Hybrid Shearlet and SURE-LET for Image Denoising
Authors: 
Xu Zhuozhi, Wei Li, Weibo DuanAuthors Info & Claims
Xu Zhuozhi, Wei Li, Weibo DuanAuthors Info & ClaimsArticle No.: 296, Pages 1 - 7
Abstract
Aiming at solving the problem that the shape feature will be lost while removing the noise in the image, this paper proposes a hybrid shear wave and sure let method. Many research has proven that Shearlets has better representation about distributed discontinuities than traditional wavelets, such as edges, and are ideal tools for edge representation. Therefore, the method proposed in this paper is as follows: firstly, the noise image is decomposed by shear wavelet to obtain from high to low frequency coefficients. Then we use Stein's unbiased risk estimation, which is an accurate and statistically unbiased MSE estimation. At the same time, it's only related to the noise image, not the clean image, to optimize the noise figure. Finally, the denoised image is obtained by inverse shearlet transformation. Experiments show that the proposed algorithm has more advantages than other algorithms.
References
[1]
M. S. Crouse, R. D. Nowak, and R. G. Baraniuki, “Wavelet-based signal processing using Hidden Markov models,” IEEE Trans. Signal Process., vol. 46, no. 4, pp. 886–902, Apr. 1998.
[2]
Candes E. J. Donoho D.L. New tight frames of curvelets and optimal representations of object with piecewise C2 singularities [J]. Communications on Pure and applied Mathematics, 2004, 57(2):219-266.
[3]
Candes E. J. Donoho D.L. el al. Fast discrete curvelet Transforms[J],Multi-Scale Modeling and Simulation, 2006,5(3):861-899
[4]
Do M. N., Vetterli M. The contourlet transform: an efficient directional multiresolution image representation [J], IEEE Trans on Image Process, 2005,14(12):2091-2106
[5]
K. Guo, D. Labate, Optimally Sparse Multidimensional Representation using Shearlets, SIAM J. Math. Anal., 39 (2007), 298-318
[6]
Easley G.,Labate D.,Lim W. Q. Sparse directional image representation using the dissrete shearlet transform [J], SIAM Journal on Mathematical Analysis, 2007, 39(1);298-318.
[7]
D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Amer. Statist. Assoc., vol. 90, no. 432, pp. 1200–1224, Dec. 1995.
[8]
F. Colonna, G. R. Easley, Generalized discrete Radon transforms and their use in the ridgelet transform, Journal of Mathematical Imaging and Vision, 23 (2005) 145-165.
[9]
R. R.Coifman, D. L.Donoho, Translation invariant de-noising, in: Wavelets and Statistics, A. Antoniadis and G. Oppenheim (eds.), pp. 125{150, Springer-Verlag, New York, 1995.
[10]
K. Guo, D. Labate, Optimally Sparse Multidimensional Representation using Shearlets, SIAM J. Math. Anal., 39 (2007), 298-318
[11]
E. Hern¶andez, G. Weiss, A first course on wavelets, CRC Press, Boca Raton, FL, 1996.
[12]
K. Guo, W. Lim, D. Labate, G. Weiss, E. Wilson, Wavelets with composite dilations, Electr. Res. Announc. of AMS 10 (2004) 78-87.
[13]
K. Guo, W. Lim, D. Labate, G. Weiss, E. Wilson, The theory of wavelets with composite dilations, in: Harmonic Analysis and Applications, C. Heil (ed.), pp. 231-249, BirkÄauser, Boston, 2006.3.1
[14]
K. Guo, W. Lim, D. Labate, G. Weiss, E. Wilson, Wavelets with composite dilations and their MRA properties, Appl. Computat. Harmon. Anal. 20 (2006) 231-249
[15]
Florian Luisier, Thierry Blu, A new sure approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding, IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 16, NO. 3, MARCH 2007, 593-606.
[16]
C. Stein, “Estimation of the mean of a multivariate normal distribution,” Ann. Statist., vol. 9, pp. 1135–1151, 1981.
[17]
J.-L. Starck, E. J. Candes, and D. L. Donoho, “The curvelet transform for image denoising,” IEEE Trans. Image Process., vol. 11, no. 6, pp. 670–684, Jun. 2002.
[18]
J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of gaussians in the wavelet domain,” IEEE Trans. Image Process., vol. 12, no. 11, pp. 1338–1351, Nov. 2003.
[19]
L. Sendur and I. W. Selesnick, “Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency,” IEEE Trans. Signal Process., vol. 50, no. 11, pp. 2744–2756, Nov. 2002.
[20]
X. Zhang, X. Feng, W. Wang. Two-direction nonlocal model for image denoising[J]. IEEE Transactions on Image Processing, 22(1): 408-412 2012.
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Published In
May 2021
2053 pages
ISBN:9781450390200
DOI:10.1145/3469213
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Published: 18 August 2021
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ICAIIS 2021
ICAIIS 2021: 2021 2nd International Conference on Artificial Intelligence and Information Systems
May 28 - 30, 2021
Chongqing, China
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