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Inverse Scattering Theory and Transmission Eigenvalues (Paperback)
Loot Price: R1,899
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Inverse Scattering Theory and Transmission Eigenvalues (Paperback)
Series: CBMS-NSF Regional Conference Series, 88
Expected to ship within 12 - 17 working days
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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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