A Variational Method in Image Recovery

SIAM Journal on Numerical Analysis

Volumn 34, Issue 5, 1997, Pages 1948-1979

  Aubert, Gilles ^a   Vese, Luminita ^a  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

Calculus of variations; Image processing; Legendre Fenchel transform; Partial differential equations

Indexed keywords

EID: 0011235023     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003614299529230X     Document Type: Article

References (29)

1. L. ALVAREZ AND L. MAZORRA, Signal and image restoration using shock filters and anisotropic diffusion, SIAM J. Numer. Anal., 31(1992), pp. 590-605.
2. F. CATTE, P. L. LIONS, J. M. MOREL, AND T. COLL, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 29(1992), pp. 182-193.
3. A. CHAMBOLLE AND P. L. LIONS, Image Recovery via Total Variation Minimization and Related Problems, Numer. Math., Vol. 76, 2(1997), pp. 167-188.
4. P. CHARBONNIER, Reconstruction d'image: Regularisation avec prise en compte des discontinuitis, Ph.D. thesis, University of Nice-Sophia Antipolis, 1994.
5. P. CHARBONNIER, G. AUBERT, L. BLANC-FERAUD, AND M. BARLAUD, Two deterministic half-quadratic regularization algorithms for computed imaging, First IEEE Internat. Conf. on Image Processing, Vol. II, Austin, TX, IEEE, Piscataway, NJ, 1994, pp. 168-172.
6. P. CHARBONNIER, L. BLANC-FERAUD, G. AUBERT, AND M. BARLAUD, Deterministic edge-preserving regularization in computed imaging, IEEE Trans. Image Processing, 6(1997), pp. 298-311.
7. P. G. CIARLET, Introduction à l'analyse numerique matricielle et à l'optimisation, Masson, Paris, 1990.
8. M. CRANDALL, H. ISHII, AND P. L. LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., 27(1992), pp. 1-67.
9. J. P. CROUZEIX, A relationship between the second derivatives of a convex function and of its conjugate, Math. Programming, 13(1977), pp. 364-365.
10. B. DACOROGNA, Direct Method in the Calculus of Variations, Springer-Verlag, Berlin, 1989.
11. F. DEMENGEL AND R. TEMAM, Convex functions of a measure and applications, Indiana Univ. Math. J., 33(1984), pp. 673-709.
12. I, EKELAND AND R. TEMAM, Analyse convexe et problhmes variationnels, Dunod-Gauthier-Villars, Paris, 1974.
13. S. GEMAN AND D. GEMAN, Stochastic relaxation, Gibbs distribution and the bayesian restoration of images, IEEE Trans. Pattern Anal. Machine Intell., 6(1984), pp. 721-741.
14. D. GEMAN AND C. YANG, Nonlinear Image Recovery with Half-Quadratic Regularization and FFt's, preprint, 1993.
15. D. GEMAN AND G. REYNOLDS, Constrained restoration and the recovery of discontinuities, IEEE Trans. Pattern Anal. Machine Intell., 14(1992), pp. 367-383.
16. D. GILBARG AND N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983.
17. O. A. LADYZENSKAYA AND N. N. URALCEVA, Equations aux dérivées partielles de type elliptique, Dunod, Paris, 1968.
18. L. LAZAROAIA-VESE, Variational Problems and P. D. E.'s in Image Analysis and Curve Evolution, Ph.D. thesis, University of Nice-Sophia Antipolis, 1996.
19. J. L. LIONS AND E. MAGENES, Problemes aux limites non homogenes, Dunod, Paris, 1968.
20. P. PERONA AND J. MALIK, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Machine Intell., 12(1990), pp. 629-639.
21. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
22. S. OSHER AND L. RUDIN, Total variation based image restoration with free local constraints, Proc. IEEE Internat. Conf. on Image Processing, Vol. I, Austin, TX, IEEE, Piscataway, NJ, 1994, pp. 31-35.
23. L. RUDIN, S. OSHER, AND E. FATEMI, Nonlinear total variation based noise removal algorithms, Phys. D, 60(1992), pp. 259-268.
24. G. STAMPPACHIA, Equations elliptiques du second ordre à coefficients discontinus, Presses de l'Université de Montréal, Canada, 1966.
25. R. TAHRAOUI, Regularité de la solution d'un problème variationnel, Ann. Inst. H. Poincaré Analyse Non Linéaire, 9(1992), pp. 51-99.
26. R. TEMAM, Solutions généralisées de certaines equations du type hypersurfaces minima, Arch. Rational Mech. Anal., 44(1971), pp. 121-156.
27. A. N. TIKHONOV AND V. Y. ARSENIN, Solutions of Ill-Posed Problems, Wiley, New York, 1977.
28. A. VISINTIN, Strong convergence results related to strict convexity, Comm. Partial Differential Equations, 9(1984), pp. 439-466.
29. C. R. VOGEL AND M. E. OMAN, Iterative Methods for Total Variation Denoising, preprint, 1994, submitted to IEEE Trans, on Image Processing.