Inverse Scattering Research Papers - Academia.edu (original) (raw)

We present an introduction to some aspects of digital signal processing and time series analysis which are not always covered in classical textbooks. One of the objectives is to illustrate how mathematics and engineering can be combined... more

We present an introduction to some aspects of digital signal processing and time series analysis which are not always covered in classical textbooks. One of the objectives is to illustrate how mathematics and engineering can be combined in a fruitful interplay, resulting in many new techniques and methods in many different fields. We shall illustrate how the prediction problem is related to linear algebra, orthogonal polynomials, classical interpolation problems, inverse scattering theory, Toeplitz operators, network theory etc.

The problem of reconstructing locations, shapes, and dielectric permittivity distributions of two-dimensional (2-D) dielectric objects from measurements of the scattered electric field is addressed in this paper. A numerical approach is... more

The problem of reconstructing locations, shapes, and dielectric permittivity distributions of two-dimensional (2-D) dielectric objects from measurements of the scattered electric field is addressed in this paper. A numerical approach is proposed which is based on a multi-illumination multiview processing. In particular, the inverse problem is recast as a global nonlinear optimization problem, which is solved by a genetic algorithm (GA). The final objective of the approach is the image reconstruction of highly contrasted bodies.

The numerical performances of Landweber iteration, the Newton-CG method, the Levenberg-Marquardt algorithm, and the iteratively Regularized Gauß-Newton method are compared for a nonlinear, severely ill-posed inverse scattering problem in... more

The numerical performances of Landweber iteration, the Newton-CG method, the Levenberg-Marquardt algorithm, and the iteratively Regularized Gauß-Newton method are compared for a nonlinear, severely ill-posed inverse scattering problem in two space dimensions. A modification of the Gauß-Newton method is suggested, which compares favorably with the above methods. A convergence proof is presented including the effects of the numerical approximation of the solution operator.

The specific properties of microwaves have been used for a while in many applications. More particularly, the penetration through opaque media makes microwuves a convenient agentjbr non invasive testing, evaluatinn cold measurements. For... more

The specific properties of microwaves have been used for a while in many applications. More particularly, the penetration through opaque media makes microwuves a convenient agentjbr non invasive testing, evaluatinn cold measurements. For example, industrial sensors have been developed, bused on the sensithrity of microwave propagation constant upon quantities of practical relevance, such as water contents, temperature or composition Sirndarly, microwaves have been considered for medical applications involving the detection of organ movements and changes in tissue water content [I]. More particularly cardiopulmonary interrogation via microwaves has resulted in various sensors for monitoring ventricular volume change or movement, arterial wall motion, respiratory movements, pulmonary oedema, etc [2]. In all these applkations, microwave sensors peform local measurements and need LO be displaced for obtaining an image reproducing the spatial variations of a gi,ven quantity. The effective startirtg of microwave imaging techniques jor biomedical applications can be dated at the beginning of the SO'S, with the pioneer contribution of Drs E.Larsen cold J. Jacobi, from the Walter Reeds Ar,ny Institute. Using the water-immersion technique [3], the first transmission and tomographic images of biologiiul targets, such a s perjiied organs, have been shown to offer promises thanks to their contrast nnd unexpect,?d spatial resoiution /4,5/. More recently, advances in i'he area of inverse scattering theory ,LWUI microwave technology have &e possible the devclopment of microwave imaging Gold tomographic instruments. This puper provides a review of such equiprnena developed at 2iupelec and UPC Barcelona, within the frame of successive French-Spanish PICASSO cooperation programs. I! reports the most significant results and gives some perspectives for future

In the framework of the extended resolvent approach the direct and inverse scattering problems for the nonstationary Schrödinger equation with a potential being a perturbation of the N-soliton potential by means of a generic bidimensional... more

In the framework of the extended resolvent approach the direct and inverse scattering problems for the nonstationary Schrödinger equation with a potential being a perturbation of the N-soliton potential by means of a generic bidimensional smooth function decaying at large spaces are introduced and investigated. The initial value problem of the Kadomtsev-Petviashvili I equation for a solution describing N wave solitons on a generic smooth decaying background is then linearized, giving the time evolution of the spectral data.

