一种双正则项各向异性扩散的纹理去噪模型研究

计算机科学 ›› 2013, Vol. 40 ›› Issue (6): 295-299.

一种双正则项各向异性扩散的纹理去噪模型研究

李晓宁,龚家强,幸浩洋

四川师范大学计算机科学学院成都610101;四川师范大学计算机科学学院成都610101;四川大学物理科学与技术学院成都610064

出版日期:2018-11-16 发布日期:2018-11-16
基金资助:
本文受国家自然科学基金(81171339),四川省科技厅苗子工程项目(2011-053),四川师范大学科研创新基金(2011-022)资助

Noise Reduction Algorithm for Texture Images Using Anisotropic Diffusion with Double-regularing Terms

LI Xiao-ning,GONG Jia-qiang and XING Hao-yang

Online:2018-11-16 Published:2018-11-16

摘要/Abstract

摘要： 为了有效滤除图像噪声,同时最大限度地保留图像纹理和边缘等细节信息,将多尺度几何分析方法和各向异性扩散模型结合,构建了一种采用双正则项各向异性扩散的反应扩散方程,并完成了目标函数的离散及其数值解收敛性证明。目标函数定义为以波原子、曲波变换后邻域内梯度值为参数的扩散控制函数,使扩散在图像信息丰富的纹理和边缘区域减弱,并通过反应项对扩散进行调节,以得到更好的平滑效果。实验结果证明,该方法较传统的反应扩散模型不仅能提高图像的信噪比,而且可以更好地保留图像边缘和纹理等细节信息。

关键词: 纹理去噪,扩散控制函数,双正则项,反应扩散方程

Abstract: Important information,such as textures or edges,is often lost or blurred in the process of smoothing algorithm based on P-M Anisotropic Diffusion．We defined a new diffusivity operator which is used to control the velocity of the diffusion and proposed a reaction-diffusion equation with double-regularizing terms to overcome this defect,besides,we analysed and verified the model’s convergence．The diffusivity operator relies on the change rules of gradient in a neighborhood to weaken the diffusion intensity in texture or edge regions．Two forcing terms were used to regulate diffusion and maintain edges,boundaries and texture．Experiment results and comparisons show the good performance of the proposed method for texture and edge preserving in the process of denoising,and demonstrate the proposed algorithm is feasible and applicable．

Key words: Texture denoising,Diffusivity operator,Double-regularing terms,Reaction-diffusion equation

李晓宁,龚家强,幸浩洋. 一种双正则项各向异性扩散的纹理去噪模型研究[J]. 计算机科学, 2013, 40(6): 295-299. https://doi.org/

LI Xiao-ning,GONG Jia-qiang and XING Hao-yang. Noise Reduction Algorithm for Texture Images Using Anisotropic Diffusion with Double-regularing Terms[J]. Computer Science, 2013, 40(6): 295-299. https://doi.org/

参考文献

[1] Chan T F,Osher S,Shen J．The digital TV filter and nonlinear denoising [J]．IEEE Transactions on Image Processing,2001,0(2):231-241
[2] Vese L,Osher S．Modeling textures with total variation minimization and oscillating patterns in image processing [J]．J．Sci．Comput,2003,9(1-3):553-572
[3] Weickert J．Anisotropic diffusion in image processing[M]．Stuttgart:B．G．Teubner-Verlag,1998
[4] 王志明,张丽．自适应的快速非局部图像去噪算法[J]．中国图象图形学报,2009,14(4):1-7
[5] Buades A,Morel J M．A non-local algorithm for image denoising [C]∥Proceeding of IEEE Computer Society Conference on Pattern Recognition．San Diego,CA,USA,2005:60-65
[6] 刘芳,刘文学,焦李成．基于复小波邻域隐马尔科夫模型的图像去噪 [J]．电子学报,2005,3(7):1284-1287
[7] Donoho D L．Adaptive wavelet threshold for image denoising [J]．Electronics Letters,2005,41(10):586-587
[8] 刘镇弢,李涛,杜慧敏,等．基于context模型的contourlet域图像去噪[J]．计算机科学,2012,9(3):243-245
[9] Plonka G．A digital diffusion-reaction type filter for nonlinear denoising [J]．Results Math,2009,53(3/4):371-381
[10] de O Casaca W C,Boaventura M．A Regularized Nonlinear Diffusion Approach for Texture Image Denoising [C]∥XXII Brazilian Symposium on Computer Graphics and Image Processing．2009:1-5
[11] Plonka G,Ma J．Nonlinear regularized reaction-diffusion filters for denoising of images with textures [J]．IEEE Transactions on Image Processing,2008,7(2):1283-1294
[12] Ma Jian-wei,Plonka G．Combined Curvelet Shrinkage and Nonlinear Anisotropic Diusion[J]．IEEE Transactions on Image Processing,2007,6(9):2198-2206
[13] 隆刚,肖磊,陈学佺．Curvelet变换在图像处理中的应用综述[J]．计算机研究与发展,2005,2(8):1331-1337
[14] Demanet L,Ying L．Wave atoms and sparsity of oscillatory patterns [J]．Appl．Comput．Harmon．Anal,2007,3(3):368-387
[15] 宋宜美,宋国乡．结合波原子和Cycle Spinning的图像去噪 [J]．西安电子科技大学学报:自然科学版,2010,7(2):1-2

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