Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

Low-rank tensor completion for visual data recovery via the tensor train rank-1 decomposition

Low-rank tensor completion for visual data recovery via the tensor train rank-1 decomposition

For access to this article, please select a purchase option:

Buy article PDF
$19.95
(plus tax if applicable)
Buy Knowledge Pack
10 articles for $120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Image Processing — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

In this study, the authors study the problem of tensor completion, in particular for three-dimensional arrays such as visual data. Previous works have shown that the low-rank constraint can produce impressive performances for tensor completion. These works are often solved by means of Tucker rank. However, Tucker rank does not capture the intrinsic correlation of the tensor entries. Therefore, the authors propose a new proximal operator for the approximation of tensor nuclear norms based on tensor-train rank-1 decomposition via the singular value decomposition. The proximal operator will perform a soft-thresholding operation on tensor singular values. In addition, the low-rank constraint can capture the global structure of data well, but it does not exploit local smooth of visual data. Therefore, they integrate total variation as a regularisation term into low-rank tensor completion. Finally, they use a primal–dual splitting to achieve optimisation. Experimental results have shown that the proposed method, can preserve the multi-dimensional nature inherent in the data, and thus provide superior results over many state-of-the-art tensor completion techniques.

References

    1. 1)
      • 34. Fazel, M.: ‘Matrix rank minimization with applications’, Ph.D. dissertation, Dept. Elect. Sci., Stanford Univ., Stanford, CA, USA, 2002, pp. 1130.
    2. 2)
      • 42. Wang, Z., Bovik, A.C., Sheikh, H.R., et al: ‘Image quality assessment: from error visibility to structural similarity’, IEEE Trans. Image Process., 2004, 13, (4), pp. 600612.
    3. 3)
      • 6. Wang, H., Cen, Y., He, Z., et al: ‘Robust generalized low-rank decomposition of multimatrices for image recovery’, IEEE Trans. Multimed., 2017, 19, (5), pp. 969983.
    4. 4)
      • 46. Gu, K., Zhai, G., Yang, X., et al: ‘Using free energy principle for blind image quality assessment’, IEEE