MATJ5130 IP2: Mathematics of Electrical Impedance Tomography (JSS35) (2 cr)

This course focuses on mathematical aspects of electrical impedance tomography (EIT). A simple pixel-based diffusion model serves as a gentle introduction to the principle of EIT measurement, illustrating key challenges. Calderón’s inverse conductivity problem is then derived from Maxwell’s equations, and basic properties of the conductivity equation are discussed. Some knowledge of elliptic partial differential equations and Fourier transforms is useful here, but there is a strong effort to make the material as self-contained as possible. Analytic expressions are computed for the Dirichlet-to-Neumann map in case of rotationally symmetric conductivities. This makes it possible to study in concrete terms (i) Alessandrini’s example showing the ill-posedness of EIT, (ii) Calder’on’s original reconstruction approach, and (iii) Ikehata’s enclosure method. The rest of the course is devoted to the use of Complex Geometric Optics solutions for uniqueness proofs and reconstruction via the D-bar method. Recommended to take together with Electrical Impedance Tomography: Computation and Applications

Insight into the theory of EIT, including nonlinearity, ill-posedness, and reconstruction approaches.

IP2: Mathematics of Electrical Impedance Tomography (JSS35)