Image denoising by random walk with restart Kernel and non-subsampled contourlet transform
Image denoising by random walk with restart Kernel and non-subsampled contourlet transform
- Author(s): G. Liu ; X. Zeng ; Y. Liu
- DOI: 10.1049/iet-spr.2010.0265
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- Author(s): G. Liu 1 ; X. Zeng 1 ; Y. Liu 1
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View affiliations
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Affiliations:
1: College of Communication Engineering, Chongqing University, Chongqing, People's Republic of China
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Affiliations:
1: College of Communication Engineering, Chongqing University, Chongqing, People's Republic of China
- Source:
Volume 6, Issue 2,
April 2012,
p.
148 – 158
DOI: 10.1049/iet-spr.2010.0265 , Print ISSN 1751-9675, Online ISSN 1751-9683
To address the drawbacks of continuous partial differential equations, a diffusion method based on spectral graph theory and random walk with restart kernel is proposed, which uses non-subsampled contourlet transform to capture the geometric feature of image. Specifically, a new graph weighting function is constructed based on the geometric feature. Moreover, a second-order random walk with restart kernel was generated. The derivation shows that the proposed method is equivalent to the denoising methods based on partial differential equations. The simulation results demonstrate that the proposed method can effectively reduce Gaussian noise and preserve image edge with superior performance compared with other graph-based partial differential equation methods.
Inspec keywords: partial differential equations; graph theory; Gaussian noise; image denoising
Other keywords:
Subjects: Mathematical analysis; Mathematical analysis; Optical, image and video signal processing; Other topics in statistics; Combinatorial mathematics; Computer vision and image processing techniques; Other topics in statistics; Combinatorial mathematics
References
-
-
1)
- J. Weickert . (1998) Anisotropic diffusion in image processing.
-
2)
- A.L. Cunha , J. Zhou , M.N. Do . “The nonsubsampled contourlet transform: theory, design and applications”. IEEE Trans. Image Process , 10 , 3089 - 3101
-
3)
- J. Weickert . Coherence-enhancing diffusion filtering. Int. J. Comput. Vis. , 111 - 127
-
4)
- P. Perona , J. Malik . Scale-space and edge detection using anistropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. , 7 , 629 - 639
-
5)
- M.J. Black , G. Sapiro , D.H. Marimont , D. Heeger . Robust anisotropic diffusion. IEEE Trans. Image Process. , 3 , 421 - 432
-
6)
- O. Lezoray , A. Elmoataz , S. Bougleux . Graph regularization for color image processing. Comput. Vis. Image Understand. , 12 , 38 - 55
-
7)
- F. Chung . (1994) Spectral graph theory.
-
8)
- J.H. Yu , Y.Y. Wang , Y.Z. Shen . Noise reduction and edge detection via kernel anisotropic diffusion. Pattern Recognit. Lett. , 10 , 1496 - 1503
-
9)
- F. Zhang , E.R. Hancock . Graph spectral image smoothing using the heat kernel. Patt. Recogn. , 11 , 3328 - 3342
-
10)
- G. Sapiro . (2001) Geometric partial differential equations and image analysis.
-
11)
- M. Mahmoudi , G. Sapiro . Fast image and video denoising via nonlocal means of similar neighborhoods. IEEE Signal Process. Lett. , 12 , 839 - 842
-
12)
- Y.J. Yu , S.T. Acton . Speckle reduction anisotropic diffusion. IEEE Trans. Image Process. , 11 , 1260 - 1270
-
13)
- K. Krissian , C.-F. Westin , R. Kikinis , K. Vosburgh . Oriented speckle reducing anisotropic diffusion. IEEE Trans. Image Process. , 5 , 1412 - 1424
-
14)
- D. Tschumperle , R. Deriche . Vector-valued image regularization with PDEs: a common framework for different applications. IEEE Trans. Patt. Anal. Mach. Intell. , 4 , 506 - 517
-
15)
- F. Catte , P.L. Lions , J.M. Morel , T. Coll . Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. , 1 , 182 - 193
-
16)
- R. Vignesh , B.T. Oh , C.-C.J. Kuo . Fast non-local means (NLM) computation with probabilistic early termination. IEEE Signal Process. Lett. , 3 , 277 - 280
-
17)
- Smola, A.J., Kondor, R.: `Kernels and regularization on graphs', The Seventh Workshop on Kernel Machines, Washington, 2003.
-
18)
- G. Liu , G. Zeng , F. Tian . Speckle reduction by adaptive window anisotropic diffusion. Signal Process. , 11 , 2233 - 2243
-
19)
- Aja-Fernández, S., Estépar, R.S., Alberola-López, C., Westin, C.F.: `Image quality assessment based on local variance', Proc. 28th IEEE EMBC, 2006, New York, USA, p. 4815–4818.
-
20)
- J. Koenderink . The structure of images. Biol. Cybern. , 363 - 370
-
21)
- M.N. Do , M. Vetterli . The contourlet transform: an efficient directional multiresolution image representation. IEEE Trans. Image Process. , 12 , 2091 - 2016
-
22)
- Witkin, A.P.: `Scale-space filtering', Proc. Eighth Int. Joint Conf. Artificial Intelligence, 1983, San Francisco, CA, USA, p. 1019–1021.
-
23)
- Y. Bao , H. Krim . Smart nonlinear diffusion: a probabilistic approach. IEEE Trans. Patt. Anal. Mach. Intell. , 1 , 63 - 72
-
24)
- A. Buades , B. Coll , J. Morel . A review of image denoising algorithms, with a new one. SIAM J. Multiscale Model. Simul. , 2 , 290 - 530
-
25)
- S. Aja-Fernández , C. Alberola-López . On the estimation of the coefficient of variation for anisotropic diffusion speckle filtering. IEEE Trans. Image Process. , 9 , 2694 - 2701
-
26)
- Kim, T.H., Lee, K.M., Lee, S.U.: `Generative image segmentation using random walks with restart', Proc. 10th European Conf. Computer Vision, 2008, Marseille, France.
-
27)
- M. Hochbruck , C. Lubich . On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. , 1911 - 1925
-
28)
- Y. Saad . Analysis of some Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. , 209 - 228
-
29)
- J. Babaud , A. Witkin , M. Baudin , R. Duda . Uniqueness of the Gaussian kernel for scale-space filtering. IEEE Trans. Patt. Anal. Mach. Intell. , 1 , 26 - 33
-
30)
- Z. Wang , A.C. Bovik , H.R. Sheikh , E.P. Simoncelli . Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. , 4 , 600 - 613
-
31)
- Pan, J.Y., Yang, H.J., Faloutsoc, C.: `Automatic multimedia crossmodal correlation discovery', Proc. Tenth ACM SIGKDD Conf., 2004, Seattle, WA.
-
32)
- G. Gilboa , N. Sochen , Y. Zeevi . Image enhancement and denoising by complex diffusion processes. IEEE Trans. Patt. Anal. Mach. Intell. , 8 , 1020 - 1036
-
1)
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