This paper presents an efficient method for the design of complex fiber Bragg gratings. The method relies on the synthesis of the impulse response of the grating by means of a differential layer-peeling algorithm. The algorithm developed... more

This paper presents an efficient method for the design of complex fiber Bragg gratings. The method relies on the synthesis of the impulse response of the grating by means of a differential layer-peeling algorithm. The algorithm developed takes into account all the multiple reflections inside the grating, giving an exact solution to the inverse scattering problem. Its low algorithmic complexity enables the synthesis of long fiber gratings. The method is illustrated by designing several filters with interest for optical fiber communication systems: dispersionless bandpass filters and second-and third-order dispersion compensators.

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically... more

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all

In this article we will retrace one of the great mathematical adventures of this century-the discovery of the soliton and the gradual explanation of its remarkable properties in terms of hidden symmetries. We will take an historical... more

In this article we will retrace one of the great mathematical adventures of this century-the discovery of the soliton and the gradual explanation of its remarkable properties in terms of hidden symmetries. We will take an historical approach, starting with a famous numerical experiment carried out by Fermi, Pasta, and Ulam on one of the first electronic computers, and with Zabusky and Kruskal's insightful explanation of the surprising results of that experiment (and of a follow-up experiment of their own) in terms of a new concept they called "solitons". Solitons however raised even more questions than they answered. In particular, the evolution equations that govern solitons were found to be Hamiltonian and have infinitely many conserved quantities, pointing to the existence of many non-obvious symmetries. We will cover next the elegant approach to solitons in terms of the Inverse Scattering Transform and Lax Pairs, and finally explain how those ideas led step-by-step to the discovery that Loop Groups, acting by "Dressing Transformations", give a conceptually satisfying explanation of the secret soliton symmetries.

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically... more

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically... more

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all

In this paper, we present the results of a diagnostics survey, based on the exploitation of ground penetrating radar (GPR) and sonic prospecting, to characterize the deterioration status of the pillars of the cathedral of Tricarico, in... more

In this paper, we present the results of a diagnostics survey, based on the exploitation of ground penetrating radar (GPR) and sonic prospecting, to characterize the deterioration status of the pillars of the cathedral of Tricarico, in the Basilicata region (Southern Italy). The prospecting falls within the more general framework of investigating the structural conditions of this monument, which is affected by heavy instability problems. This study case points out the great effectiveness of the two employed diagnostic methods, when used in an integrated way, for detecting cracks and inhomogeneities in the inner structure of masonry building elements. With regard to GPR prospecting, a comparison is made between the results obtained by a standard processing and those obtained by means of an inverse scattering algorithm. For one of the investigated pillars, the results obtained from non-invasive tests are compared with those of direct inspection. This is performed by coring the pillar and examining both the core and the hole (the latter by means of an endoscope). The seismic investigation allowed us to prove the mediocre or bad state of conservation of the pillars.

We outline two complementary approaches based on the no core shell model (NCSM) and present recent results. In the ab initio approach, nuclear properties are evaluated with two-nucleon (NN) and three-nucleon interactions (TNI) derived... more

We outline two complementary approaches based on the no core shell model (NCSM) and present recent results. In the ab initio approach, nuclear properties are evaluated with two-nucleon (NN) and three-nucleon interactions (TNI) derived within effective field theory (EFT) based on chiral perturbation theory (ChPT). Fitting two available parameters of the TNI generates good descriptions of light nuclei. In a second effort, an ab exitu approach, results are obtained with a realistic NN interaction derived by inverse scattering theory with off-shell properties tuned to fit light nuclei. Both approaches produce good results for observables sensitive to spin-orbit properties.

