臺灣博碩士論文加值系統

影像復原技術(Image restoration)主要目的是修復、重建退化或損毀之影像以改善影像品質。由於影像在傳輸過程中，資訊經通道受到雜訊干擾，使影像資訊遭破壞，造成影像品質下降，導致接收方無法收到完整的資訊，所以如何讓影像恢復到傳送前之品質，就變得相當重要。
本論文是以改善型態成分分析(Morphological component analysis, MCA)為基礎，將影像分解成影像紋理(Image texture)，影像結構(Image structure)，影像邊緣(Image edge)三部分，並分析各個影像雜訊分佈情況，再針對不同層分別移除其影像雜訊。在影像紋理部分是使用目前效果較佳的三維區塊匹配法(Block matching 3D, BM3D)，影像結構部分則使用非局部平均濾波(Non local means, NLM)，影像邊緣部分則使用K-SVD演算法來消除影像雜訊。本文將分解後影像依不同層分別處理，使其能更有效的移除雜訊，並保留影像細節部分。由電腦模擬結果顯示，本文所提去除雜訊影像復原方法之效能優於傳統僅使用單一濾波的方法。

Images are usually inevitably polluted by noise during the transmission and the reception. Image restoration technique is one of important technologies that be ignored in image processing. How to recovery the quality of pre-delivery image becomes a momentous issue.
The morphological component analysis (MCA) decomposes image into texture, structure and edges.We analyzed the noise properties and proposed three methods to remove noise from different layers in this thesis. A block matching 3D (BM3D) scheme is used to eliminate noise in the texture of image, the adaptive non local means (ANLM) scheme is used to eliminate noise in the structure of image, and the K-SVD algorithm is used to eliminate noise in the edge of image. Simulation results show that the proposed method can provide a better performance than that of the traditional denoising methods.

摘　要 I
ABSTRACT II
目 錄 IV
表目錄 VI
圖目錄 VII
第一章 緒論 1
1.1 前言 1
1.2 研究背景與動機 1
1.3 論文架構 2
第二章 影像復原去雜訊相關技術原理 3
2.1 影像雜訊模型和影像恢復 3
2.1.1 影像雜訊模型 3
2.1.2 影像復原技術 4
2.2 基於稀疏表示之影像分解 7
2.2.1 稀疏表示基本理論 7
2.2.2 基底搜尋演算法 8
2.2.3 匹配追蹤演算法 9
2.2.4 正交匹配追蹤演算法 11
2.3 型態成分分析 13
2.3.1 K-SVD演算法 15
第三章 影像復原去雜訊之改善方法 19
3.1 影像結構部分之改善方法 21
3.1.1 非局部平均濾波器 22
3.1.2 自適應搜索視窗非局部平均濾波法 24
3.2 影像紋理部分之改善方法 25
第四章 實驗結果與討論 33
4.1 評估方法 33
4.1.1 峰值訊雜比 33
4.1.2 均方根誤差 33
4.1.3 絕對平均誤差 34
4.2 實驗資料及環境 34
4.3 分解影像紋理之實驗結果 35
4.4 分解影像結構之實驗結果 40
4.5 完整復原影像之實驗結果 46
第五章 結論與未來展望 51
參考文獻 52
符號彙編 54

