Electrical properties reconstruction from MRI data: theoretical and numerical aspects

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 with synthetic data from both a 2D phantom and a 2D brain slice. The finite element method is used to discretize the boundary value problems, allowing complex geometries and realistic boundary conditions to be handled accurately.