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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 532-533Wavelet Shrinkage Based Variational Image...

Wavelet Shrinkage Based Variational Image Decomposition Model

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Abstract:

A new class of variational models based on Besov spaces B_1,1^s (s>0 ) and homogeneous Besov space E=B_∞,∞^-1 for image decomposition is proposed. The proposed models can be regarded as generalizations of Aujol-Chambolle model. The associated minimizers of variational problems can be expressed by applying different shrinkage functions which depend on the wavelet scale to each wavelet coefficient. The wavelet based treatment simplifies computation of this class of variational models. Finally, we present numerical results on denoising of both real and remote sensing images.

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Materials Science and Information Technology II

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Periodical:

Advanced Materials Research (Volumes 532-533)

Pages:

1021-1025

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.532-533.1021

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Online since:

June 2012

Authors:

Min Li, Xiao Li Sun, Chen Xu

Keywords:

Besov Spaces, Functional Minimization, Image Decomposition, Shrinkage, Wavelet

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© 2012 Trans Tech Publications Ltd. All Rights Reserved

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[1] D. Mumford, and J. Shah, Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems, Comm. Pure Applied Mathematics, 42(5): 577-685, (1989).

DOI: 10.1002/cpa.3160420503

[2] A. Chambolle. An algorithm for total variation minimization and applications. JMIV, 20: 89-97, (2004).

[3] L. Vese, and S. Osher, Modeling Textures with Total Variation Minimization and Oscillating Patterns in Image Processing, Journal of Scientific Computing, 19 (1-3), 553-572, (2003).

[4] L. Rudin, S. Osher, and E. Fatemi, Nonlinear Total Variation Based Noise Removal Algorithms, Physica D, 60: 259-268, (1992).

DOI: 10.1016/0167-2789(92)90242-f

[5] S. Osher, A. Sole, and L. Vese, Image Decomposition and Restoration Using Total Variation Minimization and Norm, Multiscale Modeling and Simulation 1 (3): 349-370, (2003).

DOI: 10.1137/s1540345902416247

[6] J. F. Aujol and A. Chambolle, Dual Norms and Image Decomposition Models, International Journal of Computer Vision 63(1): 85-104, (2005).

DOI: 10.1007/s11263-005-4948-3

[7] I. Daubechies and G. Teschke, Wavelet based image decomposition by variational functionals, Proc. SPIE Vol. 5266, pp.94-105, Wavelet Applications in Industrial Processing, Frederic Truchetet, Ed., (2004).

DOI: 10.1117/12.516051

[8] Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, University Lecture Series, Col. 22, Amer. Math. Soc., (2001).

DOI: 10.1090/ulect/022

[9] F. John and L. Nirenberg, On Functions of Bounded Mean Oscillation, Comm. Pure. Appl. Math., vol. 14, 415-547, (1999).

DOI: 10.1002/cpa.3160140317

[10] J. B. Garnett, T. M. Le, Y. Meyer and L. A. Vese, Image decomposition Using Bounded Variation and Homogeneous Besov Spaces, UCLA CAM Report 05-57, (2005).

[11] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Verlag der Wissenschaften, Berlin, (1978).

[12] A. Chambolle, R. A. DeVore, N. Y. Lee, and B. J. Lucier, Nonlinear wavelet image processing: Variational problems, compression and noise removal through wavelet shrinkage, IEEE Transactions of Image Processing, Vol. 7, No. 3, pp.319-335, (1998).

DOI: 10.1109/83.661182

[13] D. Donoho, and I. Johnstone, Ideal spatial adaptation via wavlet shrinkage, Biometrika, 81: 425-455, (1994).

DOI: 10.1093/biomet/81.3.425

[14] Dirk A. Lorenz, Wavelet Shrinkage in Signal and Image Processing - An Investigation of Relations and Equivalences, Ph. D thesis, University of Bremen, (2005).

[15] L. Vese, and S. J. Osher, Image Denoising and Decomposition with Total Variation Minimization and Oscillatory Functions, Special Issue on Mathematics and Image Analysis, Journal of Mathematical Imaging and Vision, 20: 7-18, (2004).

DOI: 10.1023/b:jmiv.0000011316.54027.6a

[16] T. M. Le and L. A. Vese, Image Decomposition Using Total Variation and , Multiscale Model. Simul., 4(2): 390-423, (2005).

DOI: 10.1137/040610052

[17] Tieyong Zeng and Michael K. Ng. Correspondence—on the total variation Dictionary Model. IEEE Trans. Image Processing. 19(3): 821-825, (2010).

DOI: 10.1109/tip.2009.2034701

[18] W. Yin, S. Osher, D. Goldfarb and J. Darbon. Bregman iterative algorithms for l1-minimization with application to compressed sensing. SIAM J. Imag. Sci. 1(1): 143-146, (2008).

DOI: 10.1137/070703983