Postprocessing of the linear sampling method by means of deformable models

SIAM Journal on Scientific Computing

Volumn 30, Issue 5, 2007, Pages 2613-2634

  Aramini, R ^a   Brignone, M ^a   Coyle, J ^b   Piana, M ^c  

^a UNIVERSITY OF GENOA   (Italy)

^b MONMOUTH UNIVERSITY   (United States)

^c UNIVERSITY OF VERONA   (Italy)

Author keywords

Active contours; Inverse scattering; Linear sampling method; Regularization

Indexed keywords

EDGE DETECTION; INTEGRAL EQUATIONS; INVERSE PROBLEMS; NUMERICAL METHODS;

ACTIVE CONTOURS; DEFORMABLE MODELS; ILL POSED; INTEGRAL EQUATION OF THE FIRST KINDS; INVERSE-SCATTERING; LINEAR SAMPLING; LINEAR SAMPLING METHODS; NUMERICAL EFFECTIVENESS; REGULARISATION; REGULARIZATION ALGORITHMS;

VISUALIZATION;

EID: 55349144133     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/070701583     Document Type: Article

References (26)

1. R. ARAMINI, On Some Open Problems in the Implementation of the Linear Sampling Method, Ph.D. thesis. Dipartimento di Matematica, Università di Trento, 2007; also available online from http://eprints.biblio.unitn.it/archive/00001239.
2. R. ARAMINI, M. BRIGNONE, AND M. PIANA, The linear sampling method without sampling, Inverse Problems, 22 (2006), pp. 2237-2254.
3. F. CAKONI AND D. COLTON, On the mathematical basis of the linear sampling method, Georgian Math. J., 10 (2003), pp. 911-925.
4. F. CAKONI AND D. COLTON, Qualitative Methods in Inverse Scattering Theory, Springer, Berlin, 2006.
5. F. CAKONI, M. FARES, AND H. HADDAR, Analysis of two linear sampling methods applied to electromagnetic imaging of buried objects, Inverse Problems, 22 (2006), pp. 845-867.
6. I. CATAPANO, L. CROCCO, AND T. ISERNIA, On simple methods for shape reconstruction of unknown scatterers, IEEE Trans. Antennas amd Propagation, 55 (2007), pp. 1431-1436.
7. I. COHEN, L. D. COHEN, AND N. AYACHE, Using deformable surfaces to segment 3D images and infer differential structures, Comput Vision Graph. Image Process.: Image Understanding, 56 (1992), pp. 242-263.
8. L. D. COHEN, On active contour models and ballons, Comput Vision Graph. Image Process.: Image Understanding, 53 (1991), pp. 211-218.
9. F. COLLINO, M. FARES, AND H. HADDAR, Numerical and analytical studies of the linear sampling method in electromagnetic inverse scattering problems, Inverse Problems, 19 (2003), pp. 1279-1298.
10. D. COLTON, H. HADDAR, AND M. PIANA, The linear sampling method in electromagnetic scattering theory, Inverse Problems, 19 (2003), pp. S105-S137.
11. D. COLTON AND A. KIRSCH, A simple method for solving inverse scattering problems in the resonance region, Inverse Problems, 12 (1996), pp. 383-393.
12. D. COLTON AND R. KRESS, Inverse Acoustic and Electromagnetic Scattering Theory, Springer, Berlin, 1998.
13. D. COLTON AND P. MONK, Target identification of coated objects, IEEE Trans. Antennas and Propagation, 54 (2006), pp. 1232-1242.
14. D. COLTON, M. PIANA, AND R. POTTHAST, A simple method using Morozov's discrepancy principle for solving inverse scattering problems, Inverse Problems, 13 (1997), pp. 1477-1493.
15. R. COURANT AND D. HILBERT, Method of Mathematical Physics, Vol. 1, Interscience, New York, 1953.
16. J. COYLE, M. BRIGNONE, AND R. ARAMINI, The Linear Sampling Method, a New Regularized Solution and Real Data, in Proceedings of the ACES 2007 Conference, Verona, Italy, 2007, pp. 1927-1933.
17. A. J. JERRI, The Shannon sampling theorem-its various extensions and applications: A tutorial review, Proc. IEEE, 65 (1977), pp. 1565-1595.
18. M. KASS, A. WITKIN, AND A. R. TERZOPOULOS, Snakes: Active contour models, Int. J. Comput. Vision, 4-1 (1987), pp. 321-331.
19. A. KIRSCH, Characterization of the shape of a scattering obstacle using the spectral data of the far field operator, Inverse Problems, 14 (1998), pp. 1489-1512.
20. R. MCGAHAN AND R. KLEINMAN, Special session on image reconstruction using real data, IEEE Antennas and Propagation, 38 (1996), pp. 39-40.
21. A. M. OSTROWSKI, Über die Stetigkeit von charakteristischen Wurzeln in Abhängigkeit von den Matrizenelementen, Jahresber. Deutsch. Math.-Verein., 60, Abt. 1 (1957), pp. 40-42.
22. N. SHELTON AND K. F. WARNICK, Behavior of the regularized sampling inverse scattering method at internal resonance frequencies, Prog. Electromagn. Res., 38 (2002), pp. 29-45.
23. A. TACCHINO, J. COYLE, AND M. PIANA, Numerical validation of the linear sampling method, Inverse Problems, 18 (2002), pp. 511-527.
24. A. N. TIKHONOV, A. V. GONCHARSKY, V. V. STEPANOV, AND A. G. YAGOLA, Numerical Methods for the Solution of Ill-Posed Problems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
25. J. H. WILKINSON, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965.
26. C. XU AND L. PRINCE. Snakes, Shapes, and Gradient Vector Flow, IEEE Trans. Image Process., 7 (1998), pp. 359-369.