Download or read book A Direct and Inverse Scattering Transmission Problem for Periodic Inhomogeneous Media written by Beata Strycharz-Szemberg and published by . This book was released on 1996 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Factorization Method for Inverse Scattering from Periodic Inhomogeneous Media written by Kai Sandfort and published by KIT Scientific Publishing. This book was released on 2014-10-16 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the identification of the shape of penetrable periodic media by means of scattered time-harmonic waves. Mathematically, this is about the determination of the support of a function which occurs in the governing equations. Our theoretical analysis shows that this problem can be strictly solved for acoustic as well as for electromagnetic radiation by the so-called Factorization Method. We apply this method to reconstruct a couple of media from numerically simulated field data.
Download or read book The Interior Transmission Problem and Inverse Scattering from Inhomogeneous Media written by B. P. Rynne and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Scattering Theory and Transmission Eigenvalues written by Fioralba Cakoni and published by SIAM. This book was released on 2016-10-28 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory is a major theme of applied mathematics, and it has applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting particular problems in the development of efficient inversion algorithms. Although linearized models continue to play an important role in many applications, an increased need to focus on problems in which multiple scattering effects cannot be ignored has led to a central role for nonlinearity, and the possibility of collecting large amounts of data over limited regions of space means that the ill-posed nature of the inverse scattering problem has become a problem of central importance. Initial efforts to address the nonlinear and the ill-posed nature of the inverse scattering problem focused on nonlinear optimization methods. While efficient in many situations, strong a priori information is necessary for their implementation. This problem led to a qualitative approach to inverse scattering theory in which the amount of a priori information is drastically reduced, although at the expense of only obtaining limited information about the values of the constitutive parameters. This qualitative approach (the linear sampling method, the factorization method, the theory of transmission eigenvalues, etc.) is the theme of Inverse Scattering Theory and Transmission Eigenvalues. The authors begin with a basic introduction to the theory, then proceed to more recent developments, including a detailed discussion of the transmission eigenvalue problem; present the new generalized linear sampling method in addition to the well-known linear sampling and factorization methods; and in order to achieve clarification of presentation, focus on the inverse scattering problem for scalar homogeneous media.
Download or read book Point Sources and Multipoles in Inverse Scattering Theory written by Roland Potthast and published by CRC Press. This book was released on 2001-05-30 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering. The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering processes and led to remarkable advances in a range of
Download or read book Inverse Scattering Theory and Transmission Eigenvalues written by Fioralba Cakoni and published by SIAM. This book was released on 2022-12-07 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers—a subset of transmission eigenvalues—using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.
Download or read book The Factorization Method for Inverse Scattering from Periodic Inhomogeneous Media written by Kai Sandfort and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Acoustic and Electromagnetic Scattering Theory written by David Colton and published by Springer Science & Business Media. This book was released on 2012-10-26 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this third edition, new sections have been added on the linear sampling and factorization methods for solving the inverse scattering problem as well as expanded treatments of iteration methods and uniqueness theorems for the inverse obstacle problem. These additions have in turn required an expanded presentation of both transmission eigenvalues and boundary integral equations in Sobolev spaces. As in the previous editions, emphasis has been given to simplicity over generality thus providing the reader with an accessible introduction to the field of inverse scattering theory. Review of earlier editions: “Colton and Kress have written a scholarly, state of the art account of their view of direct and inverse scattering. The book is a pleasure to read as a graduate text or to dip into at leisure. It suggests a number of open problems and will be a source of inspiration for many years to come.” SIAM Review, September 1994 “This book should be on the desk of any researcher, any student, any teacher interested in scattering theory.” Mathematical Intelligencer, June 1994
