On time flows of minimizers of general convex functionals of linear growth with variable exponent in BV space and stability of pseudosolutions

Journal of Mathematical Analysis and Applications

Volumn 364, Issue 2, 2010, Pages 591-598

  Wunderli, T ^a  

^a AMERICAN UNIVERSITY OF SHARJAH   (United Arab Emirates)

Author keywords

Bounded variation; Image processing; Partial differential equation; Pseudosolution; Variable exponent

Indexed keywords

EID: 72149124788     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2009.10.064     Document Type: Article

References (19)

1. Acar R., and Vogel C.R. Analysis of bounded variation penalty methods for ill-posed problems. Inverse Problems 10 (1994) 1217
2. Andreu-Vaillo F., Caselles V., and Mazon J.M. Parabolic Quasilinear Equations Minimizing Linear Growth Functionals (2004), Springer, New York
3. Anzellotti G., and Giaquinta M. Convex functionals and partial regularity. Arch. Ration. Mech. Anal. 102 (1988) 243-272
4. Aubert G., and Vese L. A variational method in image recovery. SIAM J. Numer. Anal. 34 (1997) 1948-1979
5. Blomgren P., and Chan T. Color TV: Total variation methods for restoration of vector-valued images. IEEE Trans. Image Process. 7 (1998) 304-309
6. Blomgren P., Chan T., Mulet P., and Wong C.K. Total variation image restoration: Numerical methods and extensions. Proceedings of the 1997 IEEE International Conference on Image Processing, vol. 3 (1997) 384-387
7. Y. Chen, S. Levine, J. Stanich, Functionals with p (x)-growth in image restoration, preprint, 2003
8. Chen Y., Levine S., and Rao M. Variable exponent, linear growth functionals in image restoration. SIAM J. Appl. Math. 66 4 (2006) 1383-1406
9. Chambolle A., and Lions P.L. Image recovery via total variation minimization and related problems. Numer. Math. 76 (1997) 167-188
10. Dobson D., and Santosa F. Recovery of blocky images from noisy and blurred data. SIAM J. Appl. Math. 56 (1996) 1181-1198
11. Chen Y., Rao M., Tonegawa Y., and Wunderli T. Partial regularity for a selective smoothing functional for image restoration in BV space. SIAM J. Math. Anal. 37 4 (2005) 1098-1116
12. Giusti E. Minimal Surfaces and Functions of Bounded Variation. Monogr. Math. vol. 80 (1984), Birkhäuser, Basel/Boston/Stuttgart
13. Hardt R., and Kinderlehrer D. Elastic plastic deformation. Appl. Math. Optim. 10 (1983) 203-246
14. Ekeland I., and Temam R. Convex Analysis and Variational Problems (1976), North-Holland, Amsterdam
15. L. Rudin, S. Osher, Total variation based image restoration with free local constraints, in: Proceedings of IEEE ICIP-94, vol. 1, Austin, TX, 1994, pp. 31-35
16. Rudin L., Osher S., and Fatemi E. Nonlinear total variation based noise removal algorithms. Phys. D 60 (1992) 259-268
17. D. Strong, T. Chan, Spatially and scale adaptive total variation based regularization and anisotropic diffusion in image processing, Technical Report, University of California, Los Angeles, CA, CAM96-46, 1996
18. Strong D., and Chan T. Edge-preserving and scale-dependent properties of total variation regularization. Inverse Problems 19 (2003) S165-S187
19. Wunderli T. A partial regularity result for an anisotropic smoothing functional for image restoration in BV space. J. Math. Anal. Appl. 339 2 (2008) 1169-1178