Inverse Scattering Using a Kohn-Vogelius Formulation and Shape Optimization Method

This paper presents a method to retrieve the form of a metallic object given partial electromagnetic measurements. We propose a numerical resolution of this inverse problem based on a shape optimization method. More precisely, we aim to minimize the so-called Kohn-Vogelius functional, which is numerically more stable than the least squares functional, by computing its shape gradient. The optimization problem is then solved using a Nesterov inertial scheme to accelerate the descent algorithm. Numerical simulations in 2D are provided to highlight the efficiency of the proposed method.