The discontinuity set of solutions of the TV denoising problem and some extensions

被引：99

作者：

Caselles, Vicent ^{[1
]}

Chambolle, Antonin ^{[2
]}

Novaga, Matteo ^{[3
]}

机构：

[1] Univ Pompeu Fabra, Dept Tecnol, Barcelona 08003, Spain

[2] Ecole Polytech, CNRS, CMAP, F-91128 Palaiseau, France

[3] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

来源：

MULTISCALE MODELING & SIMULATION | 2007年 / 6卷 / 03期

关键词：

total variation; jump discontinuity set; regularity;

D O I：

10.1137/070683003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The main purpose of this paper is to prove that the jump discontinuity set of the solution of the total variation based denoising problem is contained in the jump set of the datum to be denoised. We also prove some extensions of this result for the total variation minimization flow, for anisotropic norms, and for some more general convex functionals, which include the minimal surface equation case and its anisotropic extensions.

引用

页码：879 / 894

页数：16

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