[1] Zeng Weili, Tan Xianghua, Lu Xiaobo,. Domain-based noise removal methodusing fourth-order partial differential equation [J]. Journal of Southeast University (English Edition), 2011, 27 (2): 154-158. [doi:10.3969/j.issn.1003-7985.2011.02.008]

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Domain-based noise removal methodusing fourth-order partial differential equation()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

27

Issue:

2011 2

Page:

154-158

Research Field:

Computer Science and Engineering

Publishing date:

2011-06-30

Info

Title:

Domain-based noise removal methodusing fourth-order partial differential equation

Author(s):

Zeng Weili¹;  Tan Xianghua²;  Lu Xiaobo³

¹ School of Transportation, Southeast University, Nanjing 210096, China
² School of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China
³ School of Automation, Southeast University, Nanjing 210096, China

Keywords:

fourth-order partial differential equation;  conductance coefficient;  speckle domain;  image denoising

PACS:

TP391

DOI:

10.3969/j.issn.1003-7985.2011.02.008

Abstract:

Due to the fact that the fourth-order partial differential equation(PDE)for noise removal can provide a good trade-off between noise removal and edge preservation and avoid blocky effects often caused by the second-order PDE, a domain-based fourth-order PDE method for noise removal is proposed. First, the proposed method segments the image domain into two domains, a speckle domain and a non-speckle domain, based on the statistical properties of isolated speckles in the Laplacian domain. Then, depending on the domain type, different conductance coefficients in the proposed fourth-order PDE are adopted. Moreover, the frequency approach is used to determine the optimum iteration stopping time. Compared with the existing fourth-order PDEs, the proposed fourth-order PDE can remove isolated speckles and keeps the edges from being blurred. Experimental results show the effectiveness of the proposed method.

References:

[1] Perona P, Malik J. Scale space and edge detection using anisotropic diffusion [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, 12(7): 629-639.
[2] Catte F, lions P L, Morel J M, et al. Image selective smoothing and edge detection by nonlinear diffusion [J]. SIAM Journal on Numerical Analysis, 1992, 29(1):182-193.
[3] Wei G W. Generalized Perona-Malik equation for image restoration [J]. IEEE Signal Processing Letters, 1999, 6(1): 165-167.
[4] Chen Q, Montesinos P, Sun Q S, et al. Ramp preserving Perona-Malik model [J]. Signal Processing, 2010, 90(1): 1963-1975.
[5] Rudin L I, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms [J]. Physica D: Nonlinear Phenomena, 1992, 60(1): 259-268.
[6] Kimia B, Tannenbaum A, Zucker S. On the evolution of curves via a function of curvature [J]. Journal of Mathematical Analysis and Applications, 1992, 163(1): 438-458.
[7] You Y, Xu W, Tannenbaum A, et al. Behavioral analysis of anisotropic diffusion in image processing [J]. IEEE Transactions on Image Processing, 1998, 5(11):1539-1553.
[8] You Y, Kaveh M. Fourth-order partial differential equations for noise removal [J]. IEEE Transactions on Image Processing, 2000, 9(10):1723-1730.
[9] Lysaker M, Lundervold A, Tai X C. Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time [J]. IEEE Transactions on Image Processing, 2003, 12(1):1579-1589.
[10] Liu Q, Yao Z G, Ke Y Y. Entropy solutions for a fourth-order nonlinear degenerate problem for noise removal [J]. Nonlinear Analysis, 2007, 67(1): 1908-1918.
[11] Didas S, Weickert J, Burgeth B. Properties of higher order nonlinear diffusion filtering [J]. Journal of Mathematical Imaging and Vision, 2009, 35(1): 208-226.
[12] Rajan J, Kannan K, Kaimal M R. An improved hybrid model for molecular image denoising [J]. Journal of Mathematical Imaging and Vision, 2008, 31(1): 73-79.
[13] Hamza A B, Escamilla P L, Aroza J M, et al. Removing noise and preserving details with relaxed median filters [J]. Journal of Mathematical Imaging and Vision, 1999, 11(2):161-177.
[14] Lu L, Wang M, Lai C. Image denoise by fourth-order PDE based on the changes of Laplacian [J]. Journal of Algorithms and Computational Technology, 2007, 2(1):99-110.
[15] Weickert J. Coherence-enhancing diffusion of colour images [J]. Image and Vision Computing, 1999, 17(1): 1999-212.
[16] Sporring J, Weickert J. Information measures in scale spaces [J]. IEEE Transactions on Information Theory, 2003, 45(3): 1051-1058.
[17] Ilyevsky A, Turkel E. Stopping criteria for anisotropic PDEs in image processing [J]. Journal of Scientific Computing, 2010, 45(1): 333-347.

Memo

Memo:

Biographies: Zeng Weili(1983—), male, graduate; Lu Xiaobo(corresponding author), male, doctor, professor, xblu2008@yahoo.cn.
Foundation items: The National Natural Science Foundation of China(No.60972001), the National Key Technology R & D Program of China during the 11th Five-Year Period(No.2009BAG13A06).
Citation: Zeng Weili, Tan Xianghua, Lu Xiaobo. Domain-based noise removal method using fourth-order partial differential equation[J].Journal of Southeast University(English Edition), 2011, 27(2):154-158.[doi:10.3969/j.issn.1003-7985.2011.02.008]

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