Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/17568
標題: 偏微分方程與自適區塊截斷編碼結合用於影像去雜訊與壓縮
Mixed PDE Based Methods with Adaptive Block Truncation Coding for Image De-noising and Compression
作者: 焦郁華
Chiao, Yu-Hua
關鍵字: block truncation coding method
區塊截斷編碼方法
image compression
upwind finite difference method
convection diffusion equation
image de-noise
影像壓縮
迎風有限差分法
擴散對流方程式
影像去雜訊
出版社: 應用數學系所
引用: [1] N. Ahmed, T. Natarajan, and K. R. Rao, Discrete cosine transform, IEEE Transactions on Computers, Volume 23 Issue 1, 90-93, Jan. 1974. [2] J. Canny, A Computational approach to edge detection, IEEE Transactitons Pattern Analysis and Machine Intelligence, Volume 8, 679-698, Nov. 1986. [3] F. Catte, P. L. Lione, J. M. Morel and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, SIAM Journal of Numeraical Analysis, Volume 29, 182-19, Feb. 1992. [4] R. Courant, E. Isaacson, and M. Rees, On the Solution of Nonlinear Hyperbolic Differential Equations by Finite Differences, Communication on Pure and Applied Mathematics, Volume 5, 243-255, 1952. [5] E. J. Delp and O. R. Mitchell, Image compression using block truncation coding, IEEE Transactitons on Communications, Volume 27, 1335-1342, Sep. 1979. [6] R. C. Gonzalez and R. E. Woods, Digital image processing, 3rd Edition, Prentice Hall, 2008. BOOK. [7] D. A. Huffman, ”A method for the construction of minimum-redundancy codes”, Pro- ceedings of the I.R.E., 1098-1102, Sep. 1952. [8] M. D. Lema and O. R. Mitchell, Absolute moment block truncation coding and its applications to color images, IEEE Transactitons on Communications, Volume 32, 1148- 1157, Oct. 1984. [9] S. G. Mallat, A theory for multiresolution signal decomposition: The wavelet representation, IEEE Transactitons Pattern Analysis and Machine Intelligence, Volume 11, 674-693, July 1989. [10] S. Osher, and J. A. Sethian, Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, Volume 79, 12-49, 1988. [11] P. Perona and J. Malik, Scale space and edge detection using anisotropic diffusion, IEEE Transactitons Pattern Analysis and Machine Intelligence, Volume 12, 629-639, July 1990. [12] D. Lemire, O. Kaser, K. Aouiche, Sorting improves word-aligned bitmap indexes. Jour- nal Data and Knowledge Engineering, Volume 69, 3-28, 2009. [13] Z. Liu and Q. Chang, Numerical analysis of the model of image processing with timedelay regularization, Applied Mathematics and Computation, Volume 166 Issue 2, 349- 372, July 2005. [14] N. Sae-bae and S. Udomhunsakul, Adaptive block-based singular value decomposition filtering, IEEE Computer Graphics, Imaging and Visualisation , 298-303, Aug. 2007. [15] Y. Shih and H. C. Elman, Modified streamline diffusion schemes for convection-diffusion problems, Computer Methods in Applied Mechanics and Engineering, 137-151, 1999. [16] Y. Shih, C. Rei and H.Wang, A novel PDE based image restoration: convection diffusion equation for image de-noising, Journal of Computational and Applied Mathematics, Volume 231, 771-779, 2009. [17] M. Zhu, S. J. Wright, and T. F. Chan, Duality-based algorithms for total-variationregularized image restoration, Computational Optimization and Applications, Volume 47, 2010.
摘要: 在這篇論文中,我們提出了一種新的自適應區塊截斷編碼方法(ABTC)的影像壓縮方法。為了達到更好的影像成像品質,我們提出了一種結合了迎風有限差分法求解對時間依賴的擴散對流方程式和自適應區塊截斷編碼方法來去除影像雜訊。實驗數據結果表示,我們的方法有效地去除影像雜訊,並保留影像邊緣以及對影像壓縮的過程。
In this thesis, we propose an adaptive block truncation coding method (ABTC) for image compression. For achieving a better image quality, we propose a novel algorithm by a mixture of a upwind finite difference for solving a time dependent convection diffusion equation and the ABTC algorithm to remove the image noise. The numerical results show that our proposed methods are effectively remove the noise, and preserves the edge information well during the image compression process.
URI: http://hdl.handle.net/11455/17568
其他識別: U0005-0407201111232600
文章連結: http://www.airitilibrary.com/Publication/alDetailedMesh1?DocID=U0005-0407201111232600
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