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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 nondifferentiable optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the Uzawa algorithm and unconditional convergence of the first order augmented Lagrangian schemes are discussed. A Newton type method based on an active set strategy defined by means of the dual variables is developed and analyzed. Numerical examples for blocky signals and images perturbed by very high noise are included.

Keywords

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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