Zhao Dong-Hong
Department of Applied Mathematics, School of Mathematics and Physics Science, University of Science and Technology Beijing, 100083, Beijing, People Republic of China
Wang Chen-Chen
Faculty of Science, University of Amsterdam, Netherlands
ABSTRACT
In this study, we present an adaptive anisotropic diffusion total variation method which combine wavelet transformation and total variation (TV) equations. The algorithm puts high-frequency coefficients of wavelet into the iterative total variation equations to construct new wavelet coefficients. At the same time, we introduce spread function into this algorithm. In contrast with previous work combining TV restoration with wavelet compression, this method presented in this study not only treats the numerical solution in a novel way which decreases the computational cost associated with the solution of the TV model, but also introduces spread function into this algorithm, which adds the difficulties of the problem. We present a detailed description of our method which indicates that a combination of wavelet based on restoration technique with the TV model produces superior results.
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How to cite this article
Zhao Dong-Hong and Wang Chen-Chen, 2013. Wavelet-based Total Variation Equation Image Restoration. Information Technology Journal, 12: 7778-7781.
DOI: 10.3923/itj.2013.7778.7781
URL: https://scialert.net/abstract/?doi=itj.2013.7778.7781
DOI: 10.3923/itj.2013.7778.7781
URL: https://scialert.net/abstract/?doi=itj.2013.7778.7781
REFERENCES
- Aubert, G. and L. Vese, 1997. A variational method in image recovery. SIAM J. Numeric. Anal., 34: 1948-1979.
CrossRef - Chambolle, A., R.A. De Vore, N.Y. Lee and B.J. Lucier, 1998. Nonlinear wavelet image processing: Variational problems, compression and noise removal through wavelet shrinkage. IEEE Trans. Image Process., 7: 319-335.
CrossRef - Chan, T., A. Marquina and P. Mulet, 2000. High-order total variation-based image restoration. SIAM J. Scientific Comput., 22: 503-516.
CrossRefDirect Link - Donoho, D.L. and I.M. Johnstone, 1994. Ideal spatial adaptation by wavelet shrinkage. Biometrika, 81: 425-455.
CrossRefDirect Link - Rudin, L.I., S. Osher and E. Fatemi, 1992. Nonlinear total variation based noise removal algorithms. Physica D Nonlinear Phenomena, 60: 259-268.
Direct Link - Scherzer, O., 1998. Denoising with higher order derivatives of bounded variation and an application to parameter estimation. Computing, 60: 1-27.
CrossRef - Chan, T.F. and J. Shen, 2000. Variational restoration of non-flat image features: Models and algorithms. SIAM J. Applied Math., 61: 1338-1361.
Direct Link - Shen, J. and T.F. Chan, 2002. Mathiematical models for local nontexture inpaintings. SIAM J. Applied Math., 62: 1019-1043.
CrossRefDirect Link