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Aug 31, 2022
08/22

by
Beals, Richard, 1938-

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xiii, 209 p. : 26 cm

Topics: Scattering (Mathematics), Inverse scattering transform

This paper presents a (semi-)automatic processing technique for GPR data analysis. Exploiting the generalization capabilities of artificial neural networks (ANN), it will be shown that it is possible to feed a Multi-Layer Perceptron (MLP) with a suitable set of input features in order to determine the permittivity of a ground layer. A detailed performance assessment have proven that the algorithm provides very promising results, reconstructing with high accuracy the dielectric properties of...

Topics: Inverse scattering, artificial neural networks, GPR.

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vi, 213 p. : 28 cm

Topics: Optics -- Congresses, Inverse scattering transform -- Congresses

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6.0

May 16, 2022
05/22

by
Colton, David L., 1943-

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x, 305 p. : 25 cm

Topics: Sound-waves -- Scattering, Electromagnetic waves -- Scattering, Inverse scattering transform

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Feb 21, 2022
02/22

by
Colton, David L., 1943-

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xii, 334 p. : 24 cm

Topics: Sound-waves -- Scattering, Electromagnetic waves -- Scattering, Inverse scattering transform

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4.0

May 26, 2022
05/22

by
Sarkola, Eino

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95 p. ; 25 cm

Topics: Acoustic surface waves, Electromagnetic waves, Inverse scattering transform, Scattering...

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x, 204 pages : 25 cm

Topics: Optics, Inverse scattering transform, Optica, Differentiaalvergelijkingen, Inversen,...

In this paper, numerical assessment of two UWB planar monopole patch antennas is presented. One is disc monopole patch antenna with rectangular-slot, which operates from 2.8 GHz to 11.2 GHz and the second one is rectangular patch antenna, which operates from 3.4 GHz to 14.5 GHz. These antennas perform reasonably well in terms of return loss and radiation efficiency. Radiation patterns are almost omni directional. We propose these antennas for breast tumor detection and location. Microwave...

Topics: UWB patch antenna, Dielectric permittivity and conductivity, Inverse scattering, Microwave imaging,...

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xv, 379 p. : 24 cm

Topics: Inverse problems (Differential equations) -- Numerical solutions -- Congresses, Waves --...

The results on Inverse Scattering in multidimensions and on the algebraic properties of equations in 2+1 (i.e. two spatial and one temporal) dimensions should be of particular interest: With respect to algebraic properties of equations in 2+1, the question of finding the recursion operator and the bi-Hamiltonian formulation of these equations has remained open for a rather long time. It was even doubted in the literature if the relevant results in 1+1 could be extended to 2+1. It was recently...

Topics: DTIC Archive, Fokas, A S, CLARKSON UNIV POTSDAM NY, *INVERSE SCATTERING, *WAVE EQUATIONS, ALGEBRA,...

The objective of this basic research project is to describe an imaging protocol which will allow optical imaging to resolve nanoscale features (Near Field Tomography), both a the surface and below, of various components. The AF anticipates exploiting ever smaller devices and the manufacturing/inspection of these will benefit from the basic research done here. The PI will continue his seminal research into near field EM. In this not-well understood area the classical rules of thumb regarding...

Topics: DTIC Archive, PENNSYLVANIA UNIV PHILADELPHIA, *NANOSTRUCTURES, *NEAR FIELD, *OPTICAL IMAGES,...

A paper entitled 'Curved Space Scattering' has already been sent to AFOSR. The abstracts of the paper and report contain statements of the research accomplished. In addition we have looked into the following problems: a. We have employed the Kanal-Moses variational principle to treat the synthetic data discussed in the report listed in 1.1. It was found that if the initial trial function is within 10% of the actual result, then the K-M variational principle gives the result to better than 1%....

Topics: DTIC Archive, Cohen, Jeffrey M, PENNSYLVANIA UNIV PHILADELPHIA DEPT OF PHYSICS, *IONOSPHERE,...

Distributed Radio Frequency (RF) Tomography is a novel approach for detecting underground tunnels and caves over relatively wide areas. This method requires a set of affordable transmitters and receivers randomly deployed above the ground. Using the principles of inverse scattering, it is possible to develop a simplified theory for imaging below ground, thus revealing and locating voids. In this paper, we introduce inversion schemes suited for ground penetrating radar tomography applied to...

