基于非凸[lp]范数和G?范数的图像去模糊模型

2016-05-14 01:04张凯李敏
现代电子技术 2016年5期
关键词:范数正则耦合

张凯 李敏

摘 要: 图像去模糊一直是图像修复中的重要问题,针对经典的去模糊方法,提出一种耦合非凸[lp(0≤p<1)]范数和G范数的图像去模糊方法。该方法利用[lp(0≤p<1)]范数作为正则项约束,保证了图像的稀疏性要求;利用G范数作为保真项,保证在去模糊的同时有效抑制噪声并保持图像的细小特征,同时也给出新方法基于交替最小化的有效算法。实验结果表明新模型是可行的。

关键词: 图像去模糊; [lp(0≤p<1)]范数; G范数; 交替最小化

中图分类号: TN911.73?34 文献标识码: A 文章编号: 1004?373X(2016)05?0085?04

3 结 语

针对经典的正则化去模糊方法,本文采用非凸[lp(0≤p<1)]范数作为正则项来保证图像的稀疏性。同时选取G范数来刻画噪声成分,使得复原后的图像含有较少的噪声。对于耦合非凸[lp(0≤p<1)]范数和[G]范数的变分问题,本文给出基于交替最小化迭代的算法。数值实验表明新算法是有效的。

参考文献

[1] CHELLAPPA R, FAIN A. Markov random fields: theory and applications [M]. US: Academic Press, 1993.

[2] BIOUCAS?DIAS J M. Bayesian wavelet?based image deconvolution: a GEM algorithm exploiting a class of heavy?tailed priors [J]. IEEE transaction on image processing, 2006, 15(4): 937?951.

[3] RUDIN L I, OSHER S, FATEMI E. Nonlinear total variation based noise removal algorithms [J]. Physica D?nonlinear phenomen, 1992, 60(1): 259?268.

[4] BECK A, TEBOULLE M. A fast iterative shrinkage?threshol?ding algorithm for linear inverse problem [J]. SIAM journal on imaging sciences, 2009, 2(1): 183?202.

[5] OLIVEIRA J P, BIOUCAS?DIAS J M, FIGUEIREDO M A T. Adaptive total variation image deblurring: a majorization minimization approach [J]. Signal processing, 2009, 89(9): 1683?1693.

[6] MEYER Y. Oscillating pattern in image processing and nonlinear evolution equations [R]. Boston: American Mathematical Society, 2005.

[7] AUJOL J F, AUBERT G, BLANC?FERAUD L, et al. Image decomposition application to SAR image [C]// Proceedings of 2003 4th International Conference on Scale Space. Isle of Skye: Springer Berlin Heidelberg, 2003: 297?312.

[8] EKELAND I, TEMAM R. Analyse convexe and problems variationnels [M]. 2nd ed. French: Dunod, 1986.

[9] ZUO Wangmeng, MENG Deyu, ZHANG Lei, et al. A genera?lized iterated shrinkage algorithm for non?convex sparse coding [C]// Proceedings of 2013 International Conference on Computer Vision. Sydney: IEEE, 2013: 217?224.

[10] GILLES J, OSHER S. Bregman implementation of Meyer′s G?norm for cartoon+texture decomposition [R]. [S.l.]: UCLA CAM Report, 2001.

[11] KRISHNAN D, FERGUS R. Fast image deconvolution using hyper?Laplacian priors [C]// Proceedings of 2009 23rd Annual Conference on Neural Information Processing Systems. Vancouver: IEEE, 2009: 1033?1041.

[12] LAI M J, WANG J. An unconstrained [lp]minimization with 0<[p<1] for sparse solution of under?determined linear systems [J]. SIAM journal on optimization, 2009, 21(1): 82?101.

[13] KUANG?CHIH L, JEFFREY H, KRIEGMAN D J. Acquiring linear subspaces for face recognition under variable lighting [J]. IEEE transaction on pattern analysis machine intelligence, 2005, 27(5): 684?698.

[14] LEVIN A, FERGUS R, DURAND F, et al. Image and depth form a conventional camera with a code aperture [J]. ACM transaction on graphics, 2007, 26(3): 70?74.

[15] QIN L, LIN Z, SHE Y, et al. A comparison of typical [lp]mi?nimization algorithms [J]. Neurocomputing, 2013, 119(16): 413?424.

[16] MARJANOVIC G, SOLO V. On [lp]optimization and matrix completion [J]. IEEE transactions on signal processing, 2012, 60(11): 5714?5724.

[17] GOLDSTEIN T, OSHER S. The split bregman method for [L1] regularized problems [J]. SIAM journal on imaging sciences, 2009, 2(2): 323?343.

[18] OSHER S, YIN W, GOLDFARB D, et al. An iterative regularization method for total variation?based image restoration [J]. Multiscale modeling and simulation, 2005, 14(2): 460?489.

猜你喜欢
范数正则耦合
非Lipschitz条件下超前带跳倒向耦合随机微分方程的Wong-Zakai逼近
剩余有限Minimax可解群的4阶正则自同构
类似于VNL环的环
基于加权核范数与范数的鲁棒主成分分析
矩阵酉不变范数Hölder不等式及其应用
基于“壳-固”耦合方法模拟焊接装配
有限秩的可解群的正则自同构
一类具有准齐次核的Hilbert型奇异重积分算子的范数及应用
求解奇异摄动Volterra积分微分方程的LDG-CFEM耦合方法
非线性耦合KdV方程组的精确解