Novel Inverse-Scattering Methods in Banach Spaces

The scientific community is presently strongly interested in the research of new microwave imaging methods, in order to develop reliable, safe, portable, and cost-effective tools for the non-invasive/non-destructive diagnostic in many fields (such as medicine, civil and industrial engineering, \u2026). In this framework, microwave imaging techniques addressing the full three-dimensional nature of the inspected bodies are still very challenging, since they need to cope with significant computational complexity. Moreover, non-linearity and ill-posedness issues, which usually affects the related inverse scattering problems, need to be faced, too. Another promising topic is the development of phaseless methods, in which only the amplitude of the electric field is assumed to be measurable. This leads to a significant complexity reduction and lower cost for the experimental apparatuses, but the missing information on the phase of the electric field samples exacerbates the ill-posedness problems. In the present Thesis, a novel inexact-Newton inversion algorithm is proposed, in which the iteratively linearized problems are solved in a regularized sense by using a truncated Landweber or a conjugate gradient method developed in the framework of the l^p Banach spaces. This is an improvement that allows to generalize the classic framework of the l^2 Hilbert spaces in which the inexact-Newton approaches are usually defined. The applicability of the proposed imaging method in both the 3D full-vector and 2D phaseless scenarios at microwave frequencies is assessed in this Thesis, and an extensive validation of the proposed imaging method against both synthetic and experimental data is presented, highlighting the advantages over the inexact-Newton scheme developed in the classic framework of the l^2 Hilbert spaces

Microwave Imaging of 3D Dielectric Structures by Means of a Newton-CG Method in Spaces

An increasing number of practical applications of three-dimensional microwave imaging require accurate and efficient inversion techniques. In this context, a full-wave 3D inverse-scattering method, aimed at characterizing dielectric targets, is described in this paper. In particular, the inversion approach has a Newton-based structure, in which the internal linear solver is a conjugate gradient-like algorithm in lp spaces. The presented results, which include the inversion of both numerical and experimental scattered-field data obtained in the presence of homogeneous and inhomogeneous targets, validate the reconstruction capabilities of the proposed technique

Hemorrhagic brain stroke detection by using microwaves: Preliminary two-dimensional reconstructions

Preliminary numerical results concerning the application of a Gauss-Newton method for diagnostic purposes of hemorrhagic brain strokes are reported. Interrogating microwaves are used in a multistatic and multiview arrangement. The reported results concern a two-dimensional model under transverse magnetic illumination conditions

Nonlinear electromagnetic inverse scattering in via Frozen or Broyden update of the Fr\ue9chet derivative

Microwave imaging methods are useful for non-destructive inspection of dielectric targets. In this work, a numerical technique for solving the 3D Lippmann-Schwinger integral equation of the inverse scattering problem via Gauss-Newton linearization in Banach spaces is analysed. More specifically, two different approximations of the Fr\ue9chet derivative are proposed in order to speed up the computation. Indeed it is well known that the computation of the Fr\ue9chet derivative is generally quite expensive in three dimensional restorations. Numerical tests show that the approximations give a faster restoration without loosing accuracy

Chebyshev spectral solver for vector radiative transfer in the atmosphere

A new solver based on an improved Chebyshev spectral method is proposed to simulate the atmospheric propagation in the case of parallel-plane atmosphere, Rayleigh scattering, and a Lambertian surface at the bottom of the atmosphere. A numerical validation is achieved against a publicly available benchmark dataset and an analysis of the computational burden is pursued

Improved Chebyshev Spectral Method Modeling for Vector Radiative Transfer in Atmospheric Propagation

An improved spectral coefficient method based on Chebyshev polynomials of the second kind is employed to solve the vector radiative transfer equation under the assumption of parallel-plane atmosphere and Rayleigh scattering. The solver is extended to consider a Lambertian surface at the bottom of the atmosphere. The computational properties of the proposed algorithm are analyzed and the validity of the implemented method is tested against a publicly available benchmark dataset

Chebyshev Spectral Solver for Vector Radiative Transfer in the Atmosphere

A new solver based on an improved Chebyshev spectral method is proposed to simulate the atmospheric propagation in the case of parallel-plane atmosphere, Rayleigh scattering, and a Lambertian surface at the bottom of the atmosphere. A numerical validation is achieved against a publicly available benchmark dataset and an analysis of the computational burden is pursued