Structural properties of solutions to total variation regularization problems

Wolfgang Ring

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 4, page 799-810
  • ISSN: 0764-583X

How to cite

top

Ring, Wolfgang. "Structural properties of solutions to total variation regularization problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.4 (2000): 799-810. <http://eudml.org/doc/194013>.

@article{Ring2000,
author = {Ring, Wolfgang},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {optimality system; total variation regularization; piecewise constant function; convex optimization; Lebesgue decomposition; singular measures; ill-posed problem; least-squares problem},
language = {eng},
number = {4},
pages = {799-810},
publisher = {Dunod},
title = {Structural properties of solutions to total variation regularization problems},
url = {http://eudml.org/doc/194013},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Ring, Wolfgang
TI - Structural properties of solutions to total variation regularization problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 4
SP - 799
EP - 810
LA - eng
KW - optimality system; total variation regularization; piecewise constant function; convex optimization; Lebesgue decomposition; singular measures; ill-posed problem; least-squares problem
UR - http://eudml.org/doc/194013
ER -

References

top
  1. [1] R. Acar and C. R. Vogel, Analysis of bounded variation penalty methods for ill-posed problems. Inverse Problems 10 (1994) 1217-1229. Zbl0809.35151MR1306801
  2. [2] V. Barbu, Analysis and Control of Nonlinear Infinite Dimensional Systems. Math. Sci. Engrg. 190 (1993). Zbl0776.49005MR1195128
  3. [3] A. Chambolle and P. L. Lions, Image recovery via total variation minimization and related problems. Numer. Math. 76 (1997) 167-188. Zbl0874.68299MR1440119
  4. [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. Zbl0890.49010MR1483764
  5. [5] D. Dobson and O. Scherzer, Analysis of regularized total variation penalty methods for denoising. Inverse Problems 12 (1996) 601-617. Zbl0866.65041MR1413421
  6. [6] D. C. Dobson and F. Santosa, Recovery of blocky images from noisy and blurred data. SIAM J. Appl. Math. 56 (1996) 1181-1192. Zbl0858.68121MR1398414
  7. [7] I. Ekeland and T. Turnbull, Infinite-Dimensional Optimization and Convexity. Chicago Lectures in Math., The University of Chicago Press, Chicago and London (1983). Zbl0565.49003MR769469
  8. [8] L. Evans and R. Gariepy, Measure Theory and Fine Properties of Functions. CRC Press, Boca Raton (1992). Zbl0804.28001MR1158660
  9. [9] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order. Grundlehren Math. Wiss. 224 (1977). Zbl0361.35003MR473443
  10. [10] E. Giusti, Minimal Surfaces and Functions of Bounded Variation. Monogr. Math. 80 (1984). Zbl0545.49018MR775682
  11. [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. Zbl0918.65050MR1685741
  12. [12] K. Ito and K. Kunisch, BV-type regularization methods for convoluted objects with edge-flat-grey scales. Inverse Problems 16 (2000) 909-928. Zbl0981.65149MR1776474
  13. [13] M. Z. Nashed and O. Scherzer, Least squares and bounded variation regularization with nondifferentiable functionals. Numer. Funct. Anal. Optim. 19 (1998) 873-901. Zbl0914.65067MR1642506
  14. [14] M. Nikolova, Local strong homogeneity of a regularized estimator. SIAM J. Appl. Math. (to appear). Zbl0991.94015MR1780806
  15. [15] L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithm. Physica D 60 (1992) 259-268. Zbl0780.49028
  16. [16] W. Rudin, Real and Complex Analysis, 3rd edn McGraw-Hill, New York-St Louis-San Francisco (1987). Zbl0925.00005MR924157
  17. [17] C. Vogel and M. Oman, Iterative methods for total variation denoising. SIAM J. Sci. Comp. 17 (1996) 227-238. Zbl0847.65083MR1375276
  18. [18] W. P. Ziemer, Weakly Differentiable Functions. Grad. Texts in Math. 120 (1989). Zbl0692.46022MR1014685

NotesEmbed ?

top

You must be logged in to post comments.