approach are established. Using two test problems, the robustness and ability of the numerical approach is investigated.