Cette thèse s'inscrit dans le domaine de l'imagerie non-destructive en électromagnétisme. L'originalité du travail réside, tout d'abord, dans sa forte connotation expérimentale. Celle-ci a abouti à la construction d'un prototype RADAR capable d'acquérir des données multisources-multistatiques dans la gamme de fréquence [2-4] GHz. De plus, ce système implémente la formation de voies au moyen d'un réseau d'atténuateurs/déphaseurs commandé numériquement.Les expériences menées relèvent, d'une part, de l'imagerie qualitative. Le Retournement Temporel, ainsi que les méthodes DORT et TR-MUSIC, ont été appliqués afin de détecter et localiser des cibles diffractantes. Le cas des milieux réverbérants a notamment été abordé.D'autre part, le prototype a été utilisé dans le cadre de la diffraction inverse quantitative sur des données très limitées en ouverture. Un algorithme itératif non-linéarisé prenant en compte l'aspect multi-fréquentiel des données a été adapté à la configuration expérimentale notamment grâce à une procédure de calibration performante.Enfin, la possibilité de greffer les avantages du Retournement Temporel sur ces techniques quantitatives a été étudiée. L'objectif est l'amélioration des résultats dans des milieux aléatoires proches de ceux rencontrés notamment en imagerie médicale (détection de tumeurs) ou en sondage du sous-sol (détection de mines, de nappes de pétrole). / This thesis deals with non-destructive electromagnetic imaging. Its originality lies, primarily, in a marked experimental approach, which has led to the realization of a RADAR prototype able to acquire multisource-multistatic data within the [2-4] GHz frequency band. Furthermore, the system implements beamforming through a numerically-controlled attenuator/phase shifter array.On the one hand, qualitative imaging experiments have been performed. Time Reversal, as well as DORT and TR-MUSIC methods, have been applied to detect and localize scattering objects. In particular, the case of reverberating media has been dealt with.On the other hand, the prototype has been used for quantitative inverse scattering with very aspect-limited data. A non-linearized iterative algorithm taking into account the multi-frequency nature of the data has been adapted to the experimental configuration through a performing calibration procedure.Finally, the possibility of exploiting the features of Time Reversal within the quantitative frame has been studied. The goal is the improvement of the results in random media mimicking those typical of medical imaging (tumor detection) or sub-surface probing (land mine or oil detection) applications.

Zhang, Hai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 106-109). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Preliminaries --- p.13 / Chapter 2.1 --- Maxwell equations --- p.13 / Chapter 2.2 --- Reflection principle --- p.15 / Chapter 3 --- Scattering by General Polyhedral Obstacle --- p.19 / Chapter 3.1 --- Direct problem --- p.19 / Chapter 3.2 --- Inverse problem and statement of main results --- p.21 / Chapter 3.3 --- Proof of the main results --- p.22 / Chapter 3.3.1 --- Preliminaries --- p.23 / Chapter 3.3.2 --- Properties of perfect planes --- p.24 / Chapter 3.3.3 --- Proofs --- p.33 / Chapter 4 --- Scattering by Bi-periodic Polyhedral Grating (I) --- p.35 / Chapter 4.1 --- Direct problem --- p.36 / Chapter 4.2 --- Inverse problem and statement of main results --- p.38 / Chapter 4.3 --- Preliminaries --- p.39 / Chapter 4.4 --- Classification of unidentifiable periodic structures --- p.41 / Chapter 4.4.1 --- Observations and auxiliary tools --- p.41 / Chapter 4.4.2 --- First class of unidentifiable gratings --- p.45 / Chapter 4.4.3 --- Preparation for finding other classes of unidentifiable gratings --- p.47 / Chapter 4.4.4 --- A simple transformation --- p.52 / Chapter 4.4.5 --- Second class of unidentifiable gratings --- p.53 / Chapter 4.4.6 --- Third class of unidentifiable gratings --- p.58 / Chapter 4.4.7 --- Excluding the case with L --- p.61 / Chapter 4.4.8 --- Summary on all unidentifiable gratings --- p.65 / Chapter 4.5 --- Proof of Main results --- p.65 / Chapter 5 --- Scattering by Bi-periodic Polyhedral Grating (II) --- p.69 / Chapter 5.1 --- Preliminaries --- p.70 / Chapter 5.2 --- Classification of unidentifiable periodic structures --- p.72 / Chapter 5.2.1 --- First class of unidentifiable gratings --- p.72 / Chapter 5.2.2 --- Preparation for finding other classes of unidentifiable gratings --- p.73 / Chapter 5.2.3 --- Studying of the case L --- p.76 / Chapter 5.2.4 --- Study of the case with L --- p.89 / Chapter 5.2.5 --- Study of the case with L --- p.95 / Chapter 5.2.6 --- Summary on all unidentifiable gratings --- p.104 / Chapter 5.3 --- Unique determination of bi-periodic polyhedral grating --- p.104 / Bibliography --- p.106