Topics: DTIC Archive, AIR FORCE RESEARCH LAB ROME NY, *TOMOGRAPHY, *GROUND PENETRATING RADAR, *TUNNELS,...

The activities done under the grant for the fiscal year 1982 are summarized. Primary emphasis has been the expansion of the applications of the Gelfand-Levitan formalism to provide examples of potentials for which the Schroedinger equation has unusual spectral properties and thereby generalize the kinds of spectral representation which one can have. The investigators were partially successful in considering a case in which the potential is associated with a non-analytic reflection coefficient...

Topics: DTIC Archive, Moses,H E, LOWELL UNIV MA CENTER FOR ATMOSPHERIC RESEARCH, *Inverse scattering,...

The analysis of the advantages and disadvantages of the homomorphic filtering technique applied to solve the exact inverse scattering problem has continued. There have been problems with strongly scattering objects due to phase unwrapping. Work has continued to more carefully compare the reconstruction of V(Psi) from the backpropagation of simulated data with that predicted for the direct problem, from the same data. We note that phase unwrapping is avoided with the differential cepstrum; we...

Topics: DTIC Archive, Fiddy, M A, LOWELL UNIV MA DEPT OF ELECTRICAL ENGINEERING, *QUANTUM THEORY, *INVERSE...

Through-wall imaging (TWI) consists in imaging objects hidden behind an obstacle by using electromagnetic waves at microwave frequencies. Developing systems which see through walls gives the ability to detect and localize people, observe room layouts and understand scenarios that are hidden. The crucial point to be addressed is the presence of the obstacle representing in some cases a wall structure. Indeed, the presence of the wall, on one side, can hinder a successful imaging procedure due...

Topics: DTIC Archive, SECOND UNIV OF NAPLES (ITALY), *TOMOGRAPHY, *IMAGE PROCESSING, *MICROWAVES, INVERSE...

Contents: Convergence to travelling waves of solutions of nonlinear diffusion equations; Stability of travelling pulses of systems of reaction-diffusion equations; The relation between the inverse scattering method for nonlinear wave equations and connection problems for certain nonlinear ordinary differential equations; and Stokes' conjecture concerning the existence of a wave of greatest height and the angle of its slope.

Topics: DTIC Archive, McLeod,J B, MINNESOTA UNIV MINNEAPOLIS, *WAVE PROPAGATION, *TRAVELING WAVES, REPORTS,...

Research investigations and development of the fast adaptive algorithms using orthonormal bases with controlled localization in the time- frequency domain (e.g. wavelets) have been successful and several new algorithms have been developed. Among the results is the Unequally Spaced Fast Fourier Transform (USFFT) algorithm and a new approach to numerical homogenization

Topics: DTIC Archive, Beylkin, Gregory, COLORADO UNIV AT BOULDER, *INVERSE SCATTERING, *FLUID DYNAMICS,...

The goal of this paper is to introduce the application of a globally convergent inverse scattering algorithm to estimate dielectric constants of targets using time-resolved backscattering data collected by a U.S. Army Research Laboratory forward looking radar. The processing of the data was conducted blind, i.e., without any prior knowledge of the targets. The problem is solved by formulating the scattering problem as a coefficient inverse problem for a hyperbolic partial differential equation....

Topics: DTIC Archive, NORTH CAROLINA UNIV AT CHARLOTTE DEPT OF MATHEMATICS AND STATISTICS, *BACKSCATTERING,...

The project addressed a number of fundamental aspects electromagnetic fields and their applications in inverse scattering problems. The program advanced the understanding of generation, propagation, manipulation and detection of random electromagnetic beams. The research effort comprised theoretical, numerical modeling, and experimental developments. We have demonstrated a new way of analyzing the fluctuations of scattered waves and have shown that individual members of an ensemble of...

Topics: DTIC Archive, UNIVERSITY OF CENTRAL FLORIDA ORLANDO OFFICE OF RESEARCH, *INVERSE SCATTERING,...

It is well known that the inverse scattering problem is usually computationally demanding, characterized by (1) slow convergence rate; (2) possibility of convergence to a local optimum instead of the global minimum; (3) instability in the presence of noise. The common way of solving an inverse scattering problem is to cast the problem into an optimization problem where the objective is to minimize the mismatch between the measured scattered field and the calculated scattered field. During the...

Topics: DTIC Archive, NATIONAL UNIV OF SINGAPORE DEPT OF ELECTRICAL AND COMPUTER ENGINEERING, *INVERSE...

