图像修复中截断P范数正则化的矩阵填充算法（英文）
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摘要
本文将截断核范数与Schantten-p范数结合起来,提出了一种更加灵活的矩阵填充算法,以便更好地利用图像修复中的低秩特性。我们进一步应用乘法器的交替方向法,提出了一种有效的迭代方案来解决优化问题。实验结果表明,我们提出的算法在真实的可视化数据集上展现的性能优于传统的矩阵填充算法。
In this paper,we develop a more flexible matrix completion algorithm toward better exploiting low rank property in image inpainting by jointing truncated nuclear norm and Schatten p-norm. We further apply the alternating direction method of multipliers to develop an efficient iterative scheme to solve the optimization problem.Experimental results demonstrate that our proposed algorithm can encouragingly outperform the state of the art matrix completion algorithms on real visual datasets.
In this paper,we develop a more flexible matrix completion algorithm toward better exploiting low rank property in image inpainting by jointing truncated nuclear norm and Schatten p-norm. We further apply the alternating direction method of multipliers to develop an efficient iterative scheme to solve the optimization problem.Experimental results demonstrate that our proposed algorithm can encouragingly outperform the state of the art matrix completion algorithms on real visual datasets.
引文
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[19] NIE F,WANG H,HUANG H,et al. Joint schatten p-norm and Lp-Norm robust matrix completion for missing value recovery[J]. Knowledge Info Syst,2015,42(3):525-544.
[20] LIU L,HUANG W,CHEN D R. Exact minimum rank approximation via Schatten p-norm minimization[J]. J Compu Appl Math,2014,267:218-227.
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[25] DONOHO D L. Compressed sensing[J]. IEEE Trans Infor Theor,2006,52(4):1289-1306.
[26] CANDES E J,WAKIN M B. An introduction to compressive sampling[J]. IEEE Sig Proc Mag,2008,25(2):21-30.
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[2] GUILLEMOT C,LE MEUR O. Image inpainting:Overview and recent advances[J]. IEEE Sig Proc Mag,2014,31(1):127-144.
[3] WANG J,LU K,PAN D,et al. Robust object removal with an exemplar-based image inpainting approach[J]. Neurocomputing,2014,123:150-155.
[4] LEE M C,INOUE K,KIM C S,et al. Regeneration of elemental images in integral imaging for occluded objects using a plenoptic camera[J]. Chi Opt Lett,2016,14(12):121101(1-5).
[5] KOREN Y,BELL R,VOLINSKY C. Matrix factorization techniques for recommender systems[J]. Computer,2009,42(8):30-37.
[6] RENNIE D M,SREBRO N. Fast maximum margin matrix factorization for collaborative prediction[C]//Proceedings of the 22nd international conference on Machine learning. ACM,2005:713-719.
[7] CANDES E J,RECHT B. Exact matrix completion via convex optimization[J]. Found Comput Math,2009,9(6):717-772.
[8] JI H,LIU C,SHEN Z,et al. Robust video denoising using low rank matrix completion[C]//CVPR,2010:1791-1798.
[9] JAIN P,NETRAPALLI P,SANGHAVI S. Low-rank matrix completion using alternating minimization[C]//Proceedings of the forty-fifth annual ACM symposium on Theory of computing. ACM,2013:665-674.
[10] HASTIE T,MAZUMDER R,LEE J D,et al. Matrix completion and low-rank SVD via fast alternating least squares[J]. J Machine Learn Res,2014,16(1):3367-3402.
[11] TANNER J,WEI K. Low rank matrix completion by alternating steepest descent methods[J]. Appl Comput Harm Anal,2016,40(2):417-429.
[12] RECHT B,FAZEL M,PARRILO P A. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization[J]. SIAM Rev,2010,52(3):471-501.
[13] ZHANG F,YANG J,TAI Y,et al. Double nuclear norm-based matrix decomposition for occluded image recovery and background modeling[J]. IEEE Trans Image Proc,2015,24(6):1956-1966.
[14] CAI J F,CANDES E J,SHEN Z. A singular value thresholding algorithm for matrix completion[J]. SIAM J Optim,2010,20(4):1956-1982.
[15] MA S,GOLDFARB D,CHEN L. Fixed point and Bregman iterative methods for matrix rank minimization[J]. Math Prog,2011,128(1-2):321-353.
[16] LIN Z,CHEN M,MA Y. The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices[J].ar Xiv preprint ar Xiv:1009.5055,2010.
[17] NIE F,HUANG H,DING C. Low-rank matrix recovery via efficient schatten p-norm minimization[C]//Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence. AAAI Press,2012:655-661.
[18] WANG J,WANG M,HU X,et al. Visual data denoising with a unified Schatten-p norm andq norm regularized principal component pursuit[J]. Pattern Recog,2015,48(10):3135-3144.
[19] NIE F,WANG H,HUANG H,et al. Joint schatten p-norm and Lp-Norm robust matrix completion for missing value recovery[J]. Knowledge Info Syst,2015,42(3):525-544.
[20] LIU L,HUANG W,CHEN D R. Exact minimum rank approximation via Schatten p-norm minimization[J]. J Compu Appl Math,2014,267:218-227.
[21] ZHANG D,HU Y,YE J,et al. Matrix completion by truncated nuclear norm regularization[C]//Computer Vision and Pattern Recognition(CVPR),2012 IEEE Conference IEEE,2012:2192-2199.
[22] HU Y,ZHANG D,YE J,et al. Fast and accurate matrix completion via truncated nuclear norm regularization[J]. IEEE Trans Patt Anal Machine Intel,2013,35(9):2117-2130.
[23] AL-QIZWINI M,RADHA H. Truncated and smoothed Schatten-p function for robust tensor recovery[C]//Information Sciences and Systems(CISS),2015 49th Annual Conference on. IEEE,2015:1-4.
[24] FENG L,SUN H,SUN Q,et al. Image compressive sensing via Truncated Schatten-p Norm regularization[J]. Sig Proc Image Commun,2016,47:28-41.
[25] DONOHO D L. Compressed sensing[J]. IEEE Trans Infor Theor,2006,52(4):1289-1306.
[26] CANDES E J,WAKIN M B. An introduction to compressive sampling[J]. IEEE Sig Proc Mag,2008,25(2):21-30.
[27] ZUO W,MENG D,ZHANG L,et al. A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding[C]//IEEE International Conference on Computer Vision.IEEE,2013:217-224.
[28] KESHAVAN R H,MONTANARI A,OH S. Matrix completion from a few entries[J]. IEEE Trans Info Theor,2009,56(6):2980-2998.