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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.
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Keywords:
- image diffusion filtering /
- nonlinear-diffusion /
- wave atoms /
- dual tree complex wavelet transform
[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
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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
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