Radio frequency (RF) tomography is proposed to detect underground voids, such as tunnels or caches, over relatively wide areas of regard. The RF tomography approach requires a set of low-cost transmitters and receivers arbitrarily... more

Radio frequency (RF) tomography is proposed to detect underground voids, such as tunnels or caches, over relatively wide areas of regard. The RF tomography approach requires a set of low-cost transmitters and receivers arbitrarily deployed on the surface of the ground or slightly buried. Using the principles of inverse scattering and diffraction tomography, a simplified theory for below-ground imaging is developed. In this paper, the principles and motivations in support of RF tomography are introduced. Furthermore, several inversion schemes based on arbitrarily deployed sensors are devised. Then, limitations to performance and system considerations are discussed. Finally, the effectiveness of RF tomography is demonstrated by presenting images reconstructed via the processing of synthetic data.

An iterative approach to full vector three-dimensional inverse scattering problems, where the unknown objects can have conductivity, permittivity and permeability different from the known background medium, is discussed. Since this... more

An iterative approach to full vector three-dimensional inverse scattering problems, where the unknown objects can have conductivity, permittivity and permeability different from the known background medium, is discussed. Since this problem involves a large number of unknowns, it has to be solved effectively and efficiently so that the results can be obtained in timely manner. The forward modeling is based on a domain integral equation approach formulated in terms of the electric and magnetic contrast sources normalized with the characteristic impedance of the background medium. Our numerical tests indicate that this formulation is prerequisite in order to arrive at a forward solution within an acceptable number of iterations, and hence it is also of significant importance in the optimization process of the inverse problem. The inverse scattering problem is attacked using the Multiplicative Regularized Contrast Source Inversion method as known in the literature. The complexity of this inverse method is approximately equal to the complexity of two equivalent forward algorithms of the conjugate gradient type. Furthermore, this inverse method has been armed with a weighted L 2 -norm regularizer which has been included as a multiplicative constraint. Some representative numerical testings will be presented to illustrate the ability of the our numerical algorithms.

An important problem in geophysics, medical imaging, and nondestructive imaging today is the construction of a practical, accurate, and efficient means of imaging geophysical anomalies, tumours, or material defects in layered media. This... more

An important problem in geophysics, medical imaging, and nondestructive imaging today is the construction of a practical, accurate, and efficient means of imaging geophysical anomalies, tumours, or material defects in layered media. This paper discusses such a method. The use of a ''stratified Green's function'' for the solution of the forward problem is detailed. This forward problem is then incorporated into an efficient and accurate inversion algorithm based on optimization. The method is nonperturbative, unlike diffraction tomography, which relies on linearization to make the problem tractable. In the inversion, a pair of Lippmann-Schwinger-like integral equations are solved simultaneously via the Galerkin procedure for the unknown total internal fields and speed distribution. The computational burden is high, but made manageable by utilizing BiConjugate gradients, fast fourier transforms, and ''sinc'' basis functions to speed up the solution of the forward problem. The size and contrasts for which the method converges are substantially beyond the Born or Rytov approximations, and other methods heretofore reported in the literature. The convolutional character of the layered Green's function, and thus numerical efficiency, is preserved by careful construction based on known reflection coefficients.

Efimov physics relates to 3-body systems with large 2-body scattering lengths as and small effective ranges rs. For many systems in nature the assumption of a small effective range is not valid. The present report shows binding energies... more

Efimov physics relates to 3-body systems with large 2-body scattering lengths as and small effective ranges rs. For many systems in nature the assumption of a small effective range is not valid. The present report shows binding energies E3 of three identical bosons calculated with 2-body potentials that are fitted to scattering data and momentum cutoffs Λ by inverse scattering. Results agree with previous works in the case of rs ≪ as. While energies diverge with Λ for rs = 0, they converge for rs > 0 when Λ >∼ 10/rs. With a −1 s = 0 the converged energies are given by E (n) 3 = C (n) 0 r −2 s with n labelling the energy-branch and calculated values C (0) 0 = 0.77, C (1) 0 = .0028. This gives a ratio ∼ 278 thus differing from the value ∼ 515 in the Efimov case. Efimov's angular dependent function is calculated. Good agreement with previous works is obtained for rs ≪ as. With the increased values of rs the shallow states still appear Efimov-like. For deeper states the angular dependence differs but is independent of rs.

