基于SURE无偏估计自适应字典学习图像去噪算法
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摘要
要针对以往图像去噪算法存在阈值选取仍是经验值,而非函数最优解,缺乏系统化的理论方法等问题,因此提出基于SURE无偏估计的自适应字典学习图像去噪算法.首先通过第二代Bandelet变换获得最优的几何方向,运用四叉树计算最佳几何流,从而得到Bandelet图像块,然后运用SURE无偏估计自动获得全局最优解,最后运用KSVD来训练字典,获得图像块相对应的字典.实验结果表明运用SURE无偏估计进行阈值选取,使目标函数连续可微易求导,针对平滑图像很好的去除了大量伪边缘和"块效应",使图像的连通性更加明显.
In view of the previous image denoising algorithm,the threshold selection is still the empirical value,not the function optimal solution,and the lack of systematic theoretical methods.Therefore,an adaptive dictionary learning image denoising algorithm based on SURE unbiased estimation is proposed.Firstly,the second-generation Bandelet transform can adaptively select the optimal geometric direction,and the quadratic tree segmentation is used to calculate the optimal geometric flow to obtain the Bandelet image block.Then the SURE unbiased risk estimate is used to automatically obtain the global optimal solution.Finally,the global optimal solution is obtained.K-SVD trains the dictionary and obtains a dictionary corresponding to the image block.The experimental results show that the Stein-unbiased risk estimator is used to select the threshold,so that the objective function can be easily derivable.A large number of pseudo-edges and "blockiness"are well removed for smooth images,which makes the image connectivity more obvious.
In view of the previous image denoising algorithm,the threshold selection is still the empirical value,not the function optimal solution,and the lack of systematic theoretical methods.Therefore,an adaptive dictionary learning image denoising algorithm based on SURE unbiased estimation is proposed.Firstly,the second-generation Bandelet transform can adaptively select the optimal geometric direction,and the quadratic tree segmentation is used to calculate the optimal geometric flow to obtain the Bandelet image block.Then the SURE unbiased risk estimate is used to automatically obtain the global optimal solution.Finally,the global optimal solution is obtained.K-SVD trains the dictionary and obtains a dictionary corresponding to the image block.The experimental results show that the Stein-unbiased risk estimator is used to select the threshold,so that the objective function can be easily derivable.A large number of pseudo-edges and "blockiness"are well removed for smooth images,which makes the image connectivity more obvious.
引文
[1]王芳,鲁顺昌.小波软硬阈值去噪算法的研究及改进[J].信息技术,2008(6):124-127.
[2]SHI L L,WANG M.Application of locally adaptive wavelet domain denosing to X-Ray image processing[J].Nuclear Electronics&Detection Technology,2011,31(4):455-458.
[3]KANG X,STAMM,MATTEW C,et al.Robust median filtering forensics using an autoregressive mode[J].IEEE Transactions on Information Forensics&security,2013,8(9):1456-1468.
[4]LIANG M,DU J.Self-adaptive spatial image denoising model based on scale correlation and SURE-LET in the nonsubsampled contourlet transform domain[J].Science China(Information Sciences),2014,21(11):8-11.
[5]王文庆,晏婷.基于空间域的图像去噪方法比较研究[J].西安邮电大学学报,2012,17(2):75-79.
[6]刘祝华.图像去噪方法的研究[D].南昌:江西师范大学,2005.
[7]侯建华.基于小波及其统计特性的图像去噪方法研究[D].武汉:华中科技大学,2007.
[8]焦李成,孙强.多尺度变换域图像的感知与识别:进展和展望[J].计算机学报,2006,29(2):22-30.
[9]刘志民.基于小波变换的全变分模型的图像去噪[D].合肥:安徽大学,2013.
[10]查宇飞,毕笃彦.基于小波变换的自适应多阈值图像去噪[J].中国图象图形学报,2005,10(5):10-17.
