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基于双树复小波与波原子的图像扩散滤波

刘金华 佘堃

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基于双树复小波与波原子的图像扩散滤波

刘金华, 佘堃

Image diffusion filtering based on dual tree complex wavelet and wave atoms

Liu Jin-Hua, She Kun
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  • 图像的非线性扩散滤波来源于热方程的思想,其关键在于计算适当的扩散系数和控制扩散方向. 在已有的扩散模型中,由于扩散系数仅依赖于图像的梯度,因而这类模型容易受噪声的干扰;同时,图像的细节信息(如纹理)容易被误认为是噪声而被去除. 为克服这些不足,首先给出了一种采用双树复小波变换计算扩散系数的方法;然后设计了一种用于图像滤波的非线性扩散模型,最后提出了基于双树复小波变换和波原子阈值相结合的图像滤波算法. 仿真结果表明,所提出的算法在对含噪图像滤波的同时,能够较好地保持图像的边缘和纹理等细节信息.
    The nonlinear diffusion of image filtering is from the idea of heat equations. Its key point is to choose a proper diffusion coefficient and control the diffusion direction. In the previous models, the diffusivity depends on the gradients of images, thus it is easily affected by noises. Furthermore, many fine structures such as textures are prone to being taken for noise and then will be removed. In order to overcome these shortcomings, first, in this paper we introduce a novel computational technique for diffusivity by using the dual tree complex wavelet transform. Second, we develop a nonlinear diffusion model for image filtering. Finally, an image diffusion filtering method based on the dual tree complex wavelet transform and wave atoms thresholding is presented, and also compared with the previous methods. Experimental results show that many features of image such as edges and textures can be preserved well after filtering via the proposed algorithm.
    • 基金项目: 国家自然科学基金(批准号:60873185, 60903074)和国家高技术研究发展计划(批准号:2008AA04A107)资助的课题
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    Fu M J, Zhuang J J, Hou F Z, Ning X B, Zhan Q B, Shao Y 2010 Acta Phys. Sin. 59 4343 (in Chinese) [符懋敬、庄建军、侯凤贞、宁新宝、展庆波、邵 毅 2010 物理学报 59 4343]

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    Chen S G, Ji S Y, Liu W S 2008 Acta Phys. Sin. 57 2882 (in Chinese)[陈世国、吉世印、刘万松 2008 物理学报 57 2882]

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    Ren L, Chen X G, Liu C T 2009 Acta Phys. Sin. 58 2035 (in Chinese) [任 磊、陈祥光、刘春涛 2009 物理学报 58 2035]

    [20]

    Zhao W S, He Y G 2009 Acta Phys. Sin. 58 843 (in Chinese)[赵文山、何怡刚 2009 物理学报 58 843]

    [21]
    [22]

    Donoho D L 1995 IEEE Trans. Inform. Theory 41 613

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    Selesnick I W, Baraniuk R G, Kingsbury N G 2005 IEEE Signal Proces. Mag. 22 123

    [26]

    Do M N,Vetterli M 2005 IEEE Trans. Image Proces. 14 2091

    [27]
    [28]

    Guo K, Labate D 2007 SIAM J Math. Anal. 39 298

    [29]
    [30]
    [31]

    Demanet L, Ying L X 2007 Appl. Comput. Harmon. Anal. 23 368

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    Plonka G, Ma J W 2008 IEEE Trans. Image. Proces. 17 1283

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    Jiao L C, Hou B, Wang S, Liu F 2008 Image Multiscale Analysis: Theory and Applications (Xi'an:Xi'dian University Press) p36 (in Chinese)[焦李成、侯 彪、王 爽、刘 芳 2008 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) 第36页]

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    Voci F, Eiho S, Sugimoto N, Sekiguchi H 2004 IEEE Signal Proces. Mag. 21 39

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  • [1]

