The use of constraints for solving inverse scattering problems: Physical optics and the linear sampling method

Inverse Problems

Volumn 21, Issue 1, 2005, Pages 207-222

  Brignone, Massimo ^a   Piana, Michele ^a  

^a UNIVERSITY OF GENOA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; ELECTROMAGNETIC WAVES; INVERSE PROBLEMS; LINEARIZATION; PROBLEM SOLVING; SAMPLING;

ACOUSTIC SCATTERING; INVERSE SCATTERING PROBLEMS; LINEAR SAMPLING METHOD; RECONSTRUCTION ALGORITHMS;

PHYSICAL OPTICS;

EID: 13744262155     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/21/1/013     Document Type: Article

References (25)

1. Bertero M and De Mol C 1996 Super-resolution by data inversion Prog. Opt. 36 129-78
2. Bleistein N and Bojarski N N 1974 Recently developed formulations of the inverse problem in acoustics and electromagnetics Report MS-R-7501, Department of Mathematics, University of Denver
3. Bojarski N N 1982 A survey of the physical optics inverse scattering identity IEEE Trans. Antennas Propag. 20 980-9
4. Brandfass M, Lanterman A D and Warnick K F 2001 A comparison of the Colton-Kirsch inverse scattering method with the linearized tomographic inverse scattering Inverse Problems 17 1797-816
5. Cakoni F and Colton D 2003 On the mathematical basis of the linear sampling method Geogr. Math. J. 10 911-25
6. Colton D, Coyle J and Monk P 2000 Recent developments in inverse acoustic scattering theory SIAM Rev. 42 369-414
7. Colton D, Giebermann K and Monk P 2000 The regularized sampling method SIAM J. Sc. Comput. 21 316-30
8. Colton D, Haddar H and Piana M 2003 The linear sampling method in inverse electromagnetic scattering theory Inverse Problems 19 S105-38
9. Colton D and Kress R 1998 Inverse Acoustic and Electromagnetic Scattering Theory (Berlin: Springer)
10. Colton D and Kirsch A 1996 A simple method for solving inverse scattering problems in the resonance regions Inverse Problems 13 383-93
11. Colton D and Piana M 1998 The simple method for solving the electromagnetic inverse scattering problem: the case of the TE polarized waves Inverse Problems 14 597-614
12. Colton D, Piana M and Potthast R 1997 A simple method using Morozov's discrepancy principle for solving inverse scattering problems Inverse Problems 13 1477-93
13. Das Y and Boerner W M 1978 On radar target shape estimation using algorithms for reconstruction from projections IEEE Trans. Antennas Propag. 26 274-9
14. Frieden B R 1971 Evaluation, design and extrapolation methods for optical signals, based on use of the prolate functions Prog. Opt. 9 311-406
15. Gerchberg R W 1974 Super-resolution through error energy reduction Opt. Acta 21 709-21
16. Hadamard J 1923 Lectures on Cauchy's Problem in Linear Partial Differential Equations (New Haven, CT: Yale University Press)
17. Kress R 2003 Newton's method for inverse obstacle scattering meets the method of least-squares Inverse Problems 19 S91-104
18. Lagendijk R, Biemond J and Boekee D 1988 Regularized iterative image restoration with ringing reduction IEEE Trans. Acoust. Speech Signal Process. 36 1874-88
19. Langenberg K J 1987 Applied inverse problems for acoustic, electromagnetic and elastic wave scattering Basic Methods of Tomography and Inverse Problems ed P Sabatier (Bristol: Adam Hilger) pp 127-467
20. Mager R D and Bleistein N 1978 An examination of the limited aperture problem of physical optics inverse scattering IEEE Trans. Antennas Propag. 26 695-9
21. Piana M and Bertero M 1997 Projected Landweber method and preconditioning Inverse Problems 13 441-63
22. Pratt W K 2001 Digital Image Processing (New York: Wiley)
23. Slepian D 1961 Prolate spheroidal wave functions, Fourier analysis, and uncertainty-IV Bell Syst. Tech. J. 43 3009
24. Tacchino A, Coyle J and Piana M 2002 Numerical validation of the linear sampling method Inverse Problems 18511-27
25. Tikhonov A N 1963 Regularization of incorrectly posed problems Sov. Math. Dokl. 4 1624-7