This paper deals with the inverse scattering of ultra wide band (UWB) tomography used in reconstruction the dialectic properties of the unknown targets in 2D. The image reconstruction algorithm is based on the gradient minimization of an... more

This paper deals with the inverse scattering of ultra wide band (UWB) tomography used in reconstruction the dialectic properties of the unknown targets in 2D. The image reconstruction algorithm is based on the gradient minimization of an augmented cost function defined as the different between measured and calculated fields. The computation requires two successive steps: (i) direct and (ii) adjoint solutions. The forwardbackward time stepping algorithm, implementing the finitedifference time-domain (FDTD) method with Mur's absorbing boundaries is employed in both steps. The imaging algorithm is based on non-linear optimization technique from which the single-step and iterative inversion schemes are derived. The experimental results demonstrate that the algorithms can resolve features whose sizes are comparable to the half wave-length even though scaterring data are collected only from limited view angles. These experimental evidence suggest that the technique could potentially be used to solve practical imaging problems such as detecting cancerous tumors in breast.

Blackledge, Jonathan Electromagnetic Scattering Solutions for Digital Signal Processing Jyväskylä: University of Jyväskylä, 2009, 297 p. (nid.), 2010 (PDF) (Jyväskylä Studies in Computing ISSN 1456-5390; 108) ISBN 978-951-39-3944-1 (PDF),... more

Blackledge, Jonathan Electromagnetic Scattering Solutions for Digital Signal Processing Jyväskylä: University of Jyväskylä, 2009, 297 p. (nid.), 2010 (PDF) (Jyväskylä Studies in Computing ISSN 1456-5390; 108) ISBN 978-951-39-3944-1 (PDF), 978-951-39-3741-6 (nid.) Electromagnetic scattering theory is fundamental to understanding the interaction between electromagnetic waves and inhomogeneous dielectric materials. The theory unpins the engineering of electromagnetic imaging systems over a broad range of frequencies, from optics to radio and microwave imaging, for example. Developing accurate scattering models is particularly important in the field of image understanding and the interpretation of electromagnetic signals generated by scattering events. To this end there are a number of approaches that can be taken. For relatively simple geometric configurations, approximation methods are used to develop a transformation from the object plane (where scattering events take place) to the i...

In this paper, a novel technique to synthesize microwave filters by inverse scattering is proposed. It provides an exact solution for the synthesis problem, by means of a closed-form expression, with very low computational cost. The... more

In this paper, a novel technique to synthesize microwave filters by inverse scattering is proposed. It provides an exact solution for the synthesis problem, by means of a closed-form expression, with very low computational cost. The technique is valid when the target frequency response can be expressed as a rational function. The coupled-mode theory is used to model microwave propagation along the filter, and therefore, the synthesis technique is applicable to filters implemented in a wide range of technologies, such as planar and nonplanar transmission lines, and many waveguides. The synthesis method is exact for all the frequency range of interest, preventing the degradation of the frequency response that can be troublesome for wideband applications or to satisfy the out-of-band requirements of the filter. The resulting synthesized filter is, in general, a nonuniform transmission line or waveguide that features a continuously varying smooth profile, avoiding the presence of sharp discontinuities and their detrimental effects. To demonstrate the potential of the proposed synthesis technique, a multiband microwave filter, fulfilling stringent specifications, will be designed in rectangular waveguide technology. The prototype will be fabricated by electroforming and carefully measured with a vector network analyzer, confirming the accuracy of the novel synthesis method reported. Index Terms-Coupled-mode theory, filter synthesis, inverse scattering, microwave filter, planar technology, rectangular waveguide. I. INTRODUCTION M ICROWAVE filters are defined in classical textbooks as two-port networks used to control the frequency response at a certain point in a microwave system by providing transmission at frequencies within the passband of the filter and attenuation in the stopband of the filter [1]. Following that classical definition, the typical frequency responses include lowpass, high-pass, bandpass, and band-reject characteristics. Filters are used in virtually any type of microwave communication, radar, or test and measurement system [1].

