Reconstruction of magnetic charge densities using regularization of bounded variations under noisy observations

Abstract

This paper is concerned with computational and regularization techniques for recovering induced magnetic fields due to the existence of cracks. The problem is formulated as an inverse problem with a set of source functions of the distribution type. The regularization of bounded variation is effectively used for solving the severe ill-posed problem. A iterative solver is proposed by a integro-differential equation with time marching scheme. For the practical implementation of the numerical treatment, a finite difference scheme is adopted to the proposed method with the aid of discrete fast Fourier transform. Some successful numerical experiments are demonstrated for the validity of the proposed method.