Buried Object Detection by an Inexact Newton Method Applied to Nonlinear Inverse Scattering

An approach to reconstruct buried objects is proposed. It is based on the integral equations of the electromagnetic inverse scattering problem, written in terms of the Green's function for half-space geometries. The full nonlinearity of the problem is exploited in order to inspect strong scatterers. After discretization of the continuous model, the resulting equations are solved in a regularization sense by means of a two-step inexact Newton algorithm. The capabilities and limitations of the method are evaluated by means of some numerical simulations

Microwave Imaging of Three-Dimensional Targets by Means of an Inexact-Newton-Based Inversion Algorithm

A microwave imaging method previously developed for tomographic inspection of dielectric targets is extended to three-dimensional objects. The approach is based on the full vector equations of the electromagnetic inverse scattering problem. The ill-posedness of the problem is faced by the application of an inexact-Newton method. Preliminary reconstruction results are reported

Modelling scattering of electromagnetic waves in layered media: An up-to-date perspective

This paper addresses the subject of electromagnetic wave scattering in layered media, thus covering the recent progress achieved with different approaches. Existing theories and models are analyzed, classified, and summarized on the basis of their characteristics. Emphasis is placed on both theoretical and practical application. Finally, patterns and trends in the current literature are identified and critically discussed

Signal processing based method for solving inverse scattering problems

The problem of reconstructing an image of the permittivity distribution inside a penetrable and strongly scattering object from a finite number of noisy scattered field measurements has always been very challenging because it is ill-posed in nature. Several techniques have been developed which are either computationally very expensive or typically require the object to be weakly scattering. I have developed here a non-linear signal processing method, which will recover images for both strong scatterers and weak scatterers. This nonlinear or cepstral filtering method requires that the scattered field data is first preprocessed to generate a minimum phase function in the object domain. In 2-D or higher dimensional problems, I describe the conditions for minimum phase and demonstrate how an artificial reference wave can be numerically combined with measured complex scattering data in order to enforce this condition, by satisfying Rouche‘s theorem. In the cepstral domain one can filter the frequencies associated with an object from those of the scattered field. After filtering, the next step is to inverse Fourier transform these data and exponentiate to recover the image of the object under test. In addition I also investigate the scattered field sampling requirements for the inverse scattering problem. The proposed inversion technique is applied to the measured experimental data to recover both shape and relative permittivity of unknown objects. The obtained results confirm the effectiveness of this algorithm and show that one can identify optimal parameters for the reference wave and an optimal procedure that results in good reconstructions of a penetrable, strongly scattering permittivity distribution

A subspace preconditioned LSQR Gauss-Newton method with a constrained line search path applied to 3D biomedical microwave imaging

Three contributions that can improve the performance of a Newton-type iterative quantitative microwave imaging algorithm in a biomedical context are proposed. (i) To speed up the iterative forward problem solution, we extrapolate the initial guess of the field from a few field solutions corresponding to previous source positions for the same complex permittivity (i.e., “marching on in source position”) as well as from a Born-type approximation that is computed from a field solution corresponding to one previous complex permittivity profile for the same source position. (ii) The regularized Gauss-Newton update system can be ill-conditioned; hence we propose to employ a two-level preconditioned iterative solution method. We apply the subspace preconditioned LSQR algorithm from Jacobsen et al. (2003) and we employ a 3D cosine basis. (iii) We propose a new constrained line search path in the Gauss-Newton optimization, which incorporates in a smooth manner lower and upper bounds on the object permittivity, such that these bounds never can be violated along the search path. Single-frequency reconstructions from bipolarized synthetic data are shown for various three-dimensional numerical biological phantoms, including a realistic breast phantom from the University of Wisconsin-Madison (UWCEM) online repository

Analisi di strutture nella ricostruzione di immagini e monumenti

1. Definizione ed analisi teorica di nuovi operatori di proiezione per metodi multigrid basati solo sulle informazioni algebriche del problema, applicabili sia a discretizzazioni agli elementi finiti, sia a problemi di ricostruzione di immagini ed a matrici di grafo. 2. Definizione e studio di metodi multilivello regolarizzanti per la ricostruzione di immagini sfocate ed affette da rumore, combinando tecniche nonlineari di edge-preserving con operatori di trasferimento di griglia regolarizzanti che preservano la struttura. 3. Applicazione di condizioni al contorno in grado di preservare segnali smooth a tecniche di regolarizzazione accurate e solitamente computazionalmente costose, (e.g., Total Variation (TV), Regularized Total Least Square (RTLS), preconditioned GMRES, etc.), ricorrendo a trasformate discrete veloci di recente sviluppo (generalizzazione di FFT). 4. Studio di metodi impliciti per EDP paraboliche degeneri con applicazioni sia ai modelli di degrado monumentale sia a problemi di ricostruzione di immagini sfocate con termine regolarizzante non lineare. 5. Analisi spettrale di matrici, con struttura nascosta, non Hermitiane associate a simboli a blocchi con applicazioni al precondizionamento di EDP, alla regolarizzazione non lineare, ed a problemi di ricostruzione di segnali o immagini in cui alcuni campionamenti non sono disponibili o in cui le dimensioni del dominio introducono evidenti distorsioni di tipo prospettico

Location and Shape Reconstruction of 2D Dielectric Objects by Means of a Closed-Form Method: Preliminary Experimental Results

An analytical approach to location and shape reconstruction of dielectric scatterers, that was recently proposed, is tested against experimental data. Since the cross-sections of the scatterers do not depend on the z coordinate, a 2D problem can be formulated. A closed-form singular value decomposition of the scattering integral operator is derived and is used to determine the radiating components of the equivalent source density. This is a preliminary step toward a more complete solution, which will take into account the incident field inside the investigation domain in order to provide the dielectric features of the scatterer and also the nonradiating sources. Reconstructions of the equivalent sources, performed on some scattering data belonging to the Fresnel database, show the capabilities of the method and, thanks to the closed-form solution, results are obtained in a very short computation time

Non-Linear Reconstruction Of Dielectric Target In Dispersive Media Featuring Ultra-Wide Band Sensing And Gradient Minimization

In the last decade, there has been a growing interest in using UWB signals for microwave tomography. The diversity of frequencies in the illuminating UWB signal offers a unique combination enabling scattering of very long to very short wavelengths, and thus, collecting more information about the target. While microwave in general posses properties of preference for many imaging applications, inversion algorithms leading to recovery of the dielectric profile are complex in their nature, and vulnerable to noisy experimental conditions and environment

Microwave Sensing and Imaging

In recent years, microwave sensing and imaging have acquired an ever-growing importance in several applicative fields, such as non-destructive evaluations in industry and civil engineering, subsurface prospection, security, and biomedical imaging. Indeed, microwave techniques allow, in principle, for information to be obtained directly regarding the physical parameters of the inspected targets (dielectric properties, shape, etc.) by using safe electromagnetic radiations and cost-effective systems. Consequently, a great deal of research activity has recently been devoted to the development of efficient/reliable measurement systems, which are effective data processing algorithms that can be used to solve the underlying electromagnetic inverse scattering problem, and efficient forward solvers to model electromagnetic interactions. Within this framework, this Special Issue aims to provide some insights into recent microwave sensing and imaging systems and techniques