Ensemble Kalman inversion based on level set method for inverse elastic scattering problem

Abstract

We consider an ensemble Kalman inversion scheme for inverse elastic scattering problems in which the unknown quantity is the shape of the scatterer. Assume that the scatterer is a piecewise constant function with known value inside inhomogeneities. The level set method is described as an implicit representation of the scatterer boundary, with Gaussian random fields serving as prior to provide information on the level set functions. The ensemble Kalman filter method is then employed based on the level set functions to reconstruct the shape of the scatterer. We demonstrate the effectiveness of the proposed method using several numerical examples.