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An active set strategy based on the augmented Lagrangian formulationfor image restoration

Published online by Cambridge University Press:  15 August 2002

Kazufumi Ito  and
Karl Kunisch
Kazufumi Ito
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA.
Karl Kunisch
Affiliation:
Institut für Mathematik, Universität Graz, 8010 Graz, Austria.
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Abstract

Lagrangian and augmented Lagrangian methods for nondifferentiableoptimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of theUzawa algorithm and unconditional convergence of the first order augmentedLagrangian schemes are discussed. A Newton type method based on an activeset strategy defined by means of the dual variables is developed andanalyzed. Numerical examples for blocky signals and images perturbedby very high noise are included.

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 1 , January 1999 , pp. 1 - 21
Copyright
© EDP Sciences, SMAI, 1999

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