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Nonlocal Similarity Based Tensor Train Factorization for Color Image Completion |
JIA Huidi1,2,3, HAN Zhi1,2, CHEN Xiai1,2, TANG Yandong1,2 |
1.State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016; 2.Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110016; 3.University of Chinese Academy of Sciences, Beijing 100049 |
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Abstract In data acquisition and transformation, the data are more or less lost. Therefore, the results of computer vision tasks such as object recognition and tracking are affected. In a natural image, there are many similar structures and patterns with repeated features. With these similar structures and patterns, a method of nonlocal similarity based tensor train factorization for color image completion is proposed. Nonlocal similarity of images are employed to exploit the low rank feature, and modeling is conducted by tensor train factorization to further mine low rank information through transforming a low-order tensor to higher-order one. Experimental results validate the proposed method in image completion.
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Received: 31 January 2019
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Corresponding Authors:
HAN Zhi, Ph.D., professor. His research interests include computer vision, matrix completion and illumination modeling.
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About author:: JIA Huidi, master student. Her research interests include computer vision and image processing;CHEN Xiai, Ph.D. candidate. Her research interests include image processing, noise modeling and image/video completion;TANG Yandong, Ph.D., professor. His research interests include robot vision, image processing and pattern recognition. |
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[1] CAI J F, CANDÉS E J, SHEN Z W. A Singular Value Thresholding Algorithm for Matrix Completion. SIAM Journal on Optimization, 2010, 20(4): 1956-1982. [2] JAIN P, NETRAPALLI P, SANGHAVI S. Low-Rank Matrix Completion Using Alternating Minimization // Proc of the 45th Annual ACM Symposium on Theory of Computing. New York, USA: ACM, 2013: 665-674. [3] HU Y, ZHANG D B, YE J P, et al. Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(9): 2117-2130. [4] DU B, ZHANG M F, ZHANG L F, et al. PLTD: Patch-Based Low-Rank Tensor Decomposition for Hyperspectral Images. IEEE Transa-ctions on Multimedia, 2017, 19(1): 67-79. [5] HE Z, HU J, WANG Y W. Low-Rank Tensor Learning for Classification of Hyperspectral Image with Limited Labeled Samples. Signal Processing, 2018, 145: 12-25. [6] GUO H W, WU X Y, FENG W. Multi-stream Deep Networks for Human Action Classification with Sequential Tensor Decomposition. Signal Processing, 2017, 140: 198-206. [7] VIGNERON V, KODEWITZ A, DA COSTA M N, et al. Non-negative Sub-tensor Ensemble Factorization(NsTEF) Algorithm: A New Incremental Tensor Factorization for Large Data Sets. Signal Proce-ssing, 2018, 144: 77-86. [8] PAPALEXAKIS E E, FALOUTSOS C, SIDIROPOULOS N D. Tensors for Data Mining and Data Fusion: Models, Applications, and Scalable Algorithms. ACM Transactions on Intelligent Systems and Technology, 2016, 8(2). DOI: 10.1145/2915921. [9] LIU J, MUSIALSKI P, WONKA P, et al. Tensor Completion for Estimating Missing Values in Visual Data // Proc of the IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2009: 2114-2121. [10] XU Y X, HAO R R, YIN W T, et al. Parallel Matrix Factorization for Low-Rank Tensor Completion. Inverse Problems and Imaging, 2015, 9(2): 601-624. [11] CARROLL J D, CHANG J J. Analysis of Individual Differences in Multidimensional Scaling via an N-Way Generalization of "Eckart-Young" Decomposition. Psychometrika, 1970, 35(3): 283-319. [12] TUCKER L R. Some Mathematical Notes on Three-Mode Factor Analysis. Psychometrika, 1966, 31(3): 279-311. [13] OSELEDETS I V. Tensor-Train Decomposition. SIAM Journal on Scientific Computing, 2011, 33(5): 2295-2317. [14] ACAR E, DUNLAVY D M, KOLDA T G, et al. Scalable Tensor Factorizations for Incomplete Data. Chemometrics and Intelligent Laboratory Systems, 2011, 106(1): 41-56. [15] KOLDA T G, BADER B W. Tensor Decompositions and Applications. SIAM Review, 2009, 51(3): 455-500. [16] CHEN Y L, HSU C T, LIAO H Y M. Simultaneous Tensor Decomposition and Completion Using Factor Priors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014, 36(3): 577-591. [17] BENGUA J A, PHIEN H N, TUAN H D, et al. Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train. IEEE Transactions on Image Processing, 2017, 26(5): 2466-2479. [18] BUADES A, COLL B, MOREL J M. A Non-local Algorithm for Image Denoising // Proc of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2005, II: 60-65 [19] DABOV K, FOI A, KATKOVNIK V, et al. Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering. IEEE Transac-tions on Image Processing, 2007, 16(8): 2080-2095. [20] MAIRAL J, BACH F, PONCE J, et al. Non-local Sparse Models for Image Restoration // Proc of the 12th IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2009: 2272-2279. [21] WANG S L, LEI Z, YAN L. Nonlocal Spectral Prior Model for Low-Level Vision // Proc of the 11th Asian Conference on Computer Vision. Berlin, Germany: Springer, 2012, III: 231-244. [22] MA S Q, GLODFARB D, CHEN L F. Fixed Point and Bregman Iterative Methods for Matrix Rank Minimization. Mathematical Programming, 2009, 128(1/2): 321-353. [23] BACH F R. Consistency of Trace Norm Minimization. Journal of Machine Learning Research, 2008, 9: 1019-1048. [24] LIU Y P, LONG Z, ZHU C. Image Completion Using Low Tensor Tree Rank and Total Variation Minimization. IEEE Transactions on Multimedia, 2019, 21(2): 338-350. |
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