Electrical properties reconstruction from MRI data: theoretical and numerical aspects

Overview & Synopsis

The paper presents an inverse problem for the reconstruction of the electrical properties of the human brain from Magnetic Resonance Imaging $B^+-1$-data. We establish a rigorous mathematical framework for the formulation of the inverse problem and provide an identifiability result. To achieve a robust numerical solution, the contrast source inversion method is successfully applied to both academic and realistic configurations. The finite element method is used to discretize the boundary value problems, allowing complex geometries and realistic boundary conditions to be handled accurately.