Total variation based image denoising and restoration

International Congress of Mathematicians, ICM 2006

Volumn 3, Issue , 2006, Pages 1453-1472

  Caselles, Vicent ^a  

^a UNIVERSITAT POMPEU FABRA   (Spain)

Author keywords

Image restoration; Total variation; Variational methods

Indexed keywords

DE-NOISING; EXPLICIT SOLUTIONS; IMAGE DECOMPOSITION; LOCAL CONSTRAINTS; NUMERICAL EXPERIMENTS; TOTAL VARIATION; VARIATIONAL METHODS;

IMAGE ACQUISITION; IMAGE DENOISING; IMAGE RECONSTRUCTION;

RESTORATION;

EID: 84862863424     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (32)

1. Almansa, A., Caselles, V., Haro, G., and Rougé, B., Restoration and zoom of irregularly sampled, blurred and noisy images by accurate total variation minimization with local constraints. Multiscale Model. Simul., to appear.
2. Almansa, A., C. Ballester, C., Caselles, V., Faro, L. J., and Haro, G., ATV based restoration model with local constraints. Preprint, 2006.
3. Alter, F., Caselles, V., and Chambolle, A., Evolution of Characteristic Functions of Convex Sets in the Plane by the Minimizing Total Variation Flow. Interfaces Free Bound. 7 (2005), 29-53.
4. N. Math. Ann. 332 (2005), 329-366.
5. Ambrosio, L., Fusco, N., and Pallara, D., Functions of BoundedVariation and Free Discontinuity Problems. Oxford Math. Monogr., The Clarendon Press, Oxford University Press, New York 2000
6. Andreu, F., Ballester, C., Caselles, V., and Mazón, J. M., Minimizing total variation flow. Differential Integral Equations 14 (2001), 321-360.
7. Andreu-Vaillo, F., Caselles, V., and Mazón, J. M., Parabolic Quasilinear Equations Minimizing Linear Growth Functionals. Progr. Math. 223, Birkhäuser, Basel 2004
8. Andrews, H. C., and Hunt, B. R., Digital Image Restoration. Prentice Hall, Englewood Cliffs, NJ, 1977.
9. Aujol, J. F., and Chambolle, A., Dual Norms and Image Decomposition Models. Internat. J. Computer Vision, 63 (2005), 85-104.
10. Aujol, J. F., Aubert, G., Blanc-Feraud, L., and Chambolle, A., Image Decomposition into a bounded variation component and an oscillating component. J. Math. Imaging Vision 22 (2005), 71-88.
11. Anzellotti, G., Pairings between measures and bounded functions and compensated compactness. Ann. Mat. Pura Appl. 135 (1983), 293-318.
12. N. J. Differential Equations 184 (2002), 475-525.
13. Bellettini, G., Caselles, V., and Novaga, M., Explicit solutions of the eigenvalue problem -div(Du|Du|)= u. SIAM J. Math. Anal. 36 (2005), 1095-1129.
14. Bermúdez, A., and Moreno, C., Duality methods for solving variational inequalities. Comput. Math. Appl. 7 (1981), 43-58.
15. Bertalmío, M., Caselles, V., Rougé, B., and Solé, A., TV based image restoration with local constraints. J. Sci. Comput. 19 (2003), 95-122.
16. Chambolle, A., An algorithm for total variation minimization and applications. J. Math. Imaging Vision 20 (2004), 89-97.
17. Chambolle, A., and Lions, P. L., Image recovery via total variation minimization and related problems. Numer. Math. 76 (1997), 167-188.
18. Chan, T. F., Golub, G. H., and Mulet, P., A Nonlinear Primal-Dual Method for Total Variation Based Image Restoration. SIAM J. Sci. Comput. 20 (1999), 1964-1977.
19. Demoment, G., Image reconstruction and restoration: Overview of common estimation structures and problems. IEEE Trans. Acoust. Speech Signal Process. 37 (1989), 2024-2036.
20. Donoho, D., Denoising via soft-threholding. IEEE Trans. Inform. Theory 41 (1995), 613-627.
21. Durand, S., Malgouyres, F., and Rougé, B., Image Deblurring, Spectrum Interpolation and Application to Satellite Imaging. ESAIM Control Optim. Calc. Var. 5 (2000), 445-475.
22. Geman, D., and Reynolds, G., Constrained Image Restoration and Recovery of Discontinuities. IEEE Trans. Pattern Anal. Machine Intell. 14 (1992), 367-383.
23. Gilboa, G., Sochen, N., and Zeevi, Y., PDE-based denoising of complex scenes using a spatially-varying fidelity term. In Proc. International Conference on Image Processing 2003, Barcelona, Spain, Vol. 1, 2003, 865-868.
24. Giusti, E., On the equation of surfaces of prescribed mean curvature. Existence and uniqueness without boundary conditions. Invent. Math. 46 (1978), 111-137.
25. Haddad, A., and Meyer, Y., Variational methods in image processing. CAM Reports 04-52, 2004.
26. Meyer, Y., Oscillating patterns in image processing and in some nonlinear evolution equations. The Fifteenth Dean Jacqueline B. Lewismemorial lectures, University Lecture Series 22, Amer. Math. Soc., Providence, RI, 2001.
27. Nikolova, M., Local strong homogeneity of a regularized estimator. SIAM J. Appl. Math 61 (2000), 633-658.
28. -1 norm. Multiscale Model. Simul. 1 (2003), 349-370.
29. Rougé, B., Théorie de l'echantillonage et satellites d'observation de la terre. In Analyse de Fourier et traitement d'images, Journées X-UPS 1998.
30. Rudin, L., Osher, S., and Fatemi, E., Nonlinear total variation based noise removal algorithms. Physica D 60 (1992), 259-268.
31. Tikhonov, A. N., and Arsenin, V. Y., Solutions of Ill-Posed Problems. Scripta Series in Mathematics, John Wiley & Sons, New York 1977.
32. Vese, L. A., and Osher, S. J., Modeling textures with total variation mkinimization and oscillatikng patterns in image processing. J. Sci. Comput. 19 (2003), 553-572.