Volume 34, Number 4, July/August 2000
|Page(s)||799 - 810|
|Published online||15 April 2002|
Structural Properties of Solutions to Total Variation Regularization Problems
Institut für Mathematik, Universität Graz, Heinrichstrasse 36, 8010 Graz, Austria. e-mail: email@example.com
Revised: 24 March 2000
In dimension one it is proved that the solution to a total variation-regularized least-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 operator to be inverted. A similar, but weaker result is derived in dimension two.
Mathematics Subject Classification: 26B30 46N10 47A52 49J52 49N45 65K10
Key words: Total variation regularization / piecewise constant function / convex optimization / Lebesgue decomposition / singular measures.
© EDP Sciences, SMAI, 2000
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.