Structural Properties of Solutions to Total Variation Regularization Problems

Open Access

1 July 2000

journal article
research article
Published by EDP Sciences in ESAIM: Mathematical Modelling and Numerical Analysis

Vol. 34 (4) , 799-810
https://doi.org/10.1051/m2an:2000104

Abstract

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.

Keywords

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