Total Generalized Variation

被引：1121
|
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
收藏
页码：492 / 526
页数：35
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