[11]戴维,于盛林,孙栓.基于Contourlet变换自适应阈值的图像去噪算法[J].电子学报,2007,35(10):2-9.
[12]刘成云,陈振学,马于涛.自适应阈值的小波图像去噪[J].光电工程,2007,34(6):4-11.
[13]陈晓曦,王延杰,刘恋.小波阈值去噪法的深入研究[J].激光与红外,2012,42(1):105-110.
[14]沙正虎,余剑,崔琛.基于SURE无偏估计的图像自适应稀疏收缩去噪[J].计算机工程与应用,2013,49(7):195-198.
[15]张真真,王建林.结合第二代Bandelet变换分块的字典学习图像去噪算法[J].计算机科学,2018,45(7):270-276.
[16]杨春艳.基于非局部方向修正的Bandelet域图像去噪[D].西安:西安电子科技大学.2005.
[17]黄永.Bandelet变换及其逼近特性分析[J].华侨大学学报(自然科学版),2016,37(1):62-66.
[18]ELDAR Y.Generalized SURE for exponential families:applications to regularization[J].IEEE Trans on Signal Processing,2009,57(2):471-481.
[19]AHARON M,ELAD M.K-SVD:an algorithm for designing overcomplete dictionaries for sparse representation[J].IEEE Trans on Signal Processing,2006,54(11):4311-4322.
[20]JIANG Z,LIN Z.Label consistent K-SVD:learning a discriminative dictionary for recognition[J].IEEE transaction on pattern analysis and machim intelligent,2013,35(11):2651-2664.
[21]QING G.Image denosing algorithrithm based on contourlet transform for optical coherence tomography heart tube image[J].Image Processing,IET,2013,7(5):442-450.
[22]PENNEC E L,MALLAT S.Bandelet representations for image compression[C]//International conference on Image Processing,2001.
[23]ELAD M,AHARON M.Image denoising via sparse and redundant representations over learned dictionaries[J].IEEE Trans on Image Processing,2006,15(12):36-45.
[24]王智文,李绍滋.基于多元统计模型的分形小波自适应图像去噪[J].计算机学报,2014,37(6):80-89.
[25]VIOLA P,JONES M.Rapid object detection using a boosted cascade of simple features[C]//IEEE Computer Society Conference on Computer Vision&Pattern Recognition,2003.
[26]SUNDAR H,SILVER D.Skeleton based shape matching and retrieval[C]//Shape Modeling International,2003.IEEE,2003:130-139.
[27]CORNEA N,SILVER D,MIN P.Curve-skeleton properties,applications,and algorithms[J].IEEE Transactions on Visualization&Computer Graphics,2007,5(3):530-548.
[28]HAN F.Bottom-Up/Top-Down image parsing with attribute grammar[J].IEEE Transactions on Pattern Analysis&Machine Intelligence,2008,31(1):59-73.
[29]焦李成,谭山.图像的多尺度几何分析:回顾和展望[J].电子学报,2003,31(12A):1975-1981.
[30]张春梅,尹忠科,肖明霞.基于冗余字典的信号超完备表示与稀疏分解[J].科学通报,2006,51(6):628-633.
[31]李彦,汪胜前,邓承志.多尺度几何分析的图像去噪方法综述[J].计算机工程与应用,2011,47(34):168-173.
[2]SHI L L,WANG M.Application of locally adaptive wavelet domain denosing to X-Ray image processing[J].Nuclear Electronics&Detection Technology,2011,31(4):455-458.
[3]KANG X,STAMM,MATTEW C,et al.Robust median filtering forensics using an autoregressive mode[J].IEEE Transactions on Information Forensics&security,2013,8(9):1456-1468.
[4]LIANG M,DU J.Self-adaptive spatial image denoising model based on scale correlation and SURE-LET in the nonsubsampled contourlet transform domain[J].Science China(Information Sciences),2014,21(11):8-11.
[5]王文庆,晏婷.基于空间域的图像去噪方法比较研究[J].西安邮电大学学报,2012,17(2):75-79.
