Inverse problems arising in microwave imaging suffer from high ill-posedness. As it is well known, it is necessary to employ regularized inversion methods, in order to mitigate such behavior. Usually, such approaches are formulated in standard Hilbert spaces. Recently, a more generic regularization theory, working in Banach spaces, has been investigated, in order to overcome some limitations of the Hilbert-space regularization. In this paper, a novel imaging algorithm, performing a L^p Banach-space regularization, is proposed for 2-D electromagnetic inverse scattering problems. The reconstruction capabilities of the methods are evaluated by using numerical and experimental data.

A conjugate-gradient-based regularization technique in L ^p Banach spaces, in conjunction with an inexact-Newton solving scheme, is presented in this paper. The proposed method is applied to obtain the reconstruction of the dielectric properties of human tissues in hemorrhagic brain stroke microwave imaging. The dielectric reconstruction is obtained by solving a nonlinear inverse problem, starting from a set of scattered-field measurements. The presented numerical simulations with 2-D and 3-D anatomically realistic phantoms, as well as the preliminary experimental results, show that this method can be useful for retrieving the dielectric properties of the human head with a reduced over-smoothing effect in the final images.

An approach to solve the inverse scattering problem for imaging applications is presented. The proposed algorithm is based on an inexact Newton method applied to the Lippmann-Schwinger integral equation. Inhomogeneous dielectric scatterers with high contrast in a tomographic arrangement are considered. The capabilities of the approach are assessed with reference to several different unknown objects. In particular, both noisy synthetic data and experimental data have been used. Furthermore, a comparison with a model based on the second order Born approximation is also reported.

An electromagnetic inverse scattering approach for imaging of shallow subsurface objects is reported. It extends to multifrequency processing, an efficient method previously developed for single frequency imaging. The considered approach is an iterative procedure based on an inexact-Newton method developed in L Banach spaces, which exhibits effective regularization capabilities and reduced over-smoothing effects. The approach is validated using numerical simulations in which cylindrical scatterers are reconstructed in a homogeneous lossy medium. Results are compared with those obtained using standard single frequency operating conditions.