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In image processing, in order to well preserve corners, peaks, and thin edges of the image, a new biharmonic diffusion model is established, which takes into account the stress balance of the biharmonic equation and local maximum values of higher-order partial derivatives. If the noise is very strong in the image, some isolated spots will leave on the processed image, and texture of the image has statistical properties in a large range, and the new model retains only local details, the information of image in a wide range is not kept well. Further improvement on the above model is made by using the wavelet transform to extract the high frequency part of the image, and by processing this part with stress balance to establish wave field biharmonic diffusion model, which stably controls the image details locally. Analysis and simulation results show that this model retains more image information than the Perona-Mailik model, effectively well preserves the edges, corners, peaks of the image, and also maintains thin edges of the image. So it is an ideal model.
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Keywords:
- biharmonic equation /
- wavelet transform /
- diffusion denoising /
- image denoising
[1] Gonzalez R C, Woods R E (Translated by Ruan Q Q, Ruan Y Z) 2010 Digital Image Processing (3rd Ed.) (Beijing: Publishing House of Electronics Industry) pp197-213 (in Chinese) [冈萨雷斯R C, 伍兹R E 著(阮秋琦, 阮宇智 译) 2010 (第三版)数字图像处理(北京: 电子工业出版社) 第197–213页]
[2] Li Z B, Liu Z Z, Shi W Z 2014 IEEE Geosci. Remote Sens. 11 743
[3] Bumsub H, Dongbo M, Kwanghoon S 2013 IEEE Trans. Image Process. 22 1096
[4] Anastasia S, Petros M 2008 IEEE Trans. Image Process. 17 364
[5] Wang Z, Huang X, Li Y X, Song X N 2013 Chin. Phys. B 22 010504
[6] Wang Z, Huang X, Li Y X, Song X N 2012 Chin. Phys. B 21 050506
[7] Nadernejad E, Nikpour M 2012 Digit. Signal Process. 22 913
[8] Ludusan C, Lavialle O 2012 Pattern Recogn. Lett. 33 1388
[9] Perona P, Malik J 1990 IEEE Trans. Pattern Anal. Mach. Intell. 12 629
[10] Catte F, Lions P L, Morel J M 1992 SIMA J. Math. Anal. 29 182
[11] Zhu L X, Wang P A, Xia D S 2006 J. CAD & CG 18 1519 (in Chinese) [朱立新, 王平安, 夏德深 2006 计算机辅助设计与图形学学报 18 1519]
[12] Xie M H, Yu Z M 2006 Acta Electron. Sin. 34 59 (in Chinese) [谢美华, 于正明 2006 电子学报 34 59]
[13] Chen K 2005 IEEE Trans. Pattern Anal. Mach. Intell. 27 552
[14] Li J C, Ma Z H, Peng Y X, Huang B 2013 Acta Phys. Sin. 62 099501 (in Chinese) [李金才, 马自辉, 彭宇行, 黄斌 2013 物理学报 62 099501]
[15] Zhu L, Han T Q, Shui P L, Wei J H, Gu M H 2014 Acta Phys. Sin. 63 179502 (in Chinese) [朱磊, 韩天琪, 水鹏朗, 卫建华, 顾梅花 2014 物理学报 63 179502]
[16] Donoho D L 1995 IEEE Trans. Inform. Theory 41 613
[17] Liu J H, She K 2011 Acta Phys. Sin. 60 124203 (in Chinese) [刘金华, 佘堃 2011 物理学报 60 124203]
[18] Weickert J, Bary H R, Max A V 1998 IEEE Trans. Image Process. 7 398
[19] Canny J 1986 IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8 679
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[1] Gonzalez R C, Woods R E (Translated by Ruan Q Q, Ruan Y Z) 2010 Digital Image Processing (3rd Ed.) (Beijing: Publishing House of Electronics Industry) pp197-213 (in Chinese) [冈萨雷斯R C, 伍兹R E 著(阮秋琦, 阮宇智 译) 2010 (第三版)数字图像处理(北京: 电子工业出版社) 第197–213页]
[2] Li Z B, Liu Z Z, Shi W Z 2014 IEEE Geosci. Remote Sens. 11 743
[3] Bumsub H, Dongbo M, Kwanghoon S 2013 IEEE Trans. Image Process. 22 1096
[4] Anastasia S, Petros M 2008 IEEE Trans. Image Process. 17 364
[5] Wang Z, Huang X, Li Y X, Song X N 2013 Chin. Phys. B 22 010504
[6] Wang Z, Huang X, Li Y X, Song X N 2012 Chin. Phys. B 21 050506
[7] Nadernejad E, Nikpour M 2012 Digit. Signal Process. 22 913
[8] Ludusan C, Lavialle O 2012 Pattern Recogn. Lett. 33 1388
[9] Perona P, Malik J 1990 IEEE Trans. Pattern Anal. Mach. Intell. 12 629
[10] Catte F, Lions P L, Morel J M 1992 SIMA J. Math. Anal. 29 182
[11] Zhu L X, Wang P A, Xia D S 2006 J. CAD & CG 18 1519 (in Chinese) [朱立新, 王平安, 夏德深 2006 计算机辅助设计与图形学学报 18 1519]
[12] Xie M H, Yu Z M 2006 Acta Electron. Sin. 34 59 (in Chinese) [谢美华, 于正明 2006 电子学报 34 59]
[13] Chen K 2005 IEEE Trans. Pattern Anal. Mach. Intell. 27 552
[14] Li J C, Ma Z H, Peng Y X, Huang B 2013 Acta Phys. Sin. 62 099501 (in Chinese) [李金才, 马自辉, 彭宇行, 黄斌 2013 物理学报 62 099501]
[15] Zhu L, Han T Q, Shui P L, Wei J H, Gu M H 2014 Acta Phys. Sin. 63 179502 (in Chinese) [朱磊, 韩天琪, 水鹏朗, 卫建华, 顾梅花 2014 物理学报 63 179502]
[16] Donoho D L 1995 IEEE Trans. Inform. Theory 41 613
[17] Liu J H, She K 2011 Acta Phys. Sin. 60 124203 (in Chinese) [刘金华, 佘堃 2011 物理学报 60 124203]
[18] Weickert J, Bary H R, Max A V 1998 IEEE Trans. Image Process. 7 398
[19] Canny J 1986 IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8 679
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