Inverse Problems, Tomography, and Image Processing

Ramm, Alexander G. (EDT)

ISBN 10: 1489919007 / ISBN 13: 9781489919007

Editore: Springer, 2013

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Codice articolo 20346195-n

Dati bibliografici

• Titolo: Inverse Problems, Tomography, and Image Processing
• Editore: Springer
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 1489919007
• ISBN 13: 9781489919007
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

Edge-Preserving Regularization for Quantitative Reconstruction Algorithms in Microwave Imaging . . . . . . . . . . . . . . . . . . . . . . . . .. . . 113 . . . . . . .

Contenuti

Volume One:- 1: Introduction. 1.1. Why are inverse problems interesting and practically important? 1.2. Examples of inverse problems. 1.3. Ill-posed problems. 1.4. Examples of Ill-posed problems. 2: Methods of solving ill-posed problems. 2.1. Variational regularization. 2.2. Quasisolutions, quasinversion, and Backus-Gilbert method. 2.3. Iterative methods. 2.4. Dynamical system method (DSM). 2.5. Examples of solutions of ill-posed problems. 2.6. Projection methods for ill-posed problems. 3: One-dimensional inverse scattering and spectral problems. 3.1. Introduction. 3.2. Property C for ODE. 3.3. Inverse problem with I-function as the data. 3.4. lnverse spectral problem. 3.5. Inverse scattering on half-line. 3.6. Inverse scattering problem with fixed-energy. 3.7. Inverse scattering with 'incomplete data'. 3.8. Recovery of quarkonium systems. 3.9. Krein's method in inverse scattering. 3.10. Inverse problems for the heat and wave equations. 3.11. Inverse problem for an inhomogeneous Schrödinger equation. 3.12. An inverse problem of ocean acoustics. 3.13. Theory of ground-penetrating radars. Volume Two:- 4: Inverse obstacle scattering. 4.1. Statement of the problem. 4.2. Inverse obstacle scattering problems. 4.3. Stability estimates for the solution to IOSP. 4.4. High-frequency asymptotics. 4.5. Remarks about numerical methods. 4.6. Analysis of a method for identification ofobstacles. 5: Inverse scattering problem. 5.1. Introduction. 5.2. Inverse potential scattering problem with fixed-energy data. 5.3. Inverse geophysical scattering with fixed-frequency data. 5.4. Proofs of some estimates. 5.5. Construction of the Dirichlet-to-Neumann map. 5.6. Property C. 5.7. Necessary and sufficient condition for scatterers. 5.8. The Born inversion. 5.9. Uniqueness theorems for inverse spectral problems. 6: Non-uniqueness and uniqueness results. 6.1. Examples of nonuniqueness for an inverse problem of geophysics. 6.2. A uniqueness theorem for an inverse problem. 6.3. Property C and an inverse problem for a hyperbolic equation. 6.4. Continuation of the data. 7: Inverse problems of potential theory. 7.1. Inverse problem of potential theory. 7.2. Antenna synthesis problems. 7.3. Inverse source problem for hyperbolic equations. 8: Non-overdetermined inverse problems. 8.1. Introduction. 8.2. Assumptions. 8.3. The problem and the result. 8.4. Finding lpj(s) from lp](s). 8.5. Appendix. 9: Low-frequency inversion. 9.1. Derivation of the basic equation. Uniqueness results. 9.2. Analytical solution of the basic equation. 9.3. Characterization of the low-frequency data. 9.4. Problems of numerical implementation. 9.5. Half-spaces with different properties. 9.6. Inversion of the data given on a sphere. 9.7. Inversion of the data given on a cylinder. 9.8. Two-dimensional inverse problems. 9.9.