    Kong L H, Xun Z D 2009 Acta Math. Sci. A 29 1771 (in Chinese) [孔令海、郇中丹 2009 数学物理学报 A 29 1771]

    [2]
    [3]

    Kong X L, Li Y T, Yuan X H, Yu Q Z, Zheng Z Y, Liang W X, Wang Z H, Wei Z Y, Zhang J 2006 Acta Phys. Sin. 55 2364 (in Chinese) [孔祥龙、李玉同、远晓辉、于全芝、郑志远、梁文锡、王兆华、魏志义、张 杰 2006物理学报 55 2364]

    [4]
    [5]

    Luo L, Wang L, Cheng W D, Shen M Z 2006 Acta Phys. Sin. 55 6708 (in Chinese) [罗 林、王 黎、程卫东、沈忙作 2006 物理学报 55 6708]

    [6]

    Perona P, Malik J 1990 IEEE Trans. Pattern Anal. Mach. Intell. 12 629

    [7]
    [8]
    [9]

    Catt F, Lions P L, Morel J M, Coll T 1992 SIAM J. Numer. Anal. 29 182

    [10]
    [11]

    Liu F 2006 Sci. China F 49 494

    [12]
    [13]

    Fu M J, Zhuang J J, Hou F Z, Ning X B, Zhan Q B, Shao Y 2010 Acta Phys. Sin. 59 4343 (in Chinese) [符懋敬、庄建军、侯凤贞、宁新宝、展庆波、邵 毅 2010 物理学报 59 4343]

    [14]

    Chen S G, Ji S Y, Liu W S 2008 Acta Phys. Sin. 57 2882 (in Chinese)[陈世国、吉世印、刘万松 2008 物理学报 57 2882]

    [15]
    [16]

    Wang K, Zhang H, Chang S J, Shen J Y 2007 Acta Phys. Sin. 56 3613 (in Chinese) [王 凯、张 会、常胜江、申金媛 2007 物理学报 56 3613]

    [17]
    [18]
    [19]

    Ren L, Chen X G, Liu C T 2009 Acta Phys. Sin. 58 2035 (in Chinese) [任 磊、陈祥光、刘春涛 2009 物理学报 58 2035]

    [20]

    Zhao W S, He Y G 2009 Acta Phys. Sin. 58 843 (in Chinese)[赵文山、何怡刚 2009 物理学报 58 843]

    [21]
    [22]

    Donoho D L 1995 IEEE Trans. Inform. Theory 41 613

    [23]
    [24]
    [25]

    Selesnick I W, Baraniuk R G, Kingsbury N G 2005 IEEE Signal Proces. Mag. 22 123

    [26]

    Do M N,Vetterli M 2005 IEEE Trans. Image Proces. 14 2091

    [27]
    [28]

    Guo K, Labate D 2007 SIAM J Math. Anal. 39 298

    [29]
    [30]
    [31]

    Demanet L, Ying L X 2007 Appl. Comput. Harmon. Anal. 23 368

    [32]

    Plonka G, Ma J W 2008 IEEE Trans. Image. Proces. 17 1283

    [33]
    [34]

    Jiao L C, Hou B, Wang S, Liu F 2008 Image Multiscale Analysis: Theory and Applications (Xi'an:Xi'dian University Press) p36 (in Chinese)[焦李成、侯 彪、王 爽、刘 芳 2008 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) 第36页]

    [35]
    [36]

    Voci F, Eiho S, Sugimoto N, Sekiguchi H 2004 IEEE Signal Proces. Mag. 21 39

    [37]
    [38]
    [39]

    Wang Z, Bovik A C, Sheikh H R, Simoncelli E P 2004 IEEE Trans. Image Proces. 13 600

计量
  • 文章访问数:  5909
  • PDF下载量:  896
  • 被引次数: 0
出版历程
  • 收稿日期:  2010-12-06
  • 修回日期:  2011-08-12
  • 刊出日期:  2011-06-05

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