Regularization by functions of bounded variation and applications to image enhancement

Applied Mathematics and Optimization

Volumn 40, Issue 2, 1999, Pages 229-257

  Casas, E ^a   Kunisch, K ^b   Pola, C ^a  

^a UNIVERSITY OF CANTABRIA   (Spain)

^b UNIVERSITY OF GRAZ   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; FUNCTIONS; IMAGE ENHANCEMENT; PROBLEM SOLVING; VECTORS;

BOUNDED VARIATION FUNCTIONS; OPTIMALITY CONDITIONS;

OPTIMIZATION;

EID: 0033181496     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900124     Document Type: Article

References (14)

1. R. Acar and C.R. Vogel. Analysis of bounded variation penalty methods for ill-posed problems. Inverse Problems, 10:1217-1229, 1994.
2. V. Barbu and Th. Precupanu. Convexity and Optimization in Banach Spaces. Reidel, Dordrecht, 1986.
3. 1 penalty functions. Optimization Methods and Software, 2:145-176, 1993.
4. P.G. Ciarlet. The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978.
5. D. Dobson and F. Santosa. Recovery of blocky images from noisy and blurred data. Technical Report 94-7, Department of Mathematical Sciences, University of Delaware, 1994.
6. I. Ekeland and R. Temam. Analyse Convexe et Problèmes Variationnels. Dunod-Gauthier Villars, Paris, 1974.
7. E. Giusti. Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Boston, 1984.
8. K. Ito and K. Kunisch. An active set strategy based on the augmented Lagrangian formulation for image restoration. To appear in R.A.I.R.O. MMAN.
9. Y. Li and F. Santosa. An affine scaling algorithm for minimizing total variation in image enhancement. Technical Report CTC94TR201, Cornell Theory Center, Cornell University, 1994.
10. J. Nečas. Les Méthodes Directes en Théorie des Equations Elliptiques. Editeurs Academia, Prague, 1967.
11. S. Osher and L. Rudin. Feature-oriented image enhancement using shock filters. SIAM Journal on Numerical Analysis, 27:919-940, 1990.
12. L. Rudin, S. Osher, and C. Fu. Nonlinear total variation based noise removal algorithms. Physica D, 60:259-268, 1992.
13. W. Rudin. Real and Complex Analysis. McGraw-Hill, London, 1970.
14. R. Temam. Mathematical Problems in Plasticity. Gauthier-Villars, Kent, 1985.