We simulate a three-dimensional optical diffraction tomography experiment in which superresolution is achieved by illuminating the object with evanescent waves generated by a prism. We show that accounting for multiple scattering between... more

We simulate a three-dimensional optical diffraction tomography experiment in which superresolution is achieved by illuminating the object with evanescent waves generated by a prism. We show that accounting for multiple scattering between the object and the prism interface is mandatory to obtain superresolved images. Because the Born approximation leads to poor results, we propose a nonlinear inversion method for retrieving the map of permittivity of the object from the scattered far field. We analyze the sensitivity to noise of our algorithm and point out the importance of using incident propagative waves together with evanescent waves to improve the robustness of the reconstruction without losing the superresolution.

An inverse scattering technique based on the differential E-formulation in the frequency domain is proposed. The inversion is achieved by minimizing a cost functional, taking into account the discrepancy between measured and estimated... more

An inverse scattering technique based on the differential E-formulation in the frequency domain is proposed. The inversion is achieved by minimizing a cost functional, taking into account the discrepancy between measured and estimated field values, while the Helmholtz wave equation is set as constraint. The Fréchet derivatives of the cost functional with respect to the scatterer properties are derived analytically by means of the calculus of variations. Edge elements are used for the numerical treatment of the problem.

The nucleon-nucleon interaction is constructed by means of the J-matrix version of inverse scattering theory. Ambiguities of the interaction are eliminated by postulating tridiagonal and quasi-tridiagonal forms of the potential matrix in... more

The nucleon-nucleon interaction is constructed by means of the J-matrix version of inverse scattering theory. Ambiguities of the interaction are eliminated by postulating tridiagonal and quasi-tridiagonal forms of the potential matrix in the oscillator basis in uncoupled and coupled waves, respectively. The obtained interaction is very accurate in reproducing the N N scattering data and deuteron properties. The interaction is used in the no-core shell model calculations of 3 H and 4 He nuclei. The resulting binding energies of 3 H and 4 He are very close to experimental values.

We construct new classes of exact solutions in metric-affine gravity (MAG) with string corrections by the antisymmetric H-field. The solutions are parametrized by generic off-diagonal metrics possessing noncommutative symmetry associated... more

We construct new classes of exact solutions in metric-affine gravity (MAG) with string corrections by the antisymmetric H-field. The solutions are parametrized by generic off-diagonal metrics possessing noncommutative symmetry associated to anholonomy framerelations and related nonlinear connection (N-connection) structure. We analyze the horizon and geodesic properties of a class of off-diagonal metrics with deformed spherical symmetries. The maximal analytic extension of ellipsoid type metrics are constructed and the Penrose diagrams are analyzed with respect to adapted frames. We prove that for small deformations (small eccentricities) there are such metrics that the geodesic behaviour is similar to the Schwarzcshild one. We conclude that some static and stationary ellipsoid configurations may describe black ellipsoid objects. The new class of spacetimes do not possess Killing symmetries even in the limits to the general relativity and, in consequence, they are not prohibited by black hole uniqueness theorems. Such static ellipsoid (rotoid) configurations are compatible with the cosmic cenzorship criteria. We study the perturbations of two classes of static black ellipsoid solutions of four dimensional gravitational field equations. The analysis is performed in the approximation of small eccentricity deformations of the Schwarzschild solution.

1] This paper presents two methods for ground-penetrating radar (GPR) imaging of land mines: a two-dimensional (2-D) seismic migration method and a 3-D nonlinear inverse scattering method. The seismic migration technique has been... more

1] This paper presents two methods for ground-penetrating radar (GPR) imaging of land mines: a two-dimensional (2-D) seismic migration method and a 3-D nonlinear inverse scattering method. The seismic migration technique has been successfully applied to processing field data sets collected at a test site. The results show that the seismic migration technique is a useful real-time imaging method. To image the 3-D structure of the land mine, we have developed a full 3-D nonlinear inverse scattering algorithm on the basis of the contrast source inversion method. To account for the ground surface and potentially other subsurface layers, the inverse scattering method uses a multilayered medium as a background. Preliminary results demonstrate that the 3-D inverse scattering method can successfully provide high-resolution reconstruction of high-contrast buried objects.

