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StructuralProperties of Solutions to Total Variation Regularization Problems

Published online by Cambridge University Press:  15 April 2002

Wolfgang Ring
Wolfgang Ring*
Affiliation:
Institut für Mathematik, Universität Graz, Heinrichstrasse 36, 8010 Graz, Austria. e-mail: wolfgang.ring@kfunigraz.ac.at
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Abstract

In dimension one it is proved that the solution to a total variation-regularizedleast-squares problem is always a function which is "constant almost everywhere" ,provided that the data are in a certain sense outside the range of the operatorto be inverted. A similar, but weaker result is derived in dimension two.

Keywords

Total variation regularizationpiecewise constant functionconvex optimizationLebesgue decompositionsingular measures.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 4 , July 2000 , pp. 799 - 810
Copyright
© EDP Sciences, SMAI, 2000

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