Download or read book Inverse Scattering Problems for Acoustic Waves in an Inhomogeneous Medium written by Andrzej W. Kȩdzierawski and published by . This book was released on 1990 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Qualitative Approach to Inverse Scattering Theory written by Fioralba Cakoni and published by Springer Science & Business Media. This book was released on 2013-10-28 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory is an important area of applied mathematics due to its central role in such areas as medical imaging , nondestructive testing and geophysical exploration. Until recently all existing algorithms for solving inverse scattering problems were based on using either a weak scattering assumption or on the use of nonlinear optimization techniques. The limitations of these methods have led in recent years to an alternative approach to the inverse scattering problem which avoids the incorrect model assumptions inherent in the use of weak scattering approximations as well as the strong a priori information needed in order to implement nonlinear optimization techniques. These new methods come under the general title of qualitative methods in inverse scattering theory and seek to determine an approximation to the shape of the scattering object as well as estimates on its material properties without making any weak scattering assumption and using essentially no a priori information on the nature of the scattering object. This book is designed to be an introduction to this new approach in inverse scattering theory focusing on the use of sampling methods and transmission eigenvalues. In order to aid the reader coming from a discipline outside of mathematics we have included background material on functional analysis, Sobolev spaces, the theory of ill posed problems and certain topics in in the theory of entire functions of a complex variable. This book is an updated and expanded version of an earlier book by the authors published by Springer titled Qualitative Methods in Inverse Scattering Theory Review of Qualitative Methods in Inverse Scattering Theory All in all, the authors do exceptionally well in combining such a wide variety of mathematical material and in presenting it in a well-organized and easy-to-follow fashion. This text certainly complements the growing body of work in inverse scattering and should well suit both new researchers to the field as well as those who could benefit from such a nice codified collection of profitable results combined in one bound volume. SIAM Review, 2006
Download or read book Inverse Scattering Theory and Transmission Eigenvalues written by Fioralba Cakoni and published by . This book was released on 2022-12-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers-a subset of transmission eigenvalues-using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.
Download or read book Inverse Scattering for a Penetrable Cavity and the Transmission Eigenvalue Problem written by Shixu Meng and published by . This book was released on 2016 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we consider the scattering of point sources inside a cavity surrounded by an inhomogeneous medium and its inverse problem of determining the boundary of the cavity from measurements of the scattered field inside the cavity. We apply the linear sampling method and factorization method to numerically reconstruct the boundary of the cavity. We prove that the linear sampling method works when the wave number is not an exterior transmission eigenvalue. We prove that the exterior transmission eigenvalues form a discrete set. We then consider both the exterior transmission eigenvalue problem and the interior transmission eigenvalue problem for a spherically stratified media and study the inverse spectral problem for the exterior transmission eigenvalue problem. Finally we consider the interior transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that changes sign inside its support. We prove that the set of transmission eigenvalues is nonempty discrete, infinite and without finite accumulation points.
Download or read book An Inverse Electromagnetic Scattering Problem for a Bi periodic Inhomogeneous Layer on a Perfectly Conducting Plate written by Guanghui Hu and published by . This book was released on 2010 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Resolution of Inverse Scattering Problems for the Full Three dimensional Maxwell equations in Inhomogeneous Media Using the Approximate Inverse written by Aref Lakhal and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Scattering in Inhomogeneous Background Media written by and published by . This book was released on 2005 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inverse scattering problem is solved within the distorted wave Born approximation (DWBA) using a generalized time reversal based formulation. The theory is applicable to arbitrary (non-point) N(sub alpha) element transmitter arrays and N(sub beta) element receiver arrays and to scattering systems characterized by scattering potentials interrogated in a set of scattering experiments employing single or multiple temporal frequencies. The inversion scheme generates a pseudo-inverse reconstruction of the scattering potential based on the SVD of the N(sub beta) x N(sub alpha) multistatic data matrix considered as a mapping from the Hilbert space of scattering potentials to the vector space of N(sub beta) x N(sub alpha) x N(sub omega) complex N-tuples, where N(sub omega) is equal to the number of discrete temporal frequencies employed in the set of scattering experiments. The theory and results in this report have been previously published and appear in: 1. A.J. Devaney and M. Dennison, "Inverse Scattering in Inhomogeneous Background Media," Inverse Problems 19, No. 4 (August 2003), p855-870; 2. M. Dennison and A.J. Devaney, "Inverse Scattering in Inhomogeneous Background Media: Part II, SVD analysis and multiple frequency case," Inverse Problems 20 (2004), p1307-1324.
Download or read book Time Domain Wave splittings and Inverse Problems written by Sailing He and published by . This book was released on 1998 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to recent developments in the application of wave-splitting methods to direct and inverse scattering of wave fields. Here wave-splitting refers to the decomposition of the total field into two components which propagate in opposite directions. Although the text emphasizes time domain methods, it includes some applications to frequency domain problems.
Download or read book Radiation and Scattering from Periodic Geometries in Inhomogeneous Media written by Wen-Jiunn Tsay and published by . This book was released on 1995 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:
