|
[1]
|
J. A. Bengua, H. N. Phiem, H. D. Tuan and M. N. Do, Efficient tensor completion for color image and video recovery: Low-rank tensor train, IEEE Transactions on Image Processing, 26 (2017), 2466-2479.
doi: 10.1109/TIP.2017.2672439.
|
|
[2]
|
D. P. Bertsekas, A. Nedic and A. E. Ozdaglar, Convex Analysis and Optimization, Athena Scientific, 2003.
|
|
[3]
|
M. Bertalmio, G. Sapiro, V. Caselles and C. Ballester, Image inpainting, Siggraph, 4 (2000), 417-424.
doi: 10.21236/ADA437378.
|
|
[4]
|
J.-F. Cai, E. J. Cand$\grave{e}$s and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, 20 (2010), 1956-1982.
doi: 10.1137/080738970.
|
|
[5]
|
S. H. Chan, R. Khoshabeh, K. B. Gibson, P. E. Gill and T. Q. Nguyen, An augmented Lagrangian method for total variation video restoration, IEEE Transactions on Image Processing, 20 (2011), 3097-3111.
doi: 10.1109/TIP.2011.2158229.
|
|
[6]
|
R. H. Chan, M. Tao and X. Yuan, Constrained total variation deblurring models and fast algorithms based on alternating direction method of multipliers, SIAM Journal on Imaging Sciences, 6 (2013), 680-697.
doi: 10.1137/110860185.
|
|
[7]
|
Y. Chang, L.-X. Yan and S. Zhong, Hyper-laplacian regularized unidirectional low-rank tensor recovery for multispectral image denoising, IEEE Conference on Computer Vision and Pattern Recognition, (2017), 5901–5909.
doi: 10.1109/CVPR.2017.625.
|
|
[8]
|
Y. Chen, C. Hsu and H. M. Liao, Simultaneous tensor decomposition and completion using factor priors, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20 (2014), 577-591.
|
|
[9]
|
L.-B. Cui, X.-Q. Zhang and S.-L. Wu, A new preconditioner of the tensor splitting iterative method for solving multi-linear systems with $\mathcal{M}$-tensors, Computational and Applied Mathematics, 39 (2020), 1-16.
doi: 10.1007/s40314-020-01194-8.
|
|
[10]
|
K. Dabov, A. Foi, V. Katkovnik and K. Egiazarian, Image denoising by sparse 3-D transform-domain collaborative filtering, IEEE Transactions on Image Processing, 16 (2007), 2080-2095.
doi: 10.1109/TIP.2007.901238.
|
|
[11]
|
M. Ding, T.-Z. Huang and T.-H. Ma, Cauchy noise removal using group-based low-rank prior, Applied Mathematics and Computation, 372 (2020), 124971, 15 pp.
doi: 10.1016/j.amc.2019.124971.
|
|
[12]
|
M. Ding, T.-Z. Huang, T.-Y. Ji, X.-L. Zhao and J.-H. Yang, Low-rank tensor completion using matrix factorization based on tensor train rank and total variation, Journal of Scientific Computing, 81 (2019), 941-964.
doi: 10.1007/s10915-019-01044-8.
|
|
[13]
|
M. Ding, T.-Z. Huang, S. Wang, J.-J. Mei and X.-L. Zhao, Total variation with overlapping group sparsity for deblurring images under Cauchy noise, Applied Mathematics and Computation, 341 (2019), 128-147.
doi: 10.1016/j.amc.2018.08.014.
|
|
[14]
|
Y. Du, G. Han, Y. Quan, Z. Yu, H. Wong, C. L. P. Chen and J. Zhang, Exploiting global low-rank structure and local sparsity nature for tensor completion, IEEE Transactions on Cybernetics, 49 (2019), 3898-3910.
doi: 10.1109/TCYB.2018.2853122.
|
|
[15]
|
J. Eckstein and D. P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, 55 (1992), 293-318.
doi: 10.1007/BF01581204.
|
|
[16]
|
G. Ely, S. Aeron, N. Hao and M. E. Kilmer, 5D seismic data completion and denoising using a novel class of tensor decompositions, GEOPHYSICS, 80 (2015), V83–V95.
doi: 10.1190/geo2014-0467.1.
|
|
[17]
|
X. Fu, K.-J. Huang, B. Yang, W. K. Ma and N. D. Sidiropoulos, Robust volume minimization-based matrix factorization for remote sensing and document clustering, IEEE Transactions on Signal Processing, 64 (2016), 6254-6268.
doi: 10.1109/TSP.2016.2602800.
|
|
[18]
|
S. Gandy, B. Recht and I. Yamada, Tensor completion and low-n-rank tensor recovery via convex optimization, Inverse Problems, 27 (2011), 025010, 19pp.
doi: 10.1088/0266-5611/27/2/025010.
|
|
[19]
|
T. Goldstein, B. O'Donoghue, S. Setzer and R. Baraniuk, Fast alternating direction optimization methods, SIAM Journal on Imaging Sciences, 7 (2014), 1588-1623.
doi: 10.1137/120896219.
|
|
[20]
|
L. Grasedyck, M. Kluge and S. Krämer, Alternating least squares tensor completion in the TT-format, preprint, arXiv: 1509.00311.
|
|
[21]
|
S.-H. Gu, L. Zhang, W.-M. Zuo and X.-C. Feng, Weighted nuclear norm minimization with application to image denoising, IEEE Conference on Computer Vision and Pattern Recognition, (2014), 2862–2869.
doi: 10.1109/CVPR.2014.366.
|
|
[22]
|
B.-S. He and X. Yuan, On the O(1/n) convergence rate of the douglas-rachford alternating direction method, SIAM Journal on Numerical Analysis, 50 (2012), 700-709.
doi: 10.1137/110836936.
|
|
[23]
|
W. He, H.-Y. Zhang, L.-P. Zhang and H.-F. Shen, Total-variation-regularized low-rank matrix factorization for hyperspectral image restoration, IEEE Transactions on Geoscience and Remote Sensing, 54 (2016), 178-188.
doi: 10.1109/TGRS.2015.2452812.
|
|
[24]
|
C. J. Hillar and L. H. Lim, Most tensor problems are NP-hard, Journal of the ACM, 60 (2013), Art. 45, 39 pp.
doi: 10.1145/2512329.
|
|
[25]
|
Y.-M. Huang, H.-Y. Yan, Y.-W. Wen and X. Yang, Rank minimization with applications to image noise removal, Information Sciences, 429 (2018), 147-163.
doi: 10.1016/j.ins.2017.10.047.
|
|
[26]
|
T.-X. Jiang, T.-Z. Huang, X.-L. Zhao and L.-J. Deng, Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm, Journal of Computational and Applied Mathematics, 372 (2020), 112680, 15pp.
doi: 10.1016/j.cam.2019.112680.
|
|
[27]
|
T.-X. Jiang, M. K. Ng, X.-L. Zhao and T.-Z. Huang, Framelet representation of tensor nuclear norm for third-order tensor completion, IEEE Transactions on Image Processing, 29 (2020), 7233-7244.
doi: 10.1109/TIP.2020.3000349.
|
|
[28]
|
T. G. Kolda, B. W. Bader and J. P. Kenny, Higher-order Web link analysis using multilinear algebra, IEEE International Conference on Data Mining, (2005), 242–249.
doi: 10.1109/ICDM.2005.77.
|
|
[29]
|
T. G. Kolda and B. W. Bader, Tensor decompositions and applications, SIAM Review, 51 (2009), 455-500.
doi: 10.1137/07070111X.
|
|
[30]
|
M. E. Kilmer, K. Braman, N. Hao and R. C. Hoover, Third-order tensors as operators on matrices: A theoretical and computational framework with applications in imaging, SIAM Journal on Matrix Analysis and Applications, 34 (2013), 148-172.
doi: 10.1137/110837711.
|
|
[31]
|
N. Komodakis, Image inpainting, IEEE Conference on Computer Vision and Pattern Recognition, 1 (2006), 442-452.
|
|
[32]
|
R.-J. Lai and J. Li, Manifold based low-rank regularization for image restoration and semi-supervised learning, Journal of Scientific Computing, 74 (2018), 1241-1263.
doi: 10.1007/s10915-017-0492-x.
|
|
[33]
|
J. I. Latorre, Image Compression and Entanglement, Computer Science, 2005.
|
|
[34]
|
F. Li, M. K. Ng and R. J. Plemmons, Coupled segmentation and denoising/deblurring models for hyperspectral material identification, Numerical Linear Algebra with Applications, 19 (2012), 153-173.
doi: 10.1002/nla.750.
|
|
[35]
|
Y.-P. Liu, Z. Long and C. Zhu, Image completion using low tensor tree rank and total variation minimization, IEEE Transactions on Multimedia, 21 (2019), 338-350.
doi: 10.1109/TMM.2018.2859026.
|
|
[36]
|
Y.-Y. Liu, F.-H. Shang, L.-C. Jiao, J. Cheng and H. Cheng, Trace norm regularized CANDECOMP/PARAFAC decomposition with missing data, IEEE Transactions on Cybernetics, 45 (2015), 2437-2448.
doi: 10.1109/TCYB.2014.2374695.
|
|
[37]
|
Y.-P. Liu, Z. Long, H.-Y. Huang and C. Zhu, Low CP rank and tucker rank tensor completion for estimating missing components in image data, IEEE Transactions on Circuits and Systems for Video Technology, 30 (2020), 944-954.
doi: 10.1109/TCSVT.2019.2901311.
|
|
[38]
|
J. Liu, P. Musialski, P. Wonka and J. Ye, Tensor completion for estimating missing values in visual data, IEEE Transactions on Pattern Analysis and Machine Intelligence, 35 (2013), 208-220.
doi: 10.1109/TPAMI.2012.39.
|
|
[39]
|
C.-Y. Lu, J.-S. Feng, Y.-D. Chen, W. Liu, Z.-C. Lin and S.-C. Yan, Tensor robust principal component analysis: Exact recovery of corrupted low-rank tensors via convex optimization, IEEE Conference on Computer Vision and Pattern Recognition, (2016), 5249–5257.
doi: 10.1109/CVPR.2016.567.
|
|
[40]
|
C.-Y. Lu, J.-S. Feng, Z.-C. Lin and S.-C. Yan, Exact Low Tubal Rank Tensor Recovery from Gaussian Measurements, International Joint Conference on Artificial Intelligence, 2018.
doi: 10.24963/ijcai.2018/347.
|
|
[41]
|
I. V. Oseledets, Tensor-train decomposition, SIAM Journal on Scientific Computing, 33 (2011), 2295-2317.
doi: 10.1137/090752286.
|
|
[42]
|
S. Osher, Z.-Q. Shi and W. Zhu, Low dimensional manifold model for image processing, SIAM Journal on Imaging Sciences, 10 (2017), 1669-1690.
doi: 10.1137/16M1058686.
|
|
[43]
|
E. E. Papalexakis, C. Faloutsos and N. D. Sidiropoulos, Tensors for data mining and data fusion: Models, applications, and scalable algorithms, ACM Transactions on Intelligent Systems and Technology, 8 (2017), 16: 1–16: 44.
doi: 10.1145/2915921.
|
|
[44]
|
Z.-Q. Shi, S. Osher and W. Zhu, Weighted nonlocal laplacian on interpolation from sparse data, Journal of Scientific Computing, 73 (2017), 1164-1177.
doi: 10.1007/s10915-017-0421-z.
|
|
[45]
|
N. D. Sidiropoulos, L. De Lathauwer, X. Fu, K. Huang, E. E. Papalexakis and C. Faloutsos, Tensor decomposition for signal processing and machine learning, IEEE Transactions on Signal Processing, 65 (2017), 3551-3582.
doi: 10.1109/TSP.2017.2690524.
|
|
[46]
|
G. W. Stewart, Matrix Algorithms, Vol I: Basic Decomposition, SIAM, 2001.
doi: 10.1137/1.9780898718058.
|
|
[47]
|
W. Wang, V. Aggarwal and S. Aeron, Tensor completion by alternating minimization under the tensor train (TT) model, preprint, arXiv: 1609.05587.
|
|
[48]
|
Y. Wang, J.-J. Peng, Q. Zhao, Y. Leung, X.-L. Zhao and D.-Y. Meng, Hyperspectral image restoration via total variation regularized low-rank tensor decomposition, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 11 (2018), 1227-1243.
|
|
[49]
|
Y. Wang, D.-Y. Meng and M. Yuan, Sparse recovery: From vectors to tensors, National Science Review, 5 (2018), 756-767.
doi: 10.1093/nsr/nwx069.
|
|
[50]
|
T. Xie, S.-T. Li, L.-Y. Fang and L.-C. Liu, Tensor completion via nonlocal low-rank regularization, IEEE Transactions on Cybernetics, 49 (2019), 2344-2354.
doi: 10.1109/TCYB.2018.2825598.
|
|
[51]
|
Z.-M. Xing, M.-Y. Zhou, A. Castrodad, G. Sapiro and L. Carin, Dictionary learning for noisy and incomplete hyperspectral images, SIAM Journal on Imaging Sciences, 5 (2012), 33-56.
doi: 10.1137/110837486.
|
|
[52]
|
B. Xiong, Q.-G. Liu, J.-J. Xiong, S.-Q. Li, S.-S. Wang and D. Liang, Field-of-experts filters guided tensor completion, IEEE Transactions on Multimedia, 20 (2018), 2316-2329.
doi: 10.1109/TMM.2018.2806225.
|
|
[53]
|
R.-T. Xu, Y. Xu and Y.-H. Quan, Factorized tensor dictionary learning for visual tensor data completion, IEEE Transactions on Multimedia, (2020), 1–14.
|
|
[54]
|
Y.-Y. Xu, R.-R. Hao, W.-T. Yin and Z.-X. Su, Parallel matrix factorization for low-rank tensor completion, Inverse Problems and Imaging, 9 (2017), 601-624.
doi: 10.3934/ipi.2015.9.601.
|
|
[55]
|
J.-H. Yang, X.-L. Zhao, T.-H. Ma, M. Ding and T.-Z. Huang, Tensor train rank minimization with hybrid smoothness for visual data recovery, Applied Mathematical Modelling, 81 (2020), 711-726.
doi: 10.1016/j.apm.2020.01.039.
|
|
[56]
|
J.-H. Yang, X.-L. Zhao, T.-H. Ma, Y. Chen, T.-Z. Huang and M. Ding, Remote sensing image destriping using unidirectional hybrid total variation and nonconvex low-rank regularization, Journal of Computational and Applied Mathematics, 363 (2020), 124-144.
doi: 10.1016/j.cam.2019.06.004.
|
|
[57]
|
T. Yokota, Q.-B. Zhao, C. Li and A. Cichocki, Smooth PARAFAC decomposition for tensor completion, IEEE Transactions on Signal Processing, 64 (2016), 5423-5436.
doi: 10.1109/TSP.2016.2586759.
|
|
[58]
|
Q.-B. Zhao, L-Q. Zhang and A. Cichocki, Bayesian CP factorization of incomplete tensors with automatic rank determination, IEEE Transactions on Pattern Analysis and Machine Intelligence, 37 (2015), 1751-1763.
doi: 10.1109/TPAMI.2015.2392756.
|
|
[59]
|
X.-L. Zhao, W. Wang, T.-Y. Zeng, T.-Z. Huang and M. K. Ng, Total variation structured total least squares method for image restoration, SIAM Journal on Scientific Computing, 35 (2013), 1304-1320.
doi: 10.1137/130915406.
|
|
[60]
|
X.-J. Zhang, A nonconvex relaxation approach to low-rank tensor completion, IEEE Transactions on Neural Networks and Learning Systems, 30 (2019), 1659-1671.
doi: 10.1109/TNNLS.2018.2872583.
|
|
[61]
|
K.-B. Zhang, X.-B. Gao, D. -C.Tao and X.-L. Li, Single image super-resolution with non-local means and steering kernel regression, IEEE Transactions on Image Processing, 21 (2012), 4544-4556.
doi: 10.1109/TIP.2012.2208977.
|
|
[62]
|
Z. Zhang, G. Ely and S. Aeron, Exact tensor completion using t-SVD, IEEE Transactions on Signal Processing, 65 (2017), 1511-1526.
doi: 10.1109/TSP.2016.2639466.
|
|
[63]
|
Y.-B. Zheng, T.-Z. Huang, X.-L. Zhao, Y. Chen and W. He, Double-factor-regularized low-rank tensor factorization for mixed noise removal in hyperspectral image, IEEE Transactions on Geoscience and Remote Sensing, (2020), 1–15.
|
Download:
{{journal.titleEn}} 
