若干分类字典下形态分量分析算法与图像修补应用研究
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摘要
近年来,伴随着图像处理技术的迅猛发展,利用图像的不同形态成分(如平滑成分、边缘、纹理等)来进行自适应图像分解已成为很多图像处理任务,如图像压缩、重构、去噪、修补和特征提取等的研究热点。本文系统综述了图像形态分量分析(Morphological Component Analysis:MCA)的研究现状,详细介绍了MCA的基本框架、系统模型等关键概念,依据Meyer的卡通纹理图像模型和图像超完备稀疏表示基础理论,设计对应于图像不同形态成分的过完备稀疏表示分类字典,探索了基于Gabor感知函数的过完备稀疏表示分类字典的图像形态分量分析问题、数值算法实现及在图像修补领域的应用。
本文的主要创新点包括：
首先,基于图像超完备稀疏表示模型与追踪算法理论,研究了基于贪婪策略的追踪算法,如匹配追踪算法(MP)及其变种(OMP),树追踪算法(TBP),并对树追踪算法进行改进,设计了基于字典树结构的正交匹配追踪算法(TOBP)。同时结合Gabor感知多成分字典,分别使用MP、OMP、TBP和TOBP对图像进行稀疏分解与重构,并对这四种重构算法的性能进行分析。实验表明TBP和TOBP算法在图像稀疏表示性能上逼近MP算法,同时还很大程度上减小了基于贪婪策略的追踪算法用于图像稀疏分解的计算和时间复杂度。
第二,基于Gabor感知多成分字典与图像MCA分析机理,给出了对应于图像卡通成分和纹理成分的过完备稀疏表示分类子字典的设计,提出了基于Gabor感知函数的过完备稀疏表示分类字典的MCA算法。实验表明,该算法能较好的分离出图像的卡通成分与纹理成分,实现图像的稀疏分解。
第三,基于经典MCA算法的图像修补模型,研究本文第四章提出的MCA算法在图像修补领域的应用,给出了本文的MCA算法用于图像修补的数值实现方案。实验表明,本文的修补方法能较好的同时修补图像的结构部分与纹理部分,较好的恢复图像的信息缺损区。
In recent years,along with the rapid development of image processing technology,using the different components of image(such as smooth components,edge components,texture component etc.) to decomposition image adaptive has become a hotspots of many image processing tasks, such as image compression,reconstruction,denoising,inpainting and feature extraction etc. In this dissertation, an overview of image morphological component analysis research situation was summarized firstly,and the basic framework and system model of image morphological component analysis were described in detail,and then on the basis of the Meyer's catoon-texture image model and the basic theory of the sparse and overcomplete representations of images, designed overcomplete classification dictionaries respond to the sparse representation of the different structural component of the image, explore the problem, numerical algorithm of the image morphological component analysis based on gabor overco-mplete classification dictionaries, and the application of it in image restoration areas.
The primary contributions of this dissertation contain the following points:
Firstly, based on the mode of the sparse and overcomplete representations of images and the theory of the pursuit algorithm, it researches the pursuit algorithm based on the greedy strategy,such as matching pursuit(MP),orthogonal matching pursuit(OMP),tree based pursuit (TBP)etc. and also designs the tree orthogonal based prusuit(TOBP) algorithm. At the same time, based on the multi-component Gabor perception dictionary, it decomposes image sapr-sely and reconstruction with MP, OMP, TBP and TOBP respectively, and then analysis the efficiency of these four algorithms.
Secondly, based on the multi-component Gabor perception dictionary and the mechanism of the image morphological component analysis, it designed overcomplete classification dic-tionaries respond to the cartoon and texture component of the image. An algorithm of the image morphological component analysis based on gabor overcomplete classification diction-naries was proposed. Experiments show that this algorithm could easily decompose the image into cartoon and texture component.
Thirdly, based on the image inpainting mode of the classical MCA algorithm, it researches and achieves the numerical implementation method of the image inpainting based on the MCA algorithm proposed in these paper. And Experiments show that my algorithm can simutaneously fills in the missing information well which contains the cartoon and texture component.
