A HIGHER ORDER MODEL FOR IMAGE RESTORATION: THE ONE-DIMENSIONAL CASE

被引：35

作者：

Dal Maso, G. ^{[1
]}

Fonseca, I. ^{[2
]}

Leoni, G. ^{[2
]}

Morini, M. ^{[1
]}

机构：

[1] SISSA, I-34014 Trieste, Italy

[2] Carnegie Mellon Univ, Pittsburgh, PA 15213 USA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2009年 / 40卷 / 06期

关键词：

image segmentation; total variation models; staircase effect; higher order regularization; relaxation; curvature dependent functionals; RECOVERY; SET;

D O I：

10.1137/070697823

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [SIAM J. Sci. Comput., 22 (2000), pp. 503-516] is analyzed in one dimension. A suitable functional framework in which the minimization problem is well posed is being proposed, and it is proved analytically that the higher order regularizing term prevents the occurrence of the staircase effect. The generalized version of the model considered here includes, as particular cases, some curvature dependent functionals.

引用

页码：2351 / 2391

页数：41

共 15 条

[1]

[Anonymous], 1974, REAL COMPLEX ANAL

[2]

[Anonymous], 2000, Oxford Mathematical Monographs

[3]

BLOMGREN P, 1997, P SPIE 1997

[4] Approximation by Γ-convergence of a curvature-depending functional in visual reconstruction [J].