Regularity for solutions of the total variation denoising problem

Revista Matematica Iberoamericana

Volumn 27, Issue 1, 2011, Pages 233-252

  Caselles, Vicent ^a   Chambolle, Antonin ^b   Matteo Novaga, V ^c  

^a UNIVERSITAT POMPEU FABRA   (Spain)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^c UNIVERSITY OF PADOVA   (Italy)

Author keywords

Image processing; Regularity of solutions; Variational methods

Indexed keywords

EID: 84856771727     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/634     Document Type: Article

References (23)

1. ALMGREN, F., TAYLOR, J. AND WANG, L.-H.: Curvature-driven flows: a variational approach. SIAM J. Control Optim. 31 (1993), no. 2, 387-438.
2. N. Math. Ann. 332 (2005), no. 2, 329-366.
3. AMBROSIO, L., FUSCO, N. AND PALLARA, D.: Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, 2000.
4. ANDREU, F., BALLESTER, C, CASELLES, V. AND MAZÓN, J. M.: The Dirichlet problem for the total variation flow. J. Fund. Anal. 180 (2001), no. 2, 347-403.
5. ANDREU, F., CASELLES, V. AND MAZÓN, J. M.: Parabolic quasilinear equations minimizing Unear growth functional. Progress in Mathematics 223. Birkhäuser Verlag, Basel, 2004.
6. ANZELLOTTI, G.: Pairings between measures and bounded functions and compensated compactness. Ann. Mat. Pura Appl. IV 135 (1983), 293-318.
7. BAROZZI, E., GONZALEZ, E. AND TAMANINI, I.: The mean curvature of a set of finite perimeter. Proc. Amer. Math. Soc. 99 (1987), no. 2, 313-316.
8. N. J. Di/ferentiaJ Equations 184 (2002), no. 2, 475-525.
9. 2. SIAM J. Math. Anal. 36 (2005), no. 4, 1095-1129.
10. BRÉZIS, H.: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hubert. North-Holland Math. Stud. 5, Notas Mat. 50. North-Holland, Amsterdam-London; American Elsevier, New York, 1973.
11. CASELLES, V. AND CHAMBOLLE, A.: Anisotropic curvature-driven flow of convex sets. Nonlinear Anal. 65 (2006), no. 8, 1547-1577.
12. CASELLES, V., CHAMBOLLE, A. AND NOVAGA, M.: The discontinuity set of solutions of the TV denoising problem and some extensions. Multiscale Model. Simul. 6 (2007), no. 3, 879-894.
13. CHAMBOLLE, A. AND LIONS, P.-L.: Image recovery via total variation minimization and related problems. Numer. Math. 76 (1997), no. 2, 167-188.
14. CHAN, T., GOLUB, G. H. AND MULET, P.: A nonlinear primal-dual method for total variation-based image restoration. SIAM J. Sci. Cornput. 20 (1999), no. 6, 1964-1977.
15. CRANDALL, M. G. AND LIGGETT, T. M.: Generation of semi-groups of nonlinear transformations on general Banach spaces. Amer. J. Math. 93 (1971), 265-298.
16. FEDERER, H.: Geometric measure theory. Die Grundlehren der mathematischen Wissenschaften 153. Springer-Verlag, New York, 1969.
17. GILBARG, D. AND TRUDINGER, N. S.: Elliptic partial differential equations of second order. Classics in Mathematics. Springer-Verlag, Berlin, 2001.
18. MASSARI, U.: Esistenza e regolarità delle ipersuperfice di curvatura media assegnata in R". Arch. Rational Mech. Anal. 55 (1974), 357-382.
19. MASSARI, U.: Frontiere orientate di curvatura media assegnata in IP. Rend. Sem. Mat. Univ. Padova 53 (1975), 37-52.
20. Massari, U. and Pepe, L.: Successioni convergenti di ipersuperfici di curvatura media assegnata. Rend. Sem Mat. Univ. Padova 53 (1975), 53-68.
21. p. Manuscripta Math. 97 (1998), no. 1, 15-35.
22. RUDIN, L., OSHER S. J. AND FATEMI, E.: Nonlinear total variation based noise removal algorithms. Phys. D. 60 (1992), 259-268.
23. TAMANINI, L: Boundaries of Caccioppoli sets with Holder-continuous normal vector. J. Reine Angew. Math. 334 (1982), 27-39.