[6]刘祝华.图像去噪方法的研究[D].南昌:江西师范大学,2005.
[7]侯建华.基于小波及其统计特性的图像去噪方法研究[D].武汉:华中科技大学,2007.
[8]焦李成,孙强.多尺度变换域图像的感知与识别:进展和展望[J].计算机学报,2006,29(2):22-30.
[9]刘志民.基于小波变换的全变分模型的图像去噪[D].合肥:安徽大学,2013.
[10]查宇飞,毕笃彦.基于小波变换的自适应多阈值图像去噪[J].中国图象图形学报,2005,10(5):10-17.
[11]戴维,于盛林,孙栓.基于Contourlet变换自适应阈值的图像去噪算法[J].电子学报,2007,35(10):2-9.
[12]刘成云,陈振学,马于涛.自适应阈值的小波图像去噪[J].光电工程,2007,34(6):4-11.
[13]陈晓曦,王延杰,刘恋.小波阈值去噪法的深入研究[J].激光与红外,2012,42(1):105-110.
[14]沙正虎,余剑,崔琛.基于SURE无偏估计的图像自适应稀疏收缩去噪[J].计算机工程与应用,2013,49(7):195-198.
[15]张真真,王建林.结合第二代Bandelet变换分块的字典学习图像去噪算法[J].计算机科学,2018,45(7):270-276.
[16]杨春艳.基于非局部方向修正的Bandelet域图像去噪[D].西安:西安电子科技大学.2005.
[17]黄永.Bandelet变换及其逼近特性分析[J].华侨大学学报(自然科学版),2016,37(1):62-66.
[18]ELDAR Y.Generalized SURE for exponential families:applications to regularization[J].IEEE Trans on Signal Processing,2009,57(2):471-481.
[19]AHARON M,ELAD M.K-SVD:an algorithm for designing overcomplete dictionaries for sparse representation[J].IEEE Trans on Signal Processing,2006,54(11):4311-4322.
[20]JIANG Z,LIN Z.Label consistent K-SVD:learning a discriminative dictionary for recognition[J].IEEE transaction on pattern analysis and machim intelligent,2013,35(11):2651-2664.
[21]QING G.Image denosing algorithrithm based on contourlet transform for optical coherence tomography heart tube image[J].Image Processing,IET,2013,7(5):442-450.
[22]PENNEC E L,MALLAT S.Bandelet representations for image compression[C]//International conference on Image Processing,2001.
[23]ELAD M,AHARON M.Image denoising via sparse and redundant representations over learned dictionaries[J].IEEE Trans on Image Processing,2006,15(12):36-45.
[24]王智文,李绍滋.基于多元统计模型的分形小波自适应图像去噪[J].计算机学报,2014,37(6):80-89.
[25]VIOLA P,JONES M.Rapid object detection using a boosted cascade of simple features[C]//IEEE Computer Society Conference on Computer Vision&Pattern Recognition,2003.
[26]SUNDAR H,SILVER D.Skeleton based shape matching and retrieval[C]//Shape Modeling International,2003.IEEE,2003:130-139.
[27]CORNEA N,SILVER D,MIN P.Curve-skeleton properties,applications,and algorithms[J].IEEE Transactions on Visualization&Computer Graphics,2007,5(3):530-548.
[28]HAN F.Bottom-Up/Top-Down image parsing with attribute grammar[J].IEEE Transactions on Pattern Analysis&Machine Intelligence,2008,31(1):59-73.
[29]焦李成,谭山.图像的多尺度几何分析:回顾和展望[J].电子学报,2003,31(12A):1975-1981.
[30]张春梅,尹忠科,肖明霞.基于冗余字典的信号超完备表示与稀疏分解[J].科学通报,2006,51(6):628-633.
[31]李彦,汪胜前,邓承志.多尺度几何分析的图像去噪方法综述[J].计算机工程与应用,2011,47(34):168-173.