计算机科学 ›› 2016, Vol. 43 ›› Issue (5): 274-278.doi: 10.11896/j.issn.1002-137X.2016.05.052

• 图形图像与模式识别 • 上一篇    下一篇

基于分数阶全变分正则化的超分辨率图像重建

刘亚男,杨晓梅,陈超楠   

  1. 四川大学电气信息学院 成都610065,四川大学电气信息学院 成都610065,四川大学电气信息学院 成都610065
  • 出版日期:2018-12-01 发布日期:2018-12-01

Super-resolution Image Reconstruction Based on Fractional Order Total Variation Regularization

LIU Ya-nan, YANG Xiao-mei and CHEN Chao-nan   

  • Online:2018-12-01 Published:2018-12-01

摘要: 从退化的低分辨率图像重建得到高分辨率图像的本质是一病态逆问题,针对该问题,通过添加正则项进行处理。在使用传统的全变分(TV)的基础上,添加了分数阶全变分(FOTV)作为另一正则项来约束解空间。分数阶全变分正则项的使用可以更好地重建图像的细节纹理信息,弥补了全变分算子在平滑区域易出现阶梯效应的缺陷。利用交替方向乘子(ADMM)算法将问题划分为子问题,将全变分和分数阶全变分算子作为循环矩阵,通过傅里叶变换将其对角化,降低了计算的复杂程度。实验结果表明,与已有的方法相比,所提方法有效地避免了阶梯效应的产生,较好地保持了细节信息,并且具有更好的峰值信噪比(PSNR)和结构相似度(SSIM)。

关键词: 超分辨率图像重建,全变分,分数阶全变分,交替方向乘子法,阶梯效应,纹理

Abstract: It is an ill-posed that a high resolution image is reconstructed from a degenerate low resolution image,and regularization is added to deal with the problem usually.In this paper,we introduced fractional order total variation(FOTV) as another regularization to constrain the solution space on the basis of traditional total variation(TV) operator.Detailed texture information of the image was better reconstructed by using FOTV regularization,and staircase effect was eliminated.Moreover,we divid the problem into sub-problems by alternating direction multiplier method(ADMM),and total variation and fractional total variation operators were constructed as cyclic matrices.Then,these were diagonalized by Fourier transformation.Therefore,computational complexity is reduced.Experimental results show that compared to existing methods,the proposed model does not suffer from staircase.Furthermore,the proposed model can keep the details of the information and has better value of peak signal to noise ratio(PSNR) and similarity index measure(SSIM).

Key words: Super-resolution image reconstruction,Total variation,Fractional order total variation,Alternating direction multipliers method,Staircase effect,Texture

[1] Lu Qing-chun,Hu Fang-yu.Improved super-resolution imagereconstruction algorithm based on L1 norm [J].Radio Enginee-ring,2009(9):13-15(in Chinese) 路庆春,胡访宇.L1范数的图像超分辨率重建改进算法[J].无线电工程,2009(9):13-15
[2] Luo Guo-zhong,Yin Jian-ping,Zhu En.Super-resolution image reconstruction based on nonlocal POCS[J].Computer Science,2014,41(8):47-49(in Chinese) 罗国中,殷建平,祝恩.基于非局部POCS的超分辨率图像重建[J].计算机科学,2014,41(8):47-49
[3] Rudin L I,Osher S,Fatemi E.Nonlinear total variation basednoise removal algorithms[J].Physica D:Nonlinear Phenomena,1992,60(1-4):259-268
[4] Tychonoff A N,Arsenin V Y.Solution of ill-posed problems[J].Mathematics of Computation,1978,2(144):491
[5] Yuan Q Q,Zhang L P,Shen H F.Multiframe super-resolution employing a spatially weighted total variation model[J].IEEE Transactions on Circuits and Systems for Video Technology,2012,22(3):379-392
[6] Ren Z M,He C J,Zhang Q F.Fractional order total variation regularization for image super-resolution[J].Signal Processing,2013,93(9):2408-2421
[7] Podlubny,Igor.Fractional differential equations[M].Lightning Source Inc,1998:340
[8] Zhang J,Wei Z H.A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising [J].Applied Mathematical Modelling,2011,35(5):2516-2528
[9] Jiang Wei.Fractional denoising new model based on PDE[J].Computer Applications,2011,1(3):753-756(in Chinese) 蒋伟.基于分数阶偏微分方程的图像去噪新模型[J].计算机应用,2011,1(3):753-756
[10] Tian Dan,Xue Ding-yu,Yang ya-jie.Fractional original dual denoising model and the numerical algorithm noising[J].China Image and Graphics,2014,9(6):852-858(in Chinese) 田丹,薛定宇,杨雅婕.分数阶原始对偶去噪模型及其数值算法[J].中国图象图形学报,2014,9(6):852-858
[11] Combettes P L,Wajs V R.Signal recovery by proximal forward-backward splitting[J].M ultiscale Modelin & Simulation,2005,4(4):1168-1200
[12] Purkait P,Chanda B.Super resolution image reconstruction th-rough bregman iteration using morphologic regularization[J].IEEE Transactions on Image Processing,2012,21(9):4029-4039
[13] Afonso M V,Bioucas-Dias J M,Figueiredo M A T.Fast image recovery using variable splitting and constrained optimization[J].IEEE Transactions on Image Processing,2010,19(9):2345-2356
[14] Mourad N,Reilly J P.Automatic threshold estimation for iterative shrinkage algorithms used with compressed sensing[C]∥2012 IEEE International Conference on Kyoto:Acoustics,Speech and Signal Processing(ICASSP).2012:2721-2794
[15] Xu Y,Yin W,Osher S.Learning circulant sensing kernels[J].Inverse Problems and Imaging,2014,8(3):901-923
[16] Bioucas-Dias J M,Figueiredo M A T.A New TwIST:Two-step iterative shrinkage/thresholding algorithms for image restoration[J].IEEE Transactions on Image Processing,2007,16(12):2992-3004

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