The main activity of the research has been in the following two areas: to make the back propagation stable, and to design a frequency-local but space-global algorithm for one-dimensional inverse scattering problems. These two projects are being completed. The first one is an joint effort with V. Rokhlin whereas the second with Mr. Y. Xiang, a graduate student at the Courant Institute, currently support by the ONR grant during the summer.

Topics: DTIC Archive, Chen, Yu, NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES, *MINE DETECTION,...

The objective of the project was to improve performance of accurate methods for predicting radiation characteristics of antenna mounted on large platforms. Our work concentrated mainly on an attempt of devising a viable computational scheme based on utilization of basis functions defined on large supports, and characterized by strongly collimated radiation patterns; we refer to them as directional basis functions. The main motivation for introducing the concept of directional basis functions...

Topics: DTIC Archive, Jaroszewicz, Thomas, MONOPOLE RESEARCH THOUSAND OAKS CA, *PREDICTIONS, *ANTENNA...

In this report, we construct numerical algorithms for the solution of inverse scattering problems in layered acoustic media. Our inverse scattering schemes are based on a collection of so-called trace formulae, and can be viewed as extension of the work started in [3].

Topics: DTIC Archive, Duan, Ran, YALE UNIV NEW HAVEN CT DEPT OF COMPUTER SCIENCE, *INVERSE SCATTERING,...

This report includes these topics: A Range Theorem for the Radon Transform, Multivariate Interpolation and Conditionally Positive Definite Function, Polyharmonic Cardinal Splines, Solutions of underdetermined systems of linear equations, Multivariate interpolation and conditionally positive definite functions II.

Topics: DTIC Archive, Madych, W R, CONNECTICUT UNIV STORRS DEPT OF MATHEMATICS, *INVERSE SCATTERING,...

This grant was concerned with the development of the linear sampling method to determine the location and shape of hostile structures hidden in a known background medium from measured electromagnetic scattering data. The research included the numerical investigation of the ultra-weak variational formulation for Maxwell's equations and the solution of the inverse scattering problem for partially coated obstacles. Since it has previously been shown that the scattering due to the background can be...

Topics: DTIC Archive, Colton, David, DELAWARE UNIV NEWARK, *DETECTION, *NUMERICAL ANALYSIS, *INVERSE...

A summary of a year's work is given through the abstracts of two published papers and a paper accepted for publication. (Author)

Topics: DTIC Archive, Kanal,M, LOWELL UNIV RESEARCH FOUNDATION MASS, *LINEAR SYSTEMS, *RADIATIVE TRANSFER,...

We extend the IST for the Benjamin-Ono (BO) equation in two important ways. First, we restrict the IST to purely real potentials, in which case, the scattering data and the inverse scattering equations simplify. Second, we also extend the analysis of the asymptotics of the Jost functions and the scattering data to include the non-generic classes of potentials, which include, but may not be limited to, all N-soliton solutions. In the process, we also study the adjoint equation of the eigenvalue...

Topics: DTIC Archive, Kaup, D. J., CLARKSON UNIV POTSDAM NY INST FOR NONLINEAR STUDIES, *INVERSE...

AASERT grant N00014-91-J-4037 supported the research of two graduate students, James M. Keiser and Robert Cramer. James Keiser has completed his research and defended his thesis April 17, 1995. The results of his research were described in the report submitted 5/31/95. At about the same time (May 1995) a one year no cost extension for this grant was approved in order to allow Robert Cramer to finish his research towards a Ph.D. At the time of this writing, Robert Cramer has achieved the goals...

Topics: DTIC Archive, Beylkin, Gregory, COLORADO UNIV AT BOULDER, *INVERSE SCATTERING, *FLUID DYNAMICS,...

This final report describes the research work performed by TechniScan Inc. under Air Force Office of Scientific Research contract no. F94620-95-C-0024 for the period March 1, 1995 to March 1, 1998. The principal goal of the project was to advance the imaging capability of Ground Penetrating Radar (GPR) via the application of toll wave, vector, 3D inverse scattering (IS) methods and to demonstrate the utility of this approach with a laboratory scale (1/20 th scale, 1-18 GHz) GPR scanner. Inverse...

Topics: DTIC Archive, Bourp, David T, TECHNISCAN INC SALT LAKE UT, *INVERSE SCATTERING, *GROUND PENETRATING...

