基于分数阶全变差和自适应正则化参数的图像去模糊
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摘要
为更好地复原图像的纹理细节,避免求解图像去模糊模型时面临正则化参数难以选择的问题,提出了一种基于分数阶全变差(FOTV)模型和自适应更新正则化参数的非盲去模糊图像重建方法。首先,在分析不同分数阶下FOTV的幅频响应特性的基础上,采用不同分数阶次的FOTV模型约束图像的平滑(低频)部分和纹理细节(高频)部分,从而建立图像非盲去模糊重建模型。其次,为了有效地求解重建模型和实现两个正则化参数的自适应更新,采用交替方向乘子法(ADMM)将原本含有两个正则化参数的复杂问题分解成两个相对容易的子问题进行求解,每个子问题只含一个正则化参数。最后,根据偏差准则,在迭代求解过程中实现了两个正则化参数的自适应更新。将所提算法应用于包含平滑、边缘和纹理细节的多幅图像中,测试4种不同模糊核下的去模糊效果;与传统的4种去模糊算法相比,实验结果表明所提算法能自适应地更新两个正则化参数,对于纹理细节适中的图像具有较好的去模糊效果。
In order to better recovery texture details of images,avoid the difficulty of selecting the regularization parameters when solving the image deblurring model,a novel non-blind image deblurring method by using fractional order TV(FOTV)and adaptive estimation of two regularization parameters was proposed in this paper.First,after analyzing the amplitude-frequency response of FOTV,different fractional orders of FOTV were set to the smooth(low-frequency)part and texture(high-frequency)part of the desired image,respectively,and a model of image non-blind reconstruction was modeled.Second,to effectively solve the reconstruction model and adaptively update two regularization parameters,the alternating direction multiplier method(ADMM)was used to separate the originally complex problem with two regularization parameters into two easy sub-problems.Each sub-problem has only one regularization parameter.Finally,according to the discrepancy principle,the two regularization parameters were adaptively updated and two sub-problems were solved.To test the effect of deblurring with four blurring kernels,the proposed algorithm has been applied to multiple images with smooth,edge and texture details.Compared with four traditional deblurring algorithms,the experimental results showed that the proposed algorithm can adaptively update two regularization parameters and has better deblurring performance for images with moderate texture details.
In order to better recovery texture details of images,avoid the difficulty of selecting the regularization parameters when solving the image deblurring model,a novel non-blind image deblurring method by using fractional order TV(FOTV)and adaptive estimation of two regularization parameters was proposed in this paper.First,after analyzing the amplitude-frequency response of FOTV,different fractional orders of FOTV were set to the smooth(low-frequency)part and texture(high-frequency)part of the desired image,respectively,and a model of image non-blind reconstruction was modeled.Second,to effectively solve the reconstruction model and adaptively update two regularization parameters,the alternating direction multiplier method(ADMM)was used to separate the originally complex problem with two regularization parameters into two easy sub-problems.Each sub-problem has only one regularization parameter.Finally,according to the discrepancy principle,the two regularization parameters were adaptively updated and two sub-problems were solved.To test the effect of deblurring with four blurring kernels,the proposed algorithm has been applied to multiple images with smooth,edge and texture details.Compared with four traditional deblurring algorithms,the experimental results showed that the proposed algorithm can adaptively update two regularization parameters and has better deblurring performance for images with moderate texture details.
引文
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[16]Yang Junfeng,Zhang Yin,Yin Wotao.A Fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data[J].Journal of Selected Topics in Signal Processing,2010,4(2):288-297.
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[2]Tikhonov A N,Arsenin V Y.Solutions of ill-Posed Problems[M].Washington,DC:Wiley,1977.
[3]Vogel C R,Oman M E.Fast,robust total variation-based reconstruction of noisy,blurred images[J].IEEE Transactions on Image Processing,1998,7(6):813-824.
