文摘
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We propose a new algorithm for the total variation based on image denoising problem. The split Bregman method is used to convert an unconstrained minimization denoising problem to a linear system in the outer iteration. An algebraic multi-grid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. Numerical experiments demonstrate that this algorithm is efficient even for images with large signal-to-noise ratio. |
来源
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Acta Mathematicae Applicatae Sinica-English Series
,2012,28(4):721-730 【核心库】
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DOI
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10.1007/s10255-012-0184-0
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关键词
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image denoising
;
total variation
;
split Bregman method
;
algebraic multi-grid method
;
Krylov subspace acceleration
|
地址
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School of Science, Southwest University of Science and Technology, Mianyang, 621010
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语种
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英文 |
ISSN
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0168-9673 |
学科
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数学 |
基金
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Supported by Youth Foundation of Southwest University of Science and Technology
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文献收藏号
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CSCD:4702684
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1.
Acar R. Analysis of total variation penalty methods for ill-posed problems.
Inverse Problems,1994,10:1217-1229
|
CSCD被引
33
次
|
|
|
|
2.
Alvarez L. Image selective smoothing and edge detection by nonlinear diffusion II.
SIAM J. Numer. Anal,1992,29:845-866
|
CSCD被引
111
次
|
|
|
|
3.
Barcelos C A Z. Heat flow and related minimization problem in image restoration.
Computers and Mathematics with Applications,2000,39:81-97
|
CSCD被引
9
次
|
|
|
|
4.
Barles G. Convergence of approximation schemes for fully nonlinear second order equations.
Asymptotic Analysis,1991,4:271-283
|
CSCD被引
11
次
|
|
|
|
5.
Brandt A. On recombining iterants in multigrid algorithms and problems with small islands.
SIAM J. Sci. Comput,1995,16:20-28
|
CSCD被引
3
次
|
|
|
|
6.
Chan R. Advanced signal processing algorithms.
Proceedings of the International Society of Photo-Optical Instrumentation Engineers,1995:314-325
|
CSCD被引
3
次
|
|
|
|
7.
Chan T F. A nonlinear primal-dual method for total variation-based image restoration.
SIAM J. Sci. Comput,1999,20:1964-1977
|
CSCD被引
51
次
|
|
|
|
8.
Chang Q S. Acceleration methods for total variation-based image denoising.
SIAM J. Sci. Comput,2003,25:983-994
|
CSCD被引
1
次
|
|
|
|
9.
Chang Q S. Efficient algebraic multigrid algorithms and their convergence.
SIAM J. Sci. Comput,2002,24:597-618
|
CSCD被引
12
次
|
|
|
|
10.
Chang Q S. Algebraic multigrid method for queuing networks.
Int. J. of Computer Math,1999,70:539-552
|
CSCD被引
3
次
|
|
|
|
11.
Chang Q S. On the algebraic multigrid method.
J. Comput. Phys,1996,125:279-292
|
CSCD被引
15
次
|
|
|
|
12.
Goldstein T.
The split Bregman method for L1 regularized problems,2008
|
CSCD被引
2
次
|
|
|
|
13.
Henson V E. Element-free AMGe: general algorithms for computing interpolation weights.
SIAM J. Sci. Comput,2001,23:629-650
|
CSCD被引
4
次
|
|
|
|
14.
Li Y.
An affine scaling algorithm for minimizing total variation in image enhancement. Tech. Report 12/94,1994
|
CSCD被引
1
次
|
|
|
|
15.
McCormick S.
Multigrid methods,1987
|
CSCD被引
1
次
|
|
|
|
16.
Oman M E. Fast multigrid techniques in total variation-based image reconstruction.
Preliminary Proceedings of the 1995 Copper Mountain Conference on Multigrid Methods,1995
|
CSCD被引
1
次
|
|
|
|
17.
Oosterlee C W. Krylov subspace acceleration of nonlinear multigrid with application to recirculating flows.
SIAM J. Sci. Comput,2000,21:1670-1690
|
CSCD被引
5
次
|
|
|
|
18.
Osher S. Feature-oriented image enhancement using shock filters.
SIAM J. Numer. Anal,1990,27:919-940
|
CSCD被引
76
次
|
|
|
|
19.
Rudin L. Nonlinear total variation based noise removal algorithms.
Phys. D,1992,60:259-268
|
CSCD被引
1053
次
|
|
|
|
20.
Ruge J. Algebraic multigrid.
Multigrid Methods, Frontiers Appl. Math. 3,1987:73-130
|
CSCD被引
1
次
|
|
|