An active set strategy based on the augmented lagrangian formulation for image restoration

Kazufumi Ito; Karl Kunisch

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 1, page 1-21
  • ISSN: 0764-583X

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Ito, Kazufumi, and Kunisch, Karl. "An active set strategy based on the augmented lagrangian formulation for image restoration." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.1 (1999): 1-21. <http://eudml.org/doc/193911>.

@article{Ito1999,
author = {Ito, Kazufumi, Kunisch, Karl},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {active set strategy; augmented Lagrangian formulation; image restoration; numerical examples; Hilbert spaces; convergence; Uzawa algorithm; Newton type method},
language = {eng},
number = {1},
pages = {1-21},
publisher = {Dunod},
title = {An active set strategy based on the augmented lagrangian formulation for image restoration},
url = {http://eudml.org/doc/193911},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Ito, Kazufumi
AU - Kunisch, Karl
TI - An active set strategy based on the augmented lagrangian formulation for image restoration
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 1
SP - 1
EP - 21
LA - eng
KW - active set strategy; augmented Lagrangian formulation; image restoration; numerical examples; Hilbert spaces; convergence; Uzawa algorithm; Newton type method
UR - http://eudml.org/doc/193911
ER -

References

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  1. [1] L. Alvarez, P.L. Lions and J.M. Morel, Image selective smoothing and edge detection by nonlinear diffusion, II SIAM J Numer. Anal. 29 (1992) 845-866. Zbl0766.65117MR1163360
  2. [2] R. Acar and C.R. Vogel, Analysis of bounded variation penalty methods for ill-posed problems. Inverse Problems 10 (1994) 1217-1229. Zbl0809.35151MR1306801
  3. [3] D.P. Bertsekas, Constraint Optimization and Lagrange Multiplier Methods. Academic Press, Paris (1982). Zbl0572.90067MR690767
  4. [4] F. Catte, P.L. Lions, J.M. Morel and T. Colle, Image selective smoothing and edge detection by nonlinear diffusion SIAM J. Numer. Anal. 29 (1992) 182-193. Zbl0746.65091MR1149092
  5. [5] D.C. Dobson and F. Santosa, Recovery of blocky images from noisy and blurred data. Preprint. Zbl0858.68121MR1398414
  6. [6] I. Ekeland and T. Turnbull, Infinite Dimensional Optimization and Convexity. The University of Chicago Press, Chicago (1983). Zbl0565.49003MR769469
  7. [7] E. Giusti, Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Boston (1984). Zbl0545.49018MR775682
  8. [8] K. Ito and K. Kumsch, Augmented Lagrangian methods for nonsmooth convex optimization in Hilbert spaces. To appear in Nonliner Analysis, Theory, Methods and Applications. Zbl0971.49014
  9. [9] K. Ito and K. Kunisch, Augmented Lagrangian Formulation of Nonsmooth, Convex Optimization in Hilbert Spaces, in Lecture Notes in Pure and Applied Mathematics Control of Partial Differential Equations and Applications, E. Casas. Marcel Dekker Eds., 174 (1995) 107-117. Zbl0876.49028MR1364642
  10. [10] L.I. Rudin, S. Osher and E Fatemi, Nonlinear total variation based noise removal algorithms. Physica D 60 (1992) 259-268. Zbl0780.49028
  11. [11] C.R. Vogel, Total variation regularization for ill-posed problems. Technical Report, Department of Mathematical Sciences, Montana State University. 

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