Total variation time flow with quantile regression for image restoration

Journal of Mathematical Analysis and Applications

Volumn 403, Issue 1, 2013, Pages 272-282

  Wunderli, Thomas ^a  

^a AMERICAN UNIVERSITY OF SHARJAH   (United Arab Emirates)

Author keywords

Bounded variation; Image restoration; Quantile regression; Time flows

Indexed keywords

EID: 84875612297     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2013.02.029     Document Type: Article

References (37)

1. Allard W.K. Total variation regularization for image denoising I. SIAM J. Math. Anal. 2007, 39(4):1150-1190.
2. Allard W.K. Total variation regularization for image denoising II. SIAM J. Imaging Sci. 2008, 1(4):400-417.
3. Allard W.K. Total variation regularization for image denoising III. SIAM J. Imaging Sci. 2009, 2(2):532-568.
4. Alliney S. Digital filters as absolute norm regularizers. IEEE Trans. Signal Process. 1992, 40(6):1548-1562.
5. Alliney S. Recursive median filters of increasing order: a variational approach. IEEE Trans. Signal Process. 1996, 44(6):1346-1354.
6. Alliney S. A property of the minimum vectors of a regularizing functional defined by means of the absolute norm. IEEE Trans. Signal Process. 1997, 45(4):913-917.
7. Ambrosio L., Buttazzo G., Fonseca G. Lower semicontinuity problems in Sobolev spaces with respect to a measure. J. Math. Pures Appl. 1996, 75:211-224.
8. Andreu F., Ballester C., Caselles V., Mazón J.M. Minimizing total variation flow. Differential Integral Equations 2001, 14(3):321-360.
9. Andreu F., Caselles V., Díaz J.I., Mazón J.M. Some qualitiative properties for the total variation flow. J. Funct. Anal. 2002, 188(2):516-547.
10. Andreu F., Mazón J.M., Moll J.S., Caselles V. The minimizing total variation flow with measure initial conditions. Commun. Contemp. Math. 2004, 6(3):431-494.
11. Andreu-Vaillo Fuensanta, Caselles Vincint, Mazón José M. Parabolic Quasilinear Equations Minimizing Linear Growth Functionals. Progress in Mathematics (Boston, Mass.) 2004, vol. 223:340. Birkhäuser, Basel, xiv, ISNB 3-7643-6691-2/HBK.
12. Anzellotti G., Giaquinta M. Convex functionals and partial regularity. Arch. Ration. Mech. Anal. 1988, 102:243-272.
13. Bellettini G., Caselles V., Novaga M. The total variation flow in RN. J. Differential Equations 2002, 184(2):475-525.
14. P. Blomgren, T. Chan, P. Mulet, C.K. Wong, Total variation image restoration: numerical methods and extensions, in: Proceedings of the 1997 IEEE International Conference on Image Processing, vol. 3, pp. 384-387.
15. Brezis H. Operateurs Maximaux Monotone 1993, North-Holland, Amsterdam.
16. Brück R.E. Asymptotic convergence of nonlinear contraction semigroups in Hilbert space. J. Funct. Anal. 1975, 18:15-26.
17. Chambolle A., Lions P.L. Image recovery via total variation minimization and related problems. Numer. Math. 1997, 76:167-188.
18. Chan T., Esedoglu S. Aspects of total variation regularized L1 function approximation. SIAM J. Appl. Math. 2005, 65(5):1817-1837.
19. Chen Y., Levine S., Rao M. Variable exponent, linear growth functionals in image restoration. SIAM J. Appl. Math. 2006, 66(4):1383-1406.
20. Chen Y., Wunderli T. Adaptive total variation for image restoration in BV space. J. Math. Anal. Appl. 2002, 272:117-137.
21. Demengel F., Temam R. Convex functions of a measure and applications. Indiana Univ. Math. J. 1984, 33(5):673-709.
22. Dobson D., Santosa F. Recovery of blocky images from noisy and blurred data. SIAM J. Appl. Math. 1996, 56:1181-1198.
23. Dümbgen L., Kovac A. Extensions of smoothing via taught strings. Electron. J. Stat. 2009, 3:41-75.
24. Ekeland I., Temam R. Convex Analysis and Variational Problems 1976, North Holland, Amsterdam.
25. Giusti F. Minimial Surfaces and Functions of Bounded Variation. Monographs Math. 1984, vol. 80. Birkhäuser, Basel.
26. Hardt R., Kinderlehrer D. Elastic plastic deformation. Appl. Math. Optim. 1983, 10:203-246.
27. Koenker R., Bassett G. Regression quantiles. Econometrica 1978, 46:33-50.
28. Koenker R., Hallock K. Quantile regression. J. Econ. Perspect. 2001, 15(4):143-156. Fall.
29. Lions J.L. Quelques Méthodes de Resolution des Problems aux Limites Non Linéaires 1969, Dunod/Gautheir-Villars, Paris.
30. Osher S., Esedoglu S. Decomposition of images by the anisotropic Rudin-Osher-Fatemi model. Comm. Pure Appl. Math. 2004, 57(12):1606-1626.
31. Osher S., Scherzer O. G-Norm Properties of Bounded Variation Regularization. Commun. Math. Sci. 2004, 2(2):237-254.
32. L.I. Rudin, S. Osher, Total variation based image restoration with free local constraints, in: Proc. ICIP IEEE Int. Conf. on Image Processing, Austin, TX, 1994, pp. 31-35.
33. Rudin L.I., Osher S., Fatemi E. Nonlinear total variation based noise removal algorithms. Phys. D 1992, 60:259-268.
34. Temam R. Navier-Stokes Equations, Theory and Numerican Analysis 1977, North-Holland, Amsterdam.
35. Vese L. A study in the BV space of a denoising-deblurring variational problem. Appl. Math. Optim. 2001, 44:131-161.
36. Wunderli T. On time flows of minimizers of general convex functionals of linear growth with variable exponent in BV space and stability of pseudosolutions. J. Math. Anal. Appl. 2010, 364(2):591-598.
37. Zhou X. An evolution problem for plastic antiplanar shear. Appl. Math. Optim. 1992, 25:263-285.