The wave propagation in a one-dimensional nonhomogeneous medium is considered, where the wave speed and the restoring force depend on location. In the frequency domain this is equivalent to the Schrijdinger equation d2$/dx2 + k211, =... more

The wave propagation in a one-dimensional nonhomogeneous medium is considered, where the wave speed and the restoring force depend on location. In the frequency domain this is equivalent to the Schrijdinger equation d2$/dx2 + k211, = k2P(x)II, + Q(x)Jt with an added potential proportional to energy. The scattering and bound-state solutions of this equation are studied and the properties of the scattering matrix are obtained; the inverse scattering problem of recovering the restoring force when the wave speed and the scattering data are known are also solved.

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically... more

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a ...

The problem of reconstructing the reflectivity of a threedimensional medium with density and compressibility variations is examined. For the special case of continuous-wave (CW) insonification, exact inversion formulas have recently been... more

The problem of reconstructing the reflectivity of a threedimensional medium with density and compressibility variations is examined. For the special case of continuous-wave (CW) insonification, exact inversion formulas have recently been reported for recovering an unknown scattering parameter from scattering measurements. In this work, exact solutions, or inversion formulas, are obtained for the general case of arbitrary broad-band insonification where the incident wave is assumed to be a spherically diverging broad-bandwidth pulse of arbitrary shape. Solutions are derived under the assumption that the scattering is sufficiently weak for the Born approximation to hold. Exact inversion formulas are obtained for three aperture geometries: a plane, cylindrical, or spherical recording surface enclosing the scattering region. Under most practical conditions, the process of back projection and coherent summation over spherical surfaces in image space, without prior filtering, is shown to provide a close approximation to the exact inversion procedure. Finally, in the case of the spherical geometry, the mathematical equivalence between the threedimensional inverse Radon transform and the far-field approximation to the exact solution is demonstrated.

Ground penetrating radar (GPR) surveys were carried out in the preliminary stage of a project of structural monitoring of the 42 columns inside the crypt of the 'Cattedrale di Otranto' (Lecce, Italy). Detailed knowledge of the structure... more

Ground penetrating radar (GPR) surveys were carried out in the preliminary stage of a project of structural monitoring of the 42 columns inside the crypt of the 'Cattedrale di Otranto' (Lecce, Italy). Detailed knowledge of the structure of the internal columns was a key reason for their restoration since they had several points of deterioration (i.e. fractures). The aim of this work was to test the reliability of both a standard GPR processing (in a time domain) and a linear inverse scattering algorithm (in a frequency domain) in order to detect and achieve information on the damaged zones inside the columns. First, the reliability of both the techniques was preliminarily assessed by processing synthetic data resembling the measurement conditions of the experimental cases. Then the experimental data were processed by means of the two techniques. Our comparative analysis, for both the numerical and the experimental analyses, indicates that the linear inverse scattering approach is better suited for the detection of local fractures compared to the classical time-domain processing, while increasing the computational cost at a reasonable rate.

We consider several ways of how one could classify the various types of soliton solutions related to nonlinear evolution equations which are solvable by the inverse scattering method. In doing so we make use of the fundamental analytic... more

We consider several ways of how one could classify the various types of soliton solutions related to nonlinear evolution equations which are solvable by the inverse scattering method. In doing so we make use of the fundamental analytic solutions, the dressing procedure, the reduction technique and other tools characteristic for that method.

Abstract. In this article we will retrace one of the great mathematical adventures of this century—the discovery of the soliton and the gradual explanation of its remarkable properties in terms of hidden symmetries. We will take an... more

Abstract. In this article we will retrace one of the great mathematical adventures of this century—the discovery of the soliton and the gradual explanation of its remarkable properties in terms of hidden symmetries. We will take an historical approach, starting with a famous numerical experiment carried out by Fermi, Pasta, and Ulam on one of the first electronic computers, and with Zabusky and Kruskal’s insightful explanation of the surprising results of that experiment (and of a follow-up experiment of their own) in terms of a new concept they called “solitons”. Solitons however raised even more questions than they answered. In particular, the evolution equations that govern solitons were found to be Hamiltonian and have infinitely many conserved quantities, pointing to the existence of many non-obvious symmetries. We will cover next the elegant approach to solitons in terms of the Inverse Scattering Transform and Lax Pairs, and finally explain how those ideas led step-by-step to ...