[1]繆紹綱譯，數位影像處理，培生教育出版社，2009。
[2]T. A. Nodes and N. C. Gallagher, “Median Filters: Some Modifications and Their Properties,” IEEE Trans. Acoust, Speech, Signal Process., no. 5, pp. 739-746, Oct. 1982.
[3]J. L. Starck, M. Elad, and D. Donoho, “Redundant Multiscale Transforms and Their Application for Morphological Component Separation,” Advances in Image and Electron Physics, vol. 132, pp. 288-348, 2004.
[4]J. L. Starck, M. Elad, and D. Donoho, “Image Decomposition via the Combination of Sparse Representatntions and Variational Approach,” IEEE Trans. Image Process, vol. 14, no. 10, pp. 1570-1582, 2005.
[5]X. Deng and Z. Liu, “An Improved Image Denoising Method Applied in Resisting Mixed Noise Based on MCA and Median Filter,” International Conference on Computational Intelligence and Security, pp. 162-166, 2015.
[6]S. Ruikar and D. D. Doye, “Image Denoising Using Wavelet Transform,” International Conference on Mechanical and Electrical Technology, pp. 509-515, 2010.
[7]K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering,” IEEE Trans. Image Process, vol. 16, no. 8, pp. 2080-2095, 2007.
[8]A. Buades, B. Coll, and J. M. Morel, “A Non-local Algorithm for Image Denoising,” IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 60-65, 2005.
[9]H. M. Lin and A. N. Willson, “Median Filters with Adaptive Length,” IEEE Trans. Circuits Systems, vol. 35, no. 6, pp. 675-690, 1988.
[10]O.Y. Harja, J. Astola, and Y. Neuvo, “Analysis of the Properties of Median and Weighted Median Filters Using Threshold Logic and Stack Filter Representation,” IEEE Trans. Signal Process., vol. 39, pp. 395-410, Feb. 1991.
[11]邱宇翼，基於DCT與DC-QIM技術之強健型浮水印，碩士論文，國立臺北科技大學電腦與通訊研究所，臺北，2013。
[12]S. Mallat, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representatin,” IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 674-693, 1989.
[13]I. Daubechies, “Orthonormal Bases of Compactly Supported Wavelets,” Communications on Pure and Applied Mathematics, pp. 909-996, 1988.
[14]J. Bobin, J. L. Starck, Y. Moudden, and M. J. Fadili, “Blind Source Separation: The Sparsity Revolution,” Advances in Image and Electron Physics, vol. 152, pp. 221-298, 2008.
[15]S. Chen, D. Donoho, and M. Saunder, “Atomic Decomposition by Basis Pursuit,” IEEE Trans. Signal Process., vol. 20, no. 1, pp. 33-61, Aug. 1998.
[16]S. Mallat and Z. Zhang, “Matching Pursuit in a Time-Frequency Dictionary,” IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3397-3415, Dec. 1993.
[17]Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, “Orthogonal Matching Pursuit: Recursive Function Approximation with Applications to Wavelet Decomposition,” International Conference on Signals Systems and Computers, vol. 1, pp. 40-44, 1993.
[18]M. J. Fadili, J. L. Starck, J. Bobin, and Y. Moudden, “Image Decomposition and Separation Using Sparse Representations: An Overview,” Proceedings of the IEEE, vol. 98, pp. 983-994, 2010.
[19]M. Aharon, M. Elad, and A. Bruckstein, “K-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation,” IEEE Trans. Signal Process., vol. 54, no. 11, pp. 4311-4322, 2006.
[20]E. J. Candes and D. L. Dnonoho, “Curvelets–A Surprisingly Effective Nonadaptive Representation for Objects with Edges,” TN, Nashville:Vanderbilt University Press, pp. 1-16, 1999.
[21]E. J. Candes, Ridgelets: theory and applications, Ph.D. Dissertation, Statistics, Stanford University, 1998.
[22]E. J. Candes, “Monoscale Ridgelets for the Representation of Images with Edges,” Technical Report, Statistics, Stanford University, pp. 1-26, 1999.
[23]E. Candes, L. Demanet, D. Donoho, and L. Ying, “Fast Discrete Curvelet Transforms,” Multiscale Modeling and Simulation, vol. 5, pp. 861-899, 2006.
[24]T. S. Lee, “Image Representation Using 2D Gabor Wavelets,” IEEE Trans. Pattern Anal. and Machine Intell., vol. 18, pp. 959-971, 1996.
[25]R.Verma and R. Pandey, “Non local means Algorithm with Adaptive Isotropic Search Window Size for Image Denoising,” Annual IEEE India Conference, pp. 1-5, 2015.