On the jump set of solutions of the total variation flow

Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

Volumn 130, Issue , 2013, Pages 155-168

  Caselles, V ^a   Jalalzai, K ^b   Novaga, M ^c  

^a UNIVERSITAT POMPEU FABRA   (Spain)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^c UNIVERSITY OF PADOVA   (Italy)

Author keywords

Demonising model; Functions of bounded variation; Nonlinear parabolic equations; Total variation flow

Indexed keywords

EID: 84899714150     PISSN: 00418994     EISSN: 22402926     Source Type: Journal    
DOI: 10.4171/RSMUP/130-5     Document Type: Article

References (20)

1. F. Alter - V. Caselles - A. Chambolle, A characterization of convex calibrable sets in RN. Math. Ann., 332 (2) (2005), pp. 329-366.
2. L. Ambrosio, Corso introduttivo alla teoria geometrica della misura ed alle superfici minime. Scuola Normale Superiore, Pisa, 1997.
3. L. Ambrosio - N. Fusco - D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs XVIII, Clarendon Press, 2000.
4. F. Andreu - C. Ballester - V. Caselles - J. M. MazoâN, Minimizing total variation flow. Differential Integral Equations, 14 (3) (2001), pp. 321-360.
5. F. Andreu - C. Ballester - V. Caselles - J. M. MazoâN, The Dirichlet problem for the total variation flow. Journal Functional Analysis, 180 (2001), pp. 347-403.
6. F. Andreu - V. Caselles - J. M. Mazon, Parabolic Quasilinear Equations Minimizing Linear Growth Functionals. BirkhauÈser Verlag, 2004.
7. G. Anzellotti, Pairings between measures and bounded functions and compensated compactness. Ann. Mat. Pura Appl., 135 (1983), pp. 293-318.
8. G. Bellettini - V. Caselles - M. Novaga, The total variation flow in RN. J. Differential Equations, 184 (2) (2002), pp. 475-525.
9. H. BreâZIS, OpeÂrateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Publishing Co., Amsterdam, 1973.
10. V. Caselles - A. Chambolle - M. Novaga, The discontinuity set of solutions of the TV denoising problem and some extensions. Multiscale modeling & simulation, 6 (3) (2007), pp. 879-894.
11. V. Caselles - A. Chambolle - M. Novaga, Total Variation in Imaging. Handbook of Mathematical Methods in Imaging, Springer Verlag, 2010, pp. 1016-1057.
12. A. Chambolle - V. Caselles - D. Cremers - M. Novaga - T. Pock, An introduction to Total Variation for Image Analysis. In Theoretical Foundations and Numerical Methods for Sparse Recovery, De Gruyter, Radon Series Comp. Appl. Math., vol. 9 (2010), pp. 263-340.
13. V. Caselles - A. Chambolle - M. Novaga, Regularity for solutions of the total variation denoising problem. Rev. Mat. Iberoamericana, 27 (1) (2011), pp. 233-252.
14. A. Chambolle - P.-L. Lions, Image recovery via total variation minimization and related problems. Numer. Math., 76 (1997), pp. 167-188.
15. A. Chambolle, An algorithm for mean curvature motion. Interfaces Free Bound., 6 (2) (2004), pp. 195-218.
16. T. F. Chan - G. H. Golub - P. Mulet, A nonlinear primal-dual method for total variation based image restoration. SIAM J. Sci. Computing, 20 (1999), pp. 1964-1977.
17. M. G. Crandall - T. M. Liggett, Generation of Semigroups of Nonlinear Transformations on General Banach Spaces, Amer. J. Math., 93 (1971), pp. 265-298.
18. K. Jalalzai, Regularization of inverse problems in image processing. PhD Thesis, E Â cole Polytechnique, Palaiseau, Mars 2012.
19. L. Rudin - S. Osher - E. Fatemi, Nonlinear total variation based noise removal algorithms. Physica D, 60 (1992), pp. 259-268.
20. ] W. P. Ziemer, Weakly Differentiable Functions, GTM 120, Springer Verlag, 1989.