Electromagnetic inversion for subsurface applications under the Distorted Born Approximation

The problem of reconstructing dielectric permittivity of a buried object fr om the knowledge of the scattered field is considered for a two-dimensional rectangular geometry at a fixed frequency. The linearization of the mathem atical relationship between the dielectric permittivity function and the sc attered field about a constant reference profile function and the approxima tion of actual internal field with the unperturbed field leads to the so-ca lled Distorted Born approximation. To analyze the limitations and capabilit ies of the linear inversion algorithms, we investigate the class of the ret rievable profiles. This analysis makes it possible to point out that a very reduced number of independent data is available, so requiring to employ re gularization techniques in order to perform in a reliable and stable way th e linear inversions. In this paper we present a general algorithm consistin g in a regularized Singular Value Decomposition of the matrix resulting fro m a discretization of tile problem. Finally, numerical results of linear in versions are given.