本文的主要创新点包括：
首先,基于图像超完备稀疏表示模型与追踪算法理论,研究了基于贪婪策略的追踪算法,如匹配追踪算法(MP)及其变种(OMP),树追踪算法(TBP),并对树追踪算法进行改进,设计了基于字典树结构的正交匹配追踪算法(TOBP)。同时结合Gabor感知多成分字典,分别使用MP、OMP、TBP和TOBP对图像进行稀疏分解与重构,并对这四种重构算法的性能进行分析。实验表明TBP和TOBP算法在图像稀疏表示性能上逼近MP算法,同时还很大程度上减小了基于贪婪策略的追踪算法用于图像稀疏分解的计算和时间复杂度。
第二,基于Gabor感知多成分字典与图像MCA分析机理,给出了对应于图像卡通成分和纹理成分的过完备稀疏表示分类子字典的设计,提出了基于Gabor感知函数的过完备稀疏表示分类字典的MCA算法。实验表明,该算法能较好的分离出图像的卡通成分与纹理成分,实现图像的稀疏分解。
第三,基于经典MCA算法的图像修补模型,研究本文第四章提出的MCA算法在图像修补领域的应用,给出了本文的MCA算法用于图像修补的数值实现方案。实验表明,本文的修补方法能较好的同时修补图像的结构部分与纹理部分,较好的恢复图像的信息缺损区。
In recent years,along with the rapid development of image processing technology,using the different components of image(such as smooth components,edge components,texture component etc.) to decomposition image adaptive has become a hotspots of many image processing tasks, such as image compression,reconstruction,denoising,inpainting and feature extraction etc. In this dissertation, an overview of image morphological component analysis research situation was summarized firstly,and the basic framework and system model of image morphological component analysis were described in detail,and then on the basis of the Meyer's catoon-texture image model and the basic theory of the sparse and overcomplete representations of images, designed overcomplete classification dictionaries respond to the sparse representation of the different structural component of the image, explore the problem, numerical algorithm of the image morphological component analysis based on gabor overco-mplete classification dictionaries, and the application of it in image restoration areas.
The primary contributions of this dissertation contain the following points:
Firstly, based on the mode of the sparse and overcomplete representations of images and the theory of the pursuit algorithm, it researches the pursuit algorithm based on the greedy strategy,such as matching pursuit(MP),orthogonal matching pursuit(OMP),tree based pursuit (TBP)etc. and also designs the tree orthogonal based prusuit(TOBP) algorithm. At the same time, based on the multi-component Gabor perception dictionary, it decomposes image sapr-sely and reconstruction with MP, OMP, TBP and TOBP respectively, and then analysis the efficiency of these four algorithms.
Secondly, based on the multi-component Gabor perception dictionary and the mechanism of the image morphological component analysis, it designed overcomplete classification dic-tionaries respond to the cartoon and texture component of the image. An algorithm of the image morphological component analysis based on gabor overcomplete classification diction-naries was proposed. Experiments show that this algorithm could easily decompose the image into cartoon and texture component.
Thirdly, based on the image inpainting mode of the classical MCA algorithm, it researches and achieves the numerical implementation method of the image inpainting based on the MCA algorithm proposed in these paper. And Experiments show that my algorithm can simutaneously fills in the missing information well which contains the cartoon and texture component.
引文
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[2]M. Zibulevsky, B. Pearlmutter. Blind source separation by sparse decomposition in a signal dictionary[J]. Neural Computation,2001,13(4):863-882
[3]J. L. Starck, M. Elad, D. L. Donoho. Redundant multiscale transforms and their applicati-on for morphological component analysis [J]. Advances in Imaging and Electron Physics, 2004,132(82):287-348
[4]崔雪红.基于偏微分方程的图像修复[D].青岛.青岛大学.2009
[5]刘盛朋.基于Contourlet变换的图像稀疏分量分析[D].上海.上海大学.2007
[6]J. L. Starck, M. Elad, D. L. Donoho. Image decomposition via the combination of sparse representation and a variational approach[J]. IEEE Transaction on Image Processing, 2005,14(10):1570-1582
[7]J. L. Starck, E. Candes, D. L. Donoho. Astronomical image representation by the curvelet transform[J]. Astronomy and Astrophysics,2003,398(2):785-800
[8]李映,张艳宁,许星.基于信号稀疏表示的形态成分分析：进展和展望[J].电子学报,2009,37(1)：146-152
[9]董卫军.基于小波变换的图像处理技术研究[D].西安.西北大学.2006
[10]杨维.非线性小波变换与多尺度在图像、信号处理中的应用研究[D].西安.西北电子科技大学.2005
[11]靳士利,赵志刚.基于非抽样小波的多阈值去噪[J].青岛大学学报(自然科学版),2009,22(4)：77-81
[12]赵志刚,管聪慧,吕慧显.基于非抽样小波和边缘保持的自适应图像降噪[J].电子·激光,2007,18(11)：1374-1377
[13]M. Holschneider, R. Kronland-Martinet, J. Morlet, P. Tchamitchian.Wavelets Time-Frequency Methods and Phase Space,chapter A Real-Time Algorithm for Signal Analy-sis with the Help of the Wavelet Transfrom[C]. Springer-Verlag,Berlin,1989:289-297
[14]D. L. Donoho, X. Huo. Uncertainty principles and ideal atomic decomposition[J]. IEEE Transactions on Information Theory,2001,47(7):2845-2862
[15]张莉.基于对偶复小波的图像处理研究[D].西安.陕西师范大学.2006
[16]S Mallat. Characterization of Signals from Multiscale Edges [J]. IEEE Transactions on Pattern Analysis and Machine intelligence,1992,7(14):710-732
[17]J. J. Fuchs. On sparse representations in arbitrary redundant bases[J]. IEEE Transactions on Information Theory,2004,50(6):1341-1344
[18]E. J. Candes. Ridgelet:theory and application[D]. Department of Statistics Stanford Un-iversity.1998
[19]S. Mallat.信号处理中的小波导引[M].北京：机械工业出版社,2002
[20]E. J. Candes. Monoscale Ridgelet for the representation of images with edges[R]. Depa-rtment of Statistics, Stanford University, Stanford, CA,1999
[21]E. J. Candes, D. L. Donoho. Curvelets:a surprisingly effective on adaptive represent-tation for objects with edges[C]. Nashville,TN:Vanderbilt University Press,2000:105-120
[22]R Gribonval, M Nielsen. Sparse representation in unions of bases[J]. IEEE Transactions on Information Theory,2003,49(12):3320-3325
[23]E. J. Candes, L. Demanet, D. Donoho. Fast discrete curvelet transforms[R]. Pasadena, California:California institute of Technology.2005
[24]M. N. Do, M. Vetterli. The Contourlet Transform:An Efficient Directional Multiresolu-tion Image Representation[J]. IEEE Transactions On Image Processing,2005,14(12): 2091-2106
[25]J. S. DeBonet. Multiresolution sampling procedure for analysis and synthesis of texture images[C]. Proceedings of Siggraph. Los Angeles, USA,1997:361-368
[26]A. M. Bruckstein, M. Elad. A generalized uncertainty principle and sparse representati-on in pairs of rn bases[J]. IEEE Transactions on Information Theory,2002,48(11):2558-2567
[27]徐晨,赵瑞珍,甘小冰.小波分析与算法应用[M].北京：科学出版社,2004：64-87
[28]G.Steidl, J. Weickert, T. Brox, P. Mrzek, and M Welk. On the equivalence of soft wave-let shrinkage, total variation diffusion, total variation regularization, and sides[J]. SIAM Journal on Numerical Analysis,2004,42(2):686-713
[29]Mallat S, Zhang Z. Matching pursuits with time-frequency diction-Aries[J]. IEEE Trans Signal Process,1993,41(12):3397-3415
[30]徐贵力,毛罕.利用傅里叶变换提取图像纹理特征新方法[J].广电工程,2004,31(11)：55-58
[31]王耀南,李树涛,毛建旭.计算机图像处理与识别技术[M].北京：高等教育出版社,2001
[32]D. Donoho, M. Elad. Maximal sparsity representation via 11 minimization[A]. Proceedi-ngs of the National Academy of Science[C], USA,2003:2197-2202
[33]Y. C. Pati, R. Rezaiifar, P. S. Krishnaprasad. Orthogonal matching pursuit:Recursive function approximation with applications to wavelet decomposition[A]. In Proceeding of the 27th Annual Asilomar Conference in Signals, Systems,and Computers[C], LosAlami-tos:IEEE,1993:40-44
[34]Philippe Jost, Pierre Vandergheynst. Tree-Based Pursuit:Algorithm and Properties[J]. IEEE Transactions on signal processing,2006,54(12):4685-4697
[35]孙玉宝,肖亮,韦志辉,邵文泽.基于Gabor感知多成份字典的图像稀疏表示算法研究[J].自动化学报,2008,11(34)：1379-1387
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