Inversion Methods for Malign Melanoma Detection

Abstract

This thesis concerns the coefficient inverse problem from Maxwell’s equations, related to finding the electric permittivity and conductivity using backscattered time-dependent electrical fields. The aim is to reconstruct the permittivity and conductivity of Malignant Melanoma tissues, both in shape and in values. The forward problem is solved using a Domain Decomposition method, where both the Finite Element Method and the Finite Difference Method is used. The inverse problem is solved by the Conjugate Gradient Descent method, and numerical examples are performed in a homogeneous and non-homogeneous setting while adaptively refining a finite element mesh.