Total Generalized Variation

被引：1154

作者：

Bredies, Kristian ^{[1
]}

Kunisch, Karl ^{[1
]}

Pock, Thomas ^{[2
]}

机构：

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

[2] Graz Univ Technol, Inst Comp Graph & Vis, A-8010 Graz, Austria

来源：

SIAM JOURNAL ON IMAGING SCIENCES | 2010年 / 3卷 / 03期

基金：

奥地利科学基金会;

关键词：

bounded variation; total generalized variation; tensor fields; regularization; image denoising; TOTAL VARIATION MINIMIZATION; VARIATION REGULARIZATION; ALGORITHM;

D O I：

10.1137/090769521

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The novel concept of total generalized variation of a function u is introduced, and some of its essential properties are proved. Differently from the bounded variation seminorm, the new concept involves higher-order derivatives of u. Numerical examples illustrate the high quality of this functional as a regularization term for mathematical imaging problems. In particular this functional selectively regularizes on different regularity levels and, as a side effect, does not lead to a staircasing effect.

引用

页码：492 / 526

页数：35

共 21 条

[11] A HIGHER ORDER MODEL FOR IMAGE RESTORATION: THE ONE-DIMENSIONAL CASE [J].