During the period of this grant we 1) showed that transmission eigenvalues exist and can be determined from the far field pattern of the scattered wave, 2) obtained a formula showing how accurate estimates of the permittivity can be obtained from a knowledge of the first (real) transmission eigenvalue and 3) extended the linear sampling method from the frequency domain to the time domain. In addition, we continued our study of the target identification problem for partially coated dielectric...

Topics: DTIC Archive, DELAWARE UNIV NEWARK DEPT OF MATHEMATICS, *INVERSE SCATTERING, ABSTRACTS, ANISOTROPY,...

In this paper we shall indicate some of the current directions in the study of the analytic continuation of solutions to partial differential equations. Our intended audience is not only those mathematicians working in the area of partial differential equations, but also complex analysts interested in seeing how a major topic in the theory of analytic functions can be extended to include certain classes of linear partial differential equations. Our specific aim is to provide a survey of the...

Topics: DTIC Archive, Colton,David, DELAWARE UNIV NEWARK APPLIED MATHEMATICS INST, *PARTIAL DIFFERENTIAL...

In an earlier paper, the authors derived a Fredholm integral equation of the first kind for the solution of the inverse source problem for acoustic waves. The eigenvalues of this equation were shown to converge rapidly to zero and also to include zero. Thus, the solution was shown to be non-unique and even the particular part of the solution of that equation was ill-conditioned. In this note it is shown how to obtain the non-trivial information of that integral equation in a well-conditioned...

Topics: DTIC Archive, Bleistein, Norman, DENVER UNIV CO DEPT OF MATHEMATICS, *ACOUSTIC WAVES, *INVERSE...

Our goal is the design of fast parallel algorithms statistical inference for scalar and wave propagation problems. We have looked at source inversion and inverse medium problem problems. We use a Bayesian approach in which the regularization appears as prior information and the data mismatch appears as a likelihood information, given known noise probability density functions. A key component of all of our algorithms is the approximation of the Hessian operator. Key components of our work are...

Topics: DTIC Archive, TEXAS UNIV AT AUSTIN INST FOR COMPUTATIONAL ENGINEERING AND SCIENCES, *BAYES THEOREM,...

The report is divided into four parts. Part one is about nonlinear microwave amplification and the further use of nonlinear Schroedinger equations to model amplifiers. Part two is about speeds of frequency components of electromagnetic pulses, and a related inversion method. Our numerical computation of precursors shows that damping increases the speed of frequency components to a degree that is consistent with energy velocity. The speed up here is slight, and a medium that has been called...

Topics: DTIC Archive, Roberts, Thomas, OPERATIONAL TECHNOLOGIES CORP SAN ANTONIO TX, *ELECTROMAGNETIC...

Topics: DTIC Archive, Hastings,S P, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *BOUNDARY VALUE...

This paper generalizes an integral representation formula for eigenfunctions of Strum-Liouville operators, known as the Volterra transformation operator in the theory of the inverse scattering problem, to higher-order differential operators. A specific fourth-order initial value problem is considered whose solutions are expressed as an inverse-Laplace-Borel transform.

Topics: DTIC Archive, Symes,W, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER,...

We address the inverse problem for scattering of acoustic waves due to an inhomogeneous medium. We derive and analyze the Hessian in both H older and Sobolev spaces. Using an integral equation approach based on Newton potential theory and compact embeddings in Holder and Sobolev spaces, we show that the Hessian can be decomposed into two components, both of which are shown to be compact operators. Numerical examples are presented to validate our theoretical results. The implication of the...

Topics: DTIC Archive, TEXAS UNIV AT AUSTIN INST FOR COMPUTATIONAL ENGINEERING AND SCIENCES, *INVERSE...

Starting from the Painleve-Backlund equations obtained from Painleve analysis of the Korteweg-de Vries equation, closed form solitary wave solutions are explicitly constructed. It is shown that repetitive application of the Mobius group of fractional linear transformations does not lead to new solutions. Various connections of the Painleve method with Hirota's formalism, the Backlund transformation method, the Lax approach and the Inverse Scattering Technique are discussed in detail.

Topics: DTIC Archive, Hereman, W, WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES, *PARTIAL...

This project was concerned with the inverse scattering problem for time harmonic acoustic and electromagnetic waves. A new method has been developed to solve problems of this type based on the theory of Herglotz wave functions and nonlinear optimization methods. Preliminary numerical examples have been given for the case of both acoustic and electromagnetic waves.

