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

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

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topIto, 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

top- [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] 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] D.P. Bertsekas, Constraint Optimization and Lagrange Multiplier Methods. Academic Press, Paris (1982). Zbl0572.90067MR690767
- [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] D.C. Dobson and F. Santosa, Recovery of blocky images from noisy and blurred data. Preprint. Zbl0858.68121MR1398414
- [6] I. Ekeland and T. Turnbull, Infinite Dimensional Optimization and Convexity. The University of Chicago Press, Chicago (1983). Zbl0565.49003MR769469
- [7] E. Giusti, Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Boston (1984). Zbl0545.49018MR775682
- [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] 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] L.I. Rudin, S. Osher and E Fatemi, Nonlinear total variation based noise removal algorithms. Physica D 60 (1992) 259-268. Zbl0780.49028
- [11] C.R. Vogel, Total variation regularization for ill-posed problems. Technical Report, Department of Mathematical Sciences, Montana State University.

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