Title: A Qualitative Approach to Inverse Scattering Theory /
Authors: Cakoni, Fioralba,; Colton, David,; Colton, David L., 1943-; Cakoni, Fioralba.
Year: 2014
Subjects: Fourier analysis.; Electrical engineering; Differential equations, Partial.; Mathematics; Mathematics.; Fourier analysis.; Differential equations, partial.; Computer engineering; Inverse scattering transform.; Scattering (Mathematics); Transformations (Mathematics)
Abstract: 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.
Contents: 1. Functional Analysis and Sobolev Spaces -- 2. Ill-Posed Problems -- 3. Scattering by Imperfect Conductors -- 4. Inverse Scattering Problems for Imperfect Conductors -- 5. Scattering by Orthotropic Media -- 6. Inverse Scattering Problems for Orthotropic Media -- 7. Factorization Methods -- 8. Mixed Boundary Value Problems -- 9. Inverse Spectral Problems for Transmission Eigenvalues -- 10. A Glimpse at Maxwell's Equations.