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 ...
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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 this book. 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.* In order to achieve clarification of presentation, focus on the inverse scattering problem for scalar homogeneous media.
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Add this copy of Inverse Scattering Theory and Transmission (Cbms-Nsf to cart. $16.39, Sold by Zubal Books rated 4.0 out of 5 stars, ships from Cleveland, OH, UNITED STATES, published 2016 by SIAM-Society for Industrial and Applied Mathematics.
Edition:
2016, Society for Industrial & Applied Mathematics,U.S.
Publisher:
Society for Industrial & Applied Mathematics,U.S.
Published:
2016
Alibris ID:
18026566617
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Add this copy of Inverse Scattering Theory and Transmission Eigenvalues to cart. $109.83, new condition, Sold by booksXpress, ships from Bayonne, NJ, UNITED STATES, published 2016 by Society for Industrial & Applied Mathematics,U.S..
Edition:
2016, Society for Industrial & Applied Mathematics,U.S.