Ground penetrating radar (GPR) is one of the most suitable technological solutions for timely detection of damage and leakage from pipelines, an issue of extreme importance both environmentally and from an economic perspective. However,... more

Ground penetrating radar (GPR) is one of the most suitable technological solutions for timely detection of damage and leakage from pipelines, an issue of extreme importance both environmentally and from an economic perspective. However, for GPR to be effective, there is the need of designing appropriate imaging strategies such to provide reliable information. In this paper, we address the problem of imaging leaking pipes from single-fold, multi-receiver GPR data by means of a novel microwave tomographic method based on a 2D "distorted" scattering model which incorporates the available knowledge on the investigated scenario (i.e., pipe position and size). In order to properly design the features of the approach and test its capabilities in controlled but realistic conditions, we exploit an advanced, full-wave, 2.5D Finite-Difference Time-Domain forward modeling solver capable of accurately simulating real-world GPR scenarios in electromagnetically dispersive materials. By means of this latter approach, we show that the imaging procedure is reliable, allows us to detect the presence of a leakage already in its first stages of development, is robust against uncertainties and provides information which cannot be inferred from raw-data radargrams or "conventional" tomographic methods based on a half-space background.

We consider the problem of using electromagnetic sensing to estimate targets in complex environments, such as when they are hidden behind walls and other opaque objects. The often unknown electromagnetic interactions between the target... more

We consider the problem of using electromagnetic sensing to estimate targets in complex environments, such as when they are hidden behind walls and other opaque objects. The often unknown electromagnetic interactions between the target and the surrounding area, make the problem challenging. To improve our results, we exploit information in the multipath of the objects surrounding both the target and the sensors. First, we estimate building layouts by using the jump-diffusion algorithm and employing prior knowledge about typical building layouts. We also take advantage of a detailed physical model that captures the scattering by the inner walls and efficiently utilizes the frequency bandwidth. We then localize targets hidden behind reinforced concrete walls. The sensing signals reflected from the targets are significantly distorted and attenuated by the embedded metal bars. Using the surface formulation of the method of moments, we model the response of the reinforced walls, and inco...

The interaction of matter-wave solitons in elongated Bose-Einstein condensate with time-dependent parabolic trap is investigated using the perturbation theory based on the inverse scattering transform. Regimes of parametric and main... more

The interaction of matter-wave solitons in elongated Bose-Einstein condensate with time-dependent parabolic trap is investigated using the perturbation theory based on the inverse scattering transform. Regimes of parametric and main resonances in solitons interactions are investigated for harmonic trap potentials. The predictions of the theory are confirmed by the numerical simulations of the quasi-one-dimensional Gross-Pitaevskii equation.

We use a Pohlmeyer type reduction to generate classical string solutions in AdS spacetime. In this framework we describe a correspondence between spikes in AdS 3 and soliton profiles of the sinh-Gordon equation. The null cusp string... more

We use a Pohlmeyer type reduction to generate classical string solutions in AdS spacetime. In this framework we describe a correspondence between spikes in AdS 3 and soliton profiles of the sinh-Gordon equation. The null cusp string solution and its closed spinning string counterpart are related to the sinh-Gordon vacuum. We construct classical string solutions corresponding to sinh-Gordon solitons, antisolitons and breathers by the inverse scattering technique. The breather solutions can also be reproduced by the sigma model dressing method.

A new numerical method is developed for solution of the Gel'fand -Levitan -Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz Hermitian matrix and special bordering... more

A new numerical method is developed for solution of the Gel'fand -Levitan -Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz Hermitian matrix and special bordering technique. The method is highly competitive with the known discrete layer peeling method in speed and exceeds it noticeably in accuracy at high reflectance.