Microwave imaging techniques have shown excellent capabilities in various fields such as civil engineering, nondestructive testing, industrial applications, and have in recent decades experienced strong growth as a research topic in biomedical diagnostics. Many research groups throughout the world work on prototype systems for producing images of human tissues in different biomedical applications, particularly breast tumor detection. However, the research community faces many challenges and in order to be competitive to other imaging modalities one of the means is to put emphasis on experimental work. Consequently, the use of flexible and accurate measurement systems, together with the design and fabrication of suitable antennas, are essential to the development of efficient microwave imaging systems. The first part of this thesis focuses on measurement systems for microwave imaging in terms of antenna design and development, robot controlled synthetic array geometries, permittivity measurements, and calibration. The aim was to investigate the feasibility of a flexible system for measuring the fields around an inhomogeneous object and to create quantitative images. Hence, such an aim requires solving of a nonlinear inverse scattering problem, which in turn requires accurate measurements for producing good quality experimental data. The presented solution by design of a flexible measurement system is validated by examination of microwave imaging from experimental data with a breast phantom. The second part of the thesis deals with the research challenges of designing high performance antennas to be placed in direct contact with or in close proximity to the imaged object. The need for novel antenna applicators is envisaged in the framework of the Mamacell measurement system, where the antenna applicators have to be designed and constructed to effectively couple the energy into the imaging object. For this purpose the main constraints and design requirements are a narrow lobe of the antenna, very small near-field effects, and small size. Numerical simulations and modeling shows that the proposed ridged waveguide antenna is capable of fulfilling the design requirements and the performance goals, demonstrating the potential for the future microwave imaging system called Mamacell.

Thesis (Ph.D.)--University of Delaware, 2007. / Principal faculty advisor: Daniel S. Weile, Dept. of Electrical and Computer Engineering. Includes bibliographical references.

Inverse problems arise in numerous fields of science and engineering where one tries to find out the desired information of an unknown object or the cause of an observed effect. They are of fundamental importance in many areas including radar and sonar applications, nondestructive testing, image processing, medical imaging, remote sensing, geophysics and astronomy among others. This study is concerned with three issues in scattering theory, fractional operators, as well as some of their inverse problems. The first topic is scattering problems for electromagnetic waves governed by Maxwell equations. It will be proved in the current study that an inhomogeneous EM medium with a corner on its support always scatters by assuming certain regularity and admissible conditions. This result implies that one cannot achieve invisibility for such materials. In order to verify the result, an integral of solutions to certain interior transmission problem is to be analyzed, and complex geometry optics solutions to corresponding Maxwell equations with higher order estimate for the residual will be constructed. The second problem involves the linearized elastic or seismic wave scattering described by the Lamei system. We will consider the elastic or seismic body wave which is composed of two different type of sub-waves, that is, the compressional or primary (P-) and the shear or secondary (S-) waves. We shall prove that the P- and the S-components of the total wave can be completely decoupled under certain geometric and boundary conditions. This is a surprising finding since it is known that the P- and the S-components of the elastic or seismic body wave are coupled in general. Results for decoupling around local boundary pieces, for boundary value problems, and for scattering problems are to be established. This decoupling property will be further applied to derive uniqueness and stability for the associated inverse problem of identifying polyhedral elastic obstacles by an optimal number of scattering measurements. Lastly, we consider a type of fractional (and nonlocal) elliptic operators and the associated Calderoin problem. The well-posedness for a kind of forward problems concerning the fractional operator will be established. As a consequence, the corresponding Dirichlet to Neumann map with certain mapping property is to be defined. As for the inverse problem, it will be shown that a potential can be uniquely identified by local Cauchy data of the associated nonlocal operator, in dimensions larger than or equal to two.