[4]Chan T F,Wong C K.Total variation blind deconvolution[J].Image Processing IEEE Trans on Image Processing,1998,7(3):370-375.
[5]Zhang Jun,Wei Zhihui,Xiao Liang.A fast adaptive reweighted residual-feedback iterative algorithm for fractional-order total variation regularized multiplicative noise removal of partly-textured images[J].Signal Processing,2014,98(5):381-395.
[6]Zhou L Y,Tang J X.Fraction-order total variation blind image restoration based on L1-norm[J].Applied Mathmatical Modelling,2017,51:469-476.
[7]Ren Zemin,He Chuanjiang,Zhang Qifeng.Fractional order total variation regularization for image super-resolution[J].Signal Processing,2013,93(9):2408-2421.
[8]Chan T,Marquina A,Mulet R.High-order total variationbased image restoration[J].Siam Journal on Scientific Computing,2001,22(2):503-516.
[9]Liu Jun,Huang Ting zhu,Lv Xiaoguang.High-order total variation-based Poissonian image deconvolution with spatially adapted regularization parameter[J].Applied Mathematical Modelling,2017,45:516-529.
[10]Liu Yanan,Yang Xiaomei,Chen Chaonan.Super-resolution image reconstruction based on fractional order total variation regularization[J].Compute Science,2016,43(5):274-278.[刘亚男,杨晓梅,陈超楠.基于分数阶全变分正则化的超分辨率图像重建[J].计算机科学,2016,43(5):274-278.]
[11]Xu Li,Lu Cewu,Xu Yi,et al.Image smoothing via L0,gradient minimization[C]//Proceedings of the 2011 SIGGRAPHAsia Conference.New York:ACM,2011:174.
[12]Morozov V A.Methods for solving incorrectly posed problems[M].New York:Springer-Verlag,1984.
[13]Zhang Jun,Wei Zhihui.A class of fractional-order multiscale variational models and alternating projection algorithm for image denoising[J].Applied Mathematical Modelling,2011,35(5):2516-2528.
[14]Chen Dali,Chen Yangquan,Xue Dingyu.Fractional-order total variation image restoration based on primal-dual algorithm[J].Abstract and Applied Analysis,2013:717-718.
[15]Huang Guo,Xu Li,Pu Yifei.Summary on image processing using fractional calculus[J].Application Research of Computers,2012,29(2):414-420.[黄果,许黎,蒲亦非.分数阶微积分在图像处理中的研究综述[J].计算机应用研究,2012,29(2):414-420.]
[16]Yang Junfeng,Zhang Yin,Yin Wotao.A Fast alternating direction method for TVL1-L2 signal reconstruction from partial Fourier data[J].Journal of Selected Topics in Signal Processing,2010,4(2):288-297.
[17]Goldstein T.The split bregman method for L1-regularized problems[J].SIAM Journal on Imaging Sciences,2009,2(2):323-343.
[18]Karasulu B,Korukoglu S.Moving object detection and tracking by using annealed background subtraction method in videos:Performance optimization[J].Expert Systems with Applications,2012,39(1):33-43.
[19]Wang Yilun,Yang Junfeng,Yin Wotao,et al.A new alternating minimization algorithm for total variation image reconstruction[J].SIAM Journal on Image Sciences,2008,1(3):248-272.
[20]Hore A,Ziou D.Image quality metrics:PSNR vs.SSIM[C]//2010 20th International Conference on Pattern Recognition.Istanbul:IEEE,2010:2366-2369.
[21]Bioucas-Dias J M,Figueiredo M A T,Oliveira J P.Total variation-based image deconvolution:A majorization-minimization approach[C]//International Conference on Acoustics Speech and Signal Processing Proceedings.Toulouse:IEEE,2006:Ⅱ.
[22]Bioucas-Dias J M,Figueiredo M A T.A new TwIST:Twostep iterative shrinkage/thresholding algorithms for image restoration[J].IEEE Transactions on Image processing,2007,16(12):2992-3004.