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

页码：492 / 526

页数：35

共 21 条

[1] Some First-Order Algorithms for Total Variation Based Image Restoration
Aujol, Jean-Francois
[J]. JOURNAL OF MATHEMATICAL IMAGING AND VISION, 2009, 34 (03) : 307 - 327
[2] A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
Beck, Amir
Teboulle, Marc
[J]. SIAM JOURNAL ON IMAGING SCIENCES, 2009, 2 (01): : 183 - 202
[3] Bishop R., 1968, Tensor Analysis on Manifolds
[4] CARTER JL, 2001, THESIS UCLA LOS ANGE
[5] The discontinuity set of solutions of the TV denoising problem and some extensions
Caselles, Vicent
Chambolle, Antonin
Novaga, Matteo
[J]. MULTISCALE MODELING & SIMULATION, 2007, 6 (03) : 879 - 894
[6] Image recovery via total variation minimization and related problems
Chambolle, A
Lions, PL
[J]. NUMERISCHE MATHEMATIK, 1997, 76 (02) : 167 - 188
[7] Chambolle A, 2004, J MATH IMAGING VIS, V20, P89
[8] High-order total variation-based image restoration
Chan, T
Marquina, A
Mulet, P
[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 22 (02) : 503 - 516
[9] A nonlinear primal-dual method for total variation-based image restoration
Chan, TF
Golub, GH
Mulet, P
[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1999, 20 (06) : 1964 - 1977
[10] CHAN TF, 2005, 0528 UCLA CAM

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