No description available.

The completeness of eigenfunctions for linearized equations is critical for many applications, such as the study of stability of solitary waves. In this thesis, we work with the Nonlinear Schr{\"o}dinger (NLS) equation, associated with the Zakharov-Shabat spectral problem. Firstly, we construct a complete set of eigenfunctions for the spectral problem. Our method involves working with an adjoint spectral problem and deriving completeness and orthogonality relations between eigenfunctions and adjoint eigenfunctions. Furthermore, we prove completeness of squared eigenfunctions, which are used to represent solutions of the linearized NLS equation. For this, we find relations between the variation of potential and the variation of scattering data. Moreover, we show the connection between the squared eigenfunctions of the Zakharov-Shabat spectral problem and solutions of the linearized NLS equation. / Thesis / Master of Science (MSc)

We are concerned with the quantum inverse scattering problem. The corresponding Marchenko integral equation is solved by using the collocation method together with piece-wise polynomials, namely, Hermite splines. The scarcity of experimental data and the lack of phase information necessitate the generation of the input reflection coefficient by choosing a specific profile and then applying our method to reconstruct it. Various aspects of the single and coupled channels inverse problem and details about the numerical techniques employed are discussed. We proceed to apply our approach to synthetic seismic reflection data. The transformation of the classical one-dimensional wave equation for elastic displacement into a Schr¨odinger-like equation is presented. As an application of our method, we consider the synthetic reflection travel-time data for a layered substrate from which we recover the seismic impedance of the medium. We also apply our approach to experimental seismic reflection data collected from a deep water location in the North sea. The reflectivity sequence and the relevant seismic wavelet are extracted from the seismic reflection data by applying the statistical estimation procedure known as Markov Chain Monte Carlo method to the problem of blind deconvolution. In order to implement the Marchenko inversion method, the pure spike trains have been replaced by amplitudes having a narrow bell-shaped form to facilitate the numerical solution of the Marchenko integral equation from which the underlying seismic impedance profile of the medium is obtained. / Physics / D.Phil.(Physics)

Ill-posed inverse problems have wide applications in many fields such as oceanography, signal processing, machine learning, biomedical imaging, remote sensing, geophysics, and others. In this dissertation, we address the problem of solving unstable operator equations with iteratively regularized Newton-type algorithms. Important practical questions such as selection of regularization parameters, construction of generating (filtering) functions based on a priori information available for different models, algorithms for stopping rules and error estimates are investigated with equal attention given to theoretical study and numerical experiments.

<p>The thesis addresses time-domain inverse electromagneticscattering for determining unknown characteristics of an objectfrom observations of the scattered .eld. Applications includenon-destructive characterization of media and optimization ofmaterial properties, for example the design of radar absorbingmaterials.A nother interesting application is the parameteroptimization of subcell models to avoid detailed modeling ofcomplex geometries.</p><p>The inverse problem is formulated as an optimal controlproblem where the cost function to be minimized is thedi.erence between the estimated and observed .elds, and thecontrol parameters are the unknown object characteristics. Theproblem is solved in a deterministic gradient-basedoptimization algorithm using a parallel 2D FDTD scheme for thedirect problem.This approach is computationally intensive sincethe direct problem needs to be solved in every optimizationiteration in order to compute an estimated .eld.H ighlyaccurate analytical gradients are computed from the adjointformulation.In addition to giving better accuracy than .nitedi.erences, the analytical gradients also have the advantage ofonly requiring one direct and one adjoint problem to be solvedregardless of the number of parameters.</p><p>When absorbing boundary conditions are used to truncate thecomputational domain, the equations are non-reversible and theentire time-history of the direct solution needs to be storedfor the gradient computation.Ho wever, using an additionaldirect simulation and a restart procedure it is possible tokeep the storage at an acceptable level.</p><p>The inverse method has been successfully applied to a widerange of industrial problems within the European project,IMPACT (Inverse Methods for Wave Propagation Applications inTime-Domain).T he results presented here includecharacterization of layered dispersive media, determination ofparameters in subcell models for thin sheets and narrow slotsand optimization problems where the observed .eld is given bydesign objectives.</p>