We develop and experimentally validate a method to characterize linearly chirped fiber Bragg gratings (CFBGs) under local temperature perturbations for tunable spectral shaping. The heat distribution along the FBG is modeled by a... more

We develop and experimentally validate a method to characterize linearly chirped fiber Bragg gratings (CFBGs) under local temperature perturbations for tunable spectral shaping. The heat distribution along the FBG is modeled by a Gaussian-Lorentzian function. The phase and apodization profiles of the CFBG are characterized by measuring the complex reflection spectrum and subsequently using inverse scattering. Finally, coupled mode theory is used to predict the transmittivity of the CFBG under the local temperature perturbations. As an application, we use our model to spectrally shape the spectrum of a gain-switched laser (GSL) and generate ultra-short, optimally designed pulses for high speed wireless data distribution in indoor environments.

We study the single-particle spectral properties of a model for coexisting AFM and ICDW critical fluctuations coupled to electrons, which naturally arises in the context of the stripe-quantum-critical-point scenario for high-T c... more

We study the single-particle spectral properties of a model for coexisting AFM and ICDW critical fluctuations coupled to electrons, which naturally arises in the context of the stripe-quantum-critical-point scenario for high-T c superconducting materials. Within a perturbative approach, we show that the on-shell inverse scattering time deviates from the normal Fermi-liquid behavior near the points of the Fermi surface connected by the characteristic wave-vectors of the critical fluctuations (hot spots). The anomalous behavior is stronger when the hot spots are located near singular points of the electronic spectrum.

We investigate static space dependent σ(x) = ψ ψ saddle point configurations in the two dimensional Gross-Neveu model in the large N limit. We solve the saddle point condition for σ(x) explicitly by employing supersymmetric quantum... more

We investigate static space dependent σ(x) = ψ ψ saddle point configurations in the two dimensional Gross-Neveu model in the large N limit. We solve the saddle point condition for σ(x) explicitly by employing supersymmetric quantum mechanics and using simple properties of the diagonal resolvent of one dimensional Schrödinger operators rather than inverse scattering techniques. The resulting solutions in the sector of unbroken supersymmetry are the Callan-Coleman-Gross-Zee kink configurations. We thus provide a direct and clean construction of these kinks. In the sector of broken supersymmetry we derive the DHN saddle point configurations. Our method of finding such non-trivial static configurations may be applied also in other two dimensional field theories.

In this contribution we describe some soliton based techniques for generating classical AdS string solutions. The methods introduced are useful for further understanding of rotating AdS configurations with spikes which correspond to... more

In this contribution we describe some soliton based techniques for generating classical AdS string solutions. The methods introduced are useful for further understanding of rotating AdS configurations with spikes which correspond to higher twist operators in SYM theory. The main identification (accomplished in arXiv:0712.1193) between solitons and string spikes is reviewed and extended. We describe how inverse scattering technique can be applied for reconstructing AdS string configurations from soliton solutions of sinh-Gordon theory (in the example of AdS 3 ).

The report contains discussions on (1) synthesis and analysis of guided wave optical interconnects; (2) synthesis and analysis of optical waveguides with prescribed TM modes; (3) development and testing of direct scattering solver to... more

The report contains discussions on (1) synthesis and analysis of guided wave optical interconnects; (2) synthesis and analysis of optical waveguides with prescribed TM modes; (3) development and testing of direct scattering solver to analyze optical waveguides; (4) development of inverse scattering theory for the design of planar optical waveguides with same propagation constants for different frequencies; (5) analysis of coupling in multilayered waveguides using inverse scattering techniques; and (6) soliton-soliton interaction in nonlinear optical waveguides and bistability in nonlinear periodic media.

Stieltjes' solution of the classical moment problem is the forerunner of inverse spectral theory. In the modern theory of completely integrable systems, the method of inverse scattering is used to obtain explicit solutions of a class of... more

Stieltjes' solution of the classical moment problem is the forerunner of inverse spectral theory. In the modern theory of completely integrable systems, the method of inverse scattering is used to obtain explicit solutions of a class of Hamiltonian systems which arise as isospectral deformations of a linear operator. In this lecture we explain how Stieltjes's formulas are used to obtain explicit solutions to a number of completely integrable systems, including discrete reductions of some nonlinear partial di erential equations, and the isospectral deformations of Jacobi matrices a.k.a. Toda ows.