Topics: DTIC Archive, Colton, David, DELAWARE UNIV NEWARK DEPT OF MATHEMATICAL SCIENCES, *METHODOLOGY,...

The Principal Investigator's principal research direction has been to find appropriate triangularity conditions for the Gelfand-Levitan kernel in three-dimensions. The Gelfand-Levitan kernel for the one-dimensional problem has served as a model.

Topics: DTIC Archive, Moses,Harry E, LOWELL UNIV RESEARCH FOUNDATION MA, *THREE DIMENSIONAL, *INVERSE...

During the past three years there have been 7 publications, two of which are chapters in books, in addition to 8 Program in Applied Mathematics Reports (preprints) which have been submifted for publication. Also, the PI has been invited to give approx. 20 lectures at universities and conferences in the US and abroad. The research program has been productive. A brief overview is given below; for the full details we refer to the publications.

Topics: DTIC Archive, Beylkin, Gregory, COLORADO UNIV AT BOULDER, *INVERSE SCATTERING, *FLUID DYNAMICS,...

An analytic method for the reconstruction of the profiles of refractive indices of inhomogeneous, stratified regions is presented. The reflection coefficient, r(k), for time-harmonic electromagnetic waves is represented as a rational function of k, the wave number. One-dimensional inverse scattering theory has been applied to obtain analytic, closed-form expressions for the profile functions, q(x), from r(k). The profile reconstruction method is demonstrated with a three-pole r(k), the yields...

Topics: DTIC Archive, Jordan,Arthur K, NAVAL RESEARCH LAB WASHINGTON D C, *ELECTROMAGNETIC SCATTERING,...

Topics: DTIC Archive, Weston, Vaughan H, PURDUE UNIV LAFAYETTE IN DEPT OF MATHEMATICS, *ELECTROMAGNETIC...

The Bleistein Cohen separation of a source (for the inhomogeneous Helmholtz wave equation) distribution into radiating and non-radiating portions is reformulated into a form suitable for deriving a wave equation governing the radiating portion of the source distribution. (Author)

Topics: DTIC Archive, Bojarski,Norbert N, BOJARSKI (NORBERT N) NEWPORT BEACH CA, *SOURCES, *INVERSE...

An extensive literature survey on the field of inverse scattering as it applies to determining the spatial distribution of electron density in the ionosphere is presented. The references are primarily from the period 1970-1981. Abstracts are included. (Author)

Topics: DTIC Archive, Stone,W Ross, IRT CORP SAN DIEGO CA, *IONOSPHERE, *ELECTRON DENSITY, *LITERATURE...

Topics: DTIC Archive, Morawetz, Cathleen S, NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES,...

The scattering of normal incident time harmonic TEM electromagnetic wave by a cylindrical target with axis along z direction is considered. The whole space domain 0 is divided into three connected but non-overlapping sub- domains, the interior region -01 representing the target and possessing a non- orthogonal cylindrical grid system centered in itself, the intermediate region - 02 representing the free space just outside of the target and possessing the same 03 grid system, and the exterior...

Topics: DTIC Archive, NUMERICAL COMPUTATION CORP STONY BROOK NY, *ELECTROMAGNETIC SCATTERING, *INVERSE...

We investigate several inverse methods to determine the dielectric profile of an almost periodic structure composed of several periodicities or tones. For widely spaced tones a resonance method provides the most useful solution while for closely spaced tones the Gelfand-Levitan-Marchenko theory appears to be the most promising. In this way these two methods complement each other so that a wide range of almost periodic media can be investigated. Criteria for characterizing resonant (widely...

Topics: DTIC Archive, Jordan,A K, NAVAL RESEARCH LAB WASHINGTON DC, *ELECTROMAGNETIC SCATTERING, *MEDIA,...

Research in Nonlinear Waves and Inverse Scattering is continuing with many new and interesting results obtained. In this report a summary of the key areas of research is given and a list of research publications and preprints has been compiled. The main areas of interest include: multidimensional nonlinear wave equations of physical significance, multidimensional inverse scattering, numerically induced instabilities and chaos, and forced nonlinear wave problems.

Topics: DTIC Archive, Ablowitz, Mark J, COLORADO UNIV AT BOULDER DEPT OF APPLIED MATHEMATICS, *INVERSE...