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

Soltanian, Fahimeh; Garshasbi, Morteza

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

Document Type : Research Paper

Authors

¹ Department of Mathematics, Payame Noor University, P. O. Box 19395-3697, Tehran, Iran

² Department of Mathematics, Iran University of Science and Technology, P. O. Box 16846-13114, Tehran, Iran

Abstract

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.

Keywords