基于局部竞争机制的图像稀疏表示方法研究
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摘要
寻求客观事物的“稀疏”表示方法一直是机器视觉、数据压缩等领域专家学者致力于研究的目标。由于图像稀疏表示的优良特性,目前针对图像的稀疏表示已经发展了多种算法。图像的稀疏表示也已经成功应用于图像的压缩、去噪、识别等。由于图像的稀疏表示在图像处理中的成功应用,已经引起越来越多研究人员的重视,形成对图像稀疏分解研究的热潮。
对于分段光滑信号,小波提供了一种非常简单而有效的表示方法,然而传统意义上的小波变换在高维情况下并不是最优的或者说是“最稀疏”的函数表示方法。过完备多分辨率变换能够充分利用函数本身信息,对特定的函数类达到最优逼近。不同的变换各自适合表示不同的图像特征,这给图像稀疏表示提供了更有力的理论和方法。此外,生物视觉系统的发展和进化与其感知的外界环境(自然图像)密切相关。实验表明,自然图像的非高斯统计特性与神经元的稀疏编码方式相对应。
首先,本文提出利用过完备多分辨率变换并结合视觉特性的图像稀疏表示方法。该算法用双树复数小波模拟视觉皮层简单细胞的感受野,结合相邻细胞间抑制和增强特性,用局部竞争抑制的方法从变换系数中选取少量系数稀疏表示图像。实验结果表明,其重构图像的效果较其它方法有明显的改善。
其次,本文根据Marr初级视觉理论,在一种能够从多尺度描述一幅图像的一种新的复数小波——Marr-like小波金字塔以及一种新的适应性Harr小波变换——Tetrolet变换的基础上,提出将Marr-like小波金字塔分解与Tetrolet相结合的图像稀疏表示方法。数值实验表明该算法能够更好的匹配图像的几何特征,具有更好的可控性和图像重构效果。
In the fields of machine vision and data compression, seeking for the“sparse”representation of the objective things has been the domain to which the experts and scholars devoted. Nowadays, due to the excellent characteristics of image sparse representation, numerous algorithms have been developed. As a result of the successful application of sparse representation of images in image compression, denoising, recognition, etc. an increasing number of researchers begin to attach importance to this field and form a new upsurge.
For a piecewise smooth signal, wavelet provides a very simple and effective method. However, in high-dimension circumstances, conventional wavelet transform is not the optimal or the“most sparse”representation of functions. Overcomplete multiresolution transform could take full advantage of the information, which is contained in the function itself, and achieve the optimal approximation to the specific functions. Different transforms are appropriate for describing diversified characteristics of images, which provide powerful theories and methods for sparse representation of images. In addition, the development and evolution of biological visual system is closely related to the perceived external environment (natural images). Experiments have indicated that non-gaussian statistical properties of natural images have some correspondence with the sparse coding methods of neurons.
Firstly, a sparse representation scheme of images which is inspired from overcomplete multiresolution transforms combined with visual characteristic, is proposed. The algorithm models simple cell receptive fields through Dual-Tree Complex Wavelets. The model also incorporates inhibition and facilitation interactions between neighboring cells to choose a number of coefficients of transformation to achieve the sparse representation of initial images by utilizing the local competition and inhibition method. The experiment results show that the proposed scheme outperforms others.
Secondly, according to Marr’s theory of preliminary vision, based on a new kind of complex wavelet—Marr-like wavelet, which could describe an image from multiscales, and a novel adaptive Harr-type wavelet transform—Tetrolet, we propose a new method for sparse representation of images which combines the two methods mentioned above. Numerical results show this method is capable of matching the geometrical characteristics of images and has better steerability as well as reconstruction result.
对于分段光滑信号,小波提供了一种非常简单而有效的表示方法,然而传统意义上的小波变换在高维情况下并不是最优的或者说是“最稀疏”的函数表示方法。过完备多分辨率变换能够充分利用函数本身信息,对特定的函数类达到最优逼近。不同的变换各自适合表示不同的图像特征,这给图像稀疏表示提供了更有力的理论和方法。此外,生物视觉系统的发展和进化与其感知的外界环境(自然图像)密切相关。实验表明,自然图像的非高斯统计特性与神经元的稀疏编码方式相对应。
首先,本文提出利用过完备多分辨率变换并结合视觉特性的图像稀疏表示方法。该算法用双树复数小波模拟视觉皮层简单细胞的感受野,结合相邻细胞间抑制和增强特性,用局部竞争抑制的方法从变换系数中选取少量系数稀疏表示图像。实验结果表明,其重构图像的效果较其它方法有明显的改善。
其次,本文根据Marr初级视觉理论,在一种能够从多尺度描述一幅图像的一种新的复数小波——Marr-like小波金字塔以及一种新的适应性Harr小波变换——Tetrolet变换的基础上,提出将Marr-like小波金字塔分解与Tetrolet相结合的图像稀疏表示方法。数值实验表明该算法能够更好的匹配图像的几何特征,具有更好的可控性和图像重构效果。
In the fields of machine vision and data compression, seeking for the“sparse”representation of the objective things has been the domain to which the experts and scholars devoted. Nowadays, due to the excellent characteristics of image sparse representation, numerous algorithms have been developed. As a result of the successful application of sparse representation of images in image compression, denoising, recognition, etc. an increasing number of researchers begin to attach importance to this field and form a new upsurge.
For a piecewise smooth signal, wavelet provides a very simple and effective method. However, in high-dimension circumstances, conventional wavelet transform is not the optimal or the“most sparse”representation of functions. Overcomplete multiresolution transform could take full advantage of the information, which is contained in the function itself, and achieve the optimal approximation to the specific functions. Different transforms are appropriate for describing diversified characteristics of images, which provide powerful theories and methods for sparse representation of images. In addition, the development and evolution of biological visual system is closely related to the perceived external environment (natural images). Experiments have indicated that non-gaussian statistical properties of natural images have some correspondence with the sparse coding methods of neurons.
Firstly, a sparse representation scheme of images which is inspired from overcomplete multiresolution transforms combined with visual characteristic, is proposed. The algorithm models simple cell receptive fields through Dual-Tree Complex Wavelets. The model also incorporates inhibition and facilitation interactions between neighboring cells to choose a number of coefficients of transformation to achieve the sparse representation of initial images by utilizing the local competition and inhibition method. The experiment results show that the proposed scheme outperforms others.
Secondly, according to Marr’s theory of preliminary vision, based on a new kind of complex wavelet—Marr-like wavelet, which could describe an image from multiscales, and a novel adaptive Harr-type wavelet transform—Tetrolet, we propose a new method for sparse representation of images which combines the two methods mentioned above. Numerical results show this method is capable of matching the geometrical characteristics of images and has better steerability as well as reconstruction result.
引文
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5焦李成,侯彪,王爽,等.图像多尺度几何分析理论与应用.西安:西安电子科技大学出版社, 2008:3-22
6 E. J. Candes, D. L. Donoho. New Tight Frames of Curvelets and Optimal Representations of Objects with Piecewise C 2 Singularities. Communications on Pure and Applied Mathematics, 2004,57(2):219-266
7 M. N. Do, M. Vetterli. The Contourlet Transform: an Efficient Directional Multiresolution Image Representation. IEEE Transactions on Image Processing, 2005,14(12):2091-2106
8 E. Le Pennec, S. Mallat. Sparse Geometric Image Representations with Bandelets. IEEE Transactions on Image Processing, 2005,14(4):423-438
9 Y. Tomokusa, M. Nakashizuka, Y. Iiguni. Sparse Image Representation with Shift and Rotation Invariance Constraints. Intelligent Signal Processing and Communication Systems, 2009:256-259
10 S. Mallat, Z. Zhang. Matching Pursuits with Time-frequency Dictionaries. IEEE Transactions on Signal Processing, 1993,41(12):3397-3415
11 F. Bergeau, S. Mallat. Matching Pursuit of Images. Proceedings of IEEE InternationalConference on Image Processing, 1995,1:53-56
12 R. Coifman, M. Wickerhauser. Entropy-Based Algorithms for Best Basis Selection. IEEE Transactions on Information Theory, 1992,38(2):713-718
13 B. Olshausen, D. Field. Learning Efficient Linear Codes for Natural Images: the Roles of Sparseness, Overcompleteness, and Statistical Independence. Proceedings of SPIE, 1996,2657:132-138
14 M. Nakashizuka, H. Nishiura, Y. Iiguni. Sparse Image Representations with Shift-Invariant Tree-Structured Dictionaries. IEEE International Conference on Image Processing, 2009:2145-2148
15 P. Vandergheynst, P. Frossard. Efficient Image Representation by Anistropic Refinement in Matching Pursuit. Proceedings of IEEE on ICASSP, 2001, 5(3):1757-1760
16 R. Gribonval, M. Nielsen. Sparse Decompositions in‘Incoherent’Dictionaries. Proceedings of IEEE ICIP, 2003:33-36
17 S. Chen, D. Donoho, M. Sauners. Atomic Decomposition by Basis Pursuit. SIAM REVIEW, 2001,43(1):129-159
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22 R. Neff, A. Zakhor. Very Low Bit-Rate Video Coding Based on Matching Pursuits.IEEE Transactions on Circuits and Systems for Video Technology, 1997,7(1):158-171
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24 D. L. Donoho. Wedgelets: Nearly Minimax Estimation of Edges. The Annals of Statistics, 1999,27(3):859-897
25 V. Velisavljevic, B. Beferull-Lozano, M. Vetterli, et al. Directionlets: Anisotropic Multi-Directional Representation with Separable Filtering. IEEE Transactions on Image Processing, 2006,17(7):1916-1933
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2 M. Elad, M. A. T. Figueiredo, Y. Ma. On the Role of Sparse and Redundant Representations in Image Processing. Proceedings of IEEE, 2010,(99):1-11
3 S. Samadi, M. Cetin, M. Shirazi. Sparse Signal Representation for Complex-Valued Imaging. Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, 2009:365-370
4 B. Olshausen, D. Field. Emergence of Simple-Cell Receptive Field Properties by Learning a Sparse Code for Natural Images. Nature, 1996,381(6583):607-609
5焦李成,侯彪,王爽,等.图像多尺度几何分析理论与应用.西安:西安电子科技大学出版社, 2008:3-22
6 E. J. Candes, D. L. Donoho. New Tight Frames of Curvelets and Optimal Representations of Objects with Piecewise C 2 Singularities. Communications on Pure and Applied Mathematics, 2004,57(2):219-266
7 M. N. Do, M. Vetterli. The Contourlet Transform: an Efficient Directional Multiresolution Image Representation. IEEE Transactions on Image Processing, 2005,14(12):2091-2106
8 E. Le Pennec, S. Mallat. Sparse Geometric Image Representations with Bandelets. IEEE Transactions on Image Processing, 2005,14(4):423-438
9 Y. Tomokusa, M. Nakashizuka, Y. Iiguni. Sparse Image Representation with Shift and Rotation Invariance Constraints. Intelligent Signal Processing and Communication Systems, 2009:256-259
10 S. Mallat, Z. Zhang. Matching Pursuits with Time-frequency Dictionaries. IEEE Transactions on Signal Processing, 1993,41(12):3397-3415
11 F. Bergeau, S. Mallat. Matching Pursuit of Images. Proceedings of IEEE InternationalConference on Image Processing, 1995,1:53-56
12 R. Coifman, M. Wickerhauser. Entropy-Based Algorithms for Best Basis Selection. IEEE Transactions on Information Theory, 1992,38(2):713-718
13 B. Olshausen, D. Field. Learning Efficient Linear Codes for Natural Images: the Roles of Sparseness, Overcompleteness, and Statistical Independence. Proceedings of SPIE, 1996,2657:132-138
14 M. Nakashizuka, H. Nishiura, Y. Iiguni. Sparse Image Representations with Shift-Invariant Tree-Structured Dictionaries. IEEE International Conference on Image Processing, 2009:2145-2148
15 P. Vandergheynst, P. Frossard. Efficient Image Representation by Anistropic Refinement in Matching Pursuit. Proceedings of IEEE on ICASSP, 2001, 5(3):1757-1760
16 R. Gribonval, M. Nielsen. Sparse Decompositions in‘Incoherent’Dictionaries. Proceedings of IEEE ICIP, 2003:33-36
17 S. Chen, D. Donoho, M. Sauners. Atomic Decomposition by Basis Pursuit. SIAM REVIEW, 2001,43(1):129-159
18 I. Daubechies. Time-frequency Localization Operator: A Geometric Phase Space Approach. IEEE Transactions on Information Theory, 1988,34(4):605-612
19 Y. C. Pati, R. Rezaiifar, P. S. Krishnaprasad. Orthogonal Matching Pursuits: Recursive Function Approximation with Applications to Wavelets Decomposition. Proceedings of the 27th Asilomar Conference in Signals, Systems and Computers, 1993,1:40-44
20 V. Thang Pham, W. M.Arnold Smeulers. Sparse Representation for Coarse and Fine Object Recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006,28(4):555-587
21 P. Frossard, P. Vandergheynst, M. Kunt, et al. A Posteriori Quantization of Progressive Matching Pursuit Streams. IEEE Transactions on Signal Processing, 2004,52(2):525-535
22 R. Neff, A. Zakhor. Very Low Bit-Rate Video Coding Based on Matching Pursuits.IEEE Transactions on Circuits and Systems for Video Technology, 1997,7(1):158-171
23 M. R. I.V. Rosa, P. Vandergheynst, P. Frossard. Low-Rate and Flexible Image Coding with Redundant Representations. IEEE Transactions on Image Processing, 2006,15(3):726-741
24 D. L. Donoho. Wedgelets: Nearly Minimax Estimation of Edges. The Annals of Statistics, 1999,27(3):859-897
25 V. Velisavljevic, B. Beferull-Lozano, M. Vetterli, et al. Directionlets: Anisotropic Multi-Directional Representation with Separable Filtering. IEEE Transactions on Image Processing, 2006,17(7):1916-1933
26 K. Guo, D. Labate. Optimally Sparse Multidimensional Representation Using Shearlets. SIAM Journal on Mathematical Analysis, 2007,39(1):298-318
27 A. J. Bell, T. J. Sejnowksi. An Information-Maximization Approach to Blind Seperation and Blind Deconvolution. Neural Computation, 1995,7(6):1129-1159
28 M. Lewicki, T. J. Sejnowksi. Learning Overcomplete Representation. Neural Computation, 2000,12(2):337-365
29 M. Lewicki, B. A. Olshausen. Inferring Sparse, Overcomplete Image Codes Using an Efficient Coding Framework. In Proceedings of the 1997 Conference on Advances in Neural Information Processing Systems, 1997:815-821
30 L. K. Jones. A Simple Lemma on Greedy Approximation in Hilbert Space and Convergence Rates for Projection Pursuit Regression and Neural Network Training. Annals of Statistics, 1992,20(1):608-613
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