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標題: Discrete Nonlinear Diffusion Model for Image Denoising by Using the Tailored Finite Point Method
作者: 林彥儒
Yen Ru Lin
關鍵字: 量身定做
tailored finite point
image denoising
引用: [1] P. Perona and J. Malik, 'Scale-space and edge detection using anisotropic diffusion', IEEE Trans. Pattern Anal. Machine Intell. 12(7), 1990, pp. 629-639. [2] L. I. Rudin, S. Osher, and E. Fatemi,'Nonlinear total variation based noise removal algorithms', Phys. D, 60(1-4), 1992, pp. 259-268. [3] F. Catte, P. L. Lions, J. M. Morel, T. Coll, 'Image selective smoothing and edge detection by nonlinear diffusion,' SIAM J. Numer. Anal. 29(1), 1992, pp. 182-193. [4] J. Weickert, 'Anisotropic diffusion in image processing', ECMI Series, Teubner- Verlag, Stuttgart, Germany, 1998. [5] D. Barash and D. Comaniciu, 'A common framework for nonlinear diffusion, adaptive smoothing, bilateral filtering and mean shift,' Image Vis. Comput. 22(1), 2004, pp. 73-81. [6] Feng Liu and Jingbo Liu, 'Anisotropic diffusion for image denoising based on diffusion tensors', J. Vis. Commun. Image R. 23, 2012, pp. 516-521. [7] S. M. Chao and D. M. Tsai, 'An improved anisotropic diffusion model for detail and edge preserving smoothing,' Pattern Recognit. Lett. 31(13), 2010, pp. 2012-2023. [8] Z. Guo, J. Sun, D. Zhang and B. Wu, 'Adaptive Perona-Malik model based on the variable exponent for Image denoising,' IEEE Trans. Image Process. 21(3), 2012, pp. 958-967. [9] Y. Shih, C. Rei and H. Wang,'A novel PDE based image restoration: convection-diffusion equation for image denoising,' J. Comput. Appl. Math. 231(2), 2009, pp. 771-779. [10] H. Han, Huang, Z., Kellogg, R.B., 'The tailored finite point method and a problem of P. Hemker,' Proceedings of the International Conference on Boundary and Interior Layers - Computational and Asymptotic Methods, Limerick, July, 2008. [11] H. Han, Z. Huang, R. B. Kellogg, 'A tailored finite point method for a singular perturbation problem on an unbounded domain,' J. Sci. Comput. 36(2), 2008, pp. 243-261. [12] Han, H., Huang, Z., 'Tailored finite point method for a singular perturbation problem with variable coefficients in two dimensions,' J. Sci. Comput. 41(2), 2009, pp. 200-220. [13] Y. Shih, C.S. Chien and C.Y. Chung, 'An Adaptive Parameterized Block-Based Singular Value Decomposition for Image Denoising and Compression,' Applied Mathematics and Computation. 218, 2012, pp. 10370-10385. [14] Y. Shih, R. B. Kellogg and Y. Chang, 'Characteristic tailored finite point method for convection-dominated convection-diffusion-reaction problems,' J. Sci. Comput. 47(2), 2011, pp. 198-215. [15] Z. Huang and X. Yang, 'Tailored finite point method for first order wave equation,' J. Sci. Comput. 49(3), 2011, pp. 351-366. [16] S. G. Chang, B. Yu and M. Vetterli, 'Adaptive wavelet thresholding for image denoising and compression', IEEE Trans. Image Process. 9(9), 2000, pp. 1532- 1546. [17] Shin-Yi Chiou, 'Convection-Diffusion Model for Image Denoising in Comparison with Wavelet Method and Singular Value Decomposition', Thesis, National Chung Hsing University, 2012. [18] Chia-Yung Rei, 'The Application of Diffusion Equation in Image Smoothing', Thesis, National Chung Hsing University, 2007. [19] K. Konstantinides, B. Natarajan and G. S. Yovanof, 'Noise estimation and filtering using block-based singular value decomposition', IEEE Tran. Image Process. Vol.6(3), 1997, pp. 1532-1546. [20] T. Preusser and M. Rumpf, 'An daptive finite element method for large scale image processing', Journal of Visual Comm. Image Repres. 11, 2000, pp. 183- 195.
摘要: In this thesis, we propose an anisotropic diffusion filter for image denoising, because the traditional nonlinear diffusion filter works well with Gaussian noise, but for the salt and pepper noise no effect. A novel numerical method, the tailored finite point method, is introduced for implementing the PDE-based restoration. We compare the performance of our algorithm with other traditional filters which have been widely used for removing white Gaussian noise. The numerical experiments show that the proposed anisotropic diffusion filter is effective in removing the mixture of white Gaussian and salt and pepper noises when compared with other well-known filters. In addition, the tailored finite point method in nonlinear diffusion model also has a good effect, whether it is regular or irregular grid mesh.
在這篇論文中,我們修正了非線性擴散模型,因為傳統的非線性擴散模型處 理高斯雜訊效果不錯,但是對於鹽和胡椒雜訊相對就沒有效果,所以藉由一些改 變,我們提出新的非線性擴散模型,讓它在影像處理上對於鹽和胡椒雜訊更有效 及更好的結果。後半部分我們使用新的數值離散法,量身定做有限點法,來離散 非線性擴散模型。藉由與其他傳統非線性擴散模型以及有限差分法的比較,我們 可以了解更改後的模型在影像去雜訊各方面都有較突出的表現,尤其是鹽和胡椒 雜訊雜訊,另外,量身定作有限點法應用在非線性擴散模型上也有不錯的效果, 不管是規則的網格還是不規則網格,量身定作有限點法都能處理。
文章公開時間: 2017-05-11
Appears in Collections:應用數學系所



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