Structural properties of solutions to total variation regularization problems

Mathematical Modelling and Numerical Analysis

Volumn 34, Issue 4, 2000, Pages 799-810

  Ring, Wolfgang ^a  

^a UNIVERSITY OF GRAZ   (Austria)

Author keywords

Convex optimization; Lebesgue decomposition; Piecewise constant function; Singular measures; Total variation regularization

Indexed keywords

EID: 0034412757     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2000104     Document Type: Article

References (18)

1. R. Acar and C.R. Vogel, Analysis of bounded variation penalty methods for ill-posed problems. Inverse Problems 10 (1994) 1217-1229.
2. V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems. Math. Sci. Engrg. 190 (1993).
3. A. Chambolle and P.L. Lions, Image recovery via total variation minimization and related problems. Numer. Math. 76 (1997) 167-188.
4. G. Chavent and K. Kunisch, Regularization of linear least squares problems by total bounded variation. ESAIM Control Optim. Calc. Var. 2 (1997) 359-376.
5. D. Dobson and O. Scherzer, Analysis of regularized total variation penalty methods for denoising. Inverse Problems 12 (1996) 601-617.
6. D.C. Dobson and F. Santosa, Recovery of blocky images from noisy and blurred data. SIAM J. Appl. Math. 56 (1996) 1181-1192.
7. I. Ekeland and T. Turnbull, Infinite-Dimensional Optimization and Convexity. Chicago Lectures in Math., The University of Chicago Press, Chicago and London (1983).
8. L. Evans and R. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton (1992).
9. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Grundlehren Math. Wiss. 224 (1977).
10. E. Giusti, Minimal Surfaces and Functions of Bounded Variation. Monogr. Math. 80 (1984).
11. K. Ito and K. Kunisch, An active set strategy based on the augmented lagrantian formulation for image restauration. RAIRO Modél. Math. Anal. Numér. 33 (1999) 1-21.
12. K. Ito and K. Kunisch, BV-type regularization methods for convoluted objects with edge-flat-grey scales. Inverse Problems 16 (2000) 909-928.
13. M.Z. Nashed and O. Scherzer, Least squares and bounded variation regularization with nondifferentiable functionals. Numer. Funct. Anal. Optim. 19 (1998) 873-901.
14. M. Nikolova, Local strong homogeneity of a regularized estimator. SIAM J. Appl. Math. (to appear).
15. L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithm. Physica D 60 (1992) 259-268.
16. W. Rudin, Real and Complex Analysis, 3rd edn. McGraw-Hill, New York-St Louis-San Francisco (1987).
17. C. Vogel and M. Oman, Iterative methods for total variation denoising. SIAM J. Sci. Comp. 17 (1996) 227-238.
18. W.P. Ziemer, Weakly Differentiable Functions. Grad. Texts in Math. 120 (1989).