Structural properties of solutions to total variation regularization problems

被引：103

作者：

Ring, W ^{[1
]}

机构：

[1] Graz Univ, Inst Math, A-8010 Graz, Austria

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2000年 / 34卷 / 04期

关键词：

total variation regularization; piecewise constant function; convex optimization; Lebesgue decomposition; singular measures;

D O I：

10.1051/m2an:2000104

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：799 / 810

页数：12

共 18 条

[1] ANALYSIS OF BOUNDED VARIATION PENALTY METHODS FOR ILL-POSED PROBLEMS [J].