Nonlinear multigrid method for solving the LLT model

被引：10

作者：

Zhang, Jun ^{[1
]}

Yang, Yu-Fei ^{[2
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

[2] Changsha Univ, Dept Informat & Comp Sci, Changsha 410003, Hunan, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 10期

关键词：

Image denoising; Dual algorithm; LLT model; Local Fourier analysis; Nonlinear multigrid method; PARTIAL-DIFFERENTIAL-EQUATIONS; TOTAL VARIATION MINIMIZATION; IMAGE; ALGORITHM;

D O I：

10.1016/j.amc.2012.11.060

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our goal in this paper is to study a nonlinear multigrid method for solving the LLT model. In order to improve the convergence rate of the proposed multigrid method, an improved dual iteration is proposed as its smoother. Furthermore, we give the local Fourier analysis (LFAs) of the Chambolle's dual iterations and a modified smoother for solving the LLT model, respectively. Numerical results illustrate the efficiency of the proposed method and indicate that such a multigrid method is more suitable to deal with large-sized images. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：4964 / 4976

页数：13

共 29 条

[1]

Ambrosio L., 2000, OX MATH M, pxviii, DOI 10.1017/S0024609301309281

[2]

[Anonymous], 1993, MULTIGRID METHODS

[3] Wavelet based multigrid methods for linear and nonlinear elliptic partial differential equations [J].

Avudainayagam, A ;

Vani, C .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 148 (02) :307-320

[4]

BRANDT A, 1977, MATH COMPUT, V31, P333, DOI 10.1090/S0025-5718-1977-0431719-X

[5]

Briggs W.L., 2000, A Multigrid Tutorial, V2nd

[6] Multigrid Algorithm for High Order Denoising [J].

Brito-Loeza, Carlos ;

Chen, Ke .

SIAM JOURNAL ON IMAGING SCIENCES, 2010, 3 (03) :363-389

[7] On High-Order Denoising Models and Fast Algorithms for Vector-Valued Images [J].

Brito-Loeza, Carlos ;

Chen, Ke .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 2010, 19 (06) :1518-1527

[8]

Chambolle A, 2005, LECT NOTES COMPUT SC, V3757, P136, DOI 10.1007/11585978_10

[9]

Chambolle A, 2004, J MATH IMAGING VIS, V20, P89

[10] A nonlinear primal-dual method for total variation-based image restoration [J].

Chan, TF ;

Golub, GH ;

Mulet, P .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1999, 20 (06) :1964-1977

← 1 2 3 →