Inverse Scattering Theory and Transmission Eigenvalues - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Inverse Scattering Theory and Transmission Eigenvalues write by Fioralba Cakoni. This book was released on 2016-10-28. Inverse Scattering Theory and Transmission Eigenvalues available in PDF, EPUB and Kindle. 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.
Inverse Scattering Theory and Transmission Eigenvalues
Inverse Scattering Theory and Transmission Eigenvalues - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Inverse Scattering Theory and Transmission Eigenvalues write by Fioralba Cakoni. This book was released on 2022-12-07. Inverse Scattering Theory and Transmission Eigenvalues available in PDF, EPUB and Kindle. 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.
Inverse Scattering Theory and Transmission Eigenvalues
Inverse Scattering Theory and Transmission Eigenvalues - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Inverse Scattering Theory and Transmission Eigenvalues write by Fioralba Cakoni. This book was released on 2022-12-31. Inverse Scattering Theory and Transmission Eigenvalues available in PDF, EPUB and Kindle. 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.
Inverse Acoustic and Electromagnetic Scattering Theory
Inverse Acoustic and Electromagnetic Scattering Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Inverse Acoustic and Electromagnetic Scattering Theory write by David Colton. This book was released on 2019-11-06. Inverse Acoustic and Electromagnetic Scattering Theory available in PDF, EPUB and Kindle. The inverse scattering problem is central to many areas of science and technology such as radar, 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 fourth edition, a number of significant additions have been made including a new chapter on transmission eigenvalues and a new section on the impedance boundary condition where particular attention has been made to the generalized impedance boundary condition and to nonlocal impedance boundary conditions. Brief discussions on the generalized linear sampling method, the method of recursive linearization, anisotropic media and the use of target signatures in inverse scattering theory have also been added.
Qualitative Methods in Inverse Scattering Theory
Qualitative Methods in Inverse Scattering Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Qualitative Methods in Inverse Scattering Theory write by Fioralba Cakoni. This book was released on 2005-12-29. Qualitative Methods in Inverse Scattering Theory available in PDF, EPUB and Kindle. Inverse scattering theory has been a particularly active and successful field in applied mathematics and engineering for the past twenty years. The increasing demands of imaging and target identification require new powerful and flexible techniques besides the existing weak scattering approximation or nonlinear optimization methods. One class of such methods comes under the general description of qualitative methods in inverse scattering theory. This textbook is an easily-accessible "class-tested" introduction to the field. It is accessible also to readers who are not professional mathematicians, thus making these new mathematical ideas in inverse scattering theory available to the wider scientific and engineering community.
