Tommaso Isernia

Multiresolution techniques in microwave tomography and subsurface sensing

The application of multiresolution techniques to subsurface sensing in the framework of linearized models of the scattering equation and in 2D geometry is considered. In particular, two approaches based on the so called fixed and adaptive multiresolution schemes, are been proposed.

2D inverse scattering: degree of nonlinearity, solution strategies, and polarization effects

Quantifying the degree of non linearity with respect to the permittivity profile represents in interesting possibility for quantifying the difficulty of both forward and inverse scattering problems. With reference to the 2D case, in this paper new tools are proposed that allow to determine the degree of non linearity while changing maximum value, dimensions and spatial frequency content of the unknown permittivity profile, as well as polarization of the incident field. As such, the proposed tools allow to identify new solution strategy for the inverse problem and the simpler nature of the TE (vectorial) problem. Numerical examples support the conclusion.

A bilinear approach for subsurface sensing: numerical results

A bilinear approach for the solution of the ill posed problem of subsurface imaging by ground penetrating radar is proposed and discussed. A numerical validation showing the usefulness of the technique is also reported.

Wavelets in non-linear inverse scattering

In Chiappinelli et al. (1999) we have shown the usefulness of wavelet expansions in linearized inverse scattering problems. In this communication we motivate the use of wavelet expansions and show their usefulness in the non-linearized case through numerical examples. Two different approaches, which we call fixed and adaptive multiresolution respectively, are dealt with.

3D Markov Random Field in realistic inverse scattering

This communication deals with the reconstruction of three-dimensional target from experimental multiple-frequency data measured in the anechoic chamber of the Institut Fresnel (Marseille, France). In order to take into account the random noise present in the experiments, a Bayesian approach is considered. In particular, the inversion procedure takes advantage from the joint use of the Contrast Source-Extended Born model and of a Markov Random Field regularization. We also considered a cost functional appropriately weighted by coefficients which change with the frequency, the incident angle and the receiving angle. In fact, each scattered field measurement is balanced with the noise disturbing the data.

Reconstruction of complex dielectric profiles via quadratic models

The electromagnetic inverse scattering problem deserves special attention in many branches of applied science. Besides theoretical uniqueness of a solution and limitations induced from measurement errors, the development of solution algorithms effectively capable to retrieve the unknown parameters in a reliable way should be addressed. In order to discuss factors affecting accuracy and reliability of solution algorithms the authors refer in the following, by the sake of simplicity, to a two dimensional (2D) geometry. All results can be extended to the 3D case. The authors consider an inhomogeneous object, whose compact support is /spl Omega/, imbedded in an homogeneous medium. Equations are developed for the scattered field. The inverse scattering problem is solved by a quadratic model.

SAR constrained focusing through multi-frequency array applicators

A method for constrained focusing or shaping of the Specific Absorption Rate deposition is proposed and discussed. The approach contemporarily takes advantage from multifre-quency applicators, which allow a better control of possible hot-spots, as well as from the proposed formulation, which allows to reduce the problem to a single or a series of Convex programming problems. The approach is presented for the case of scalar fields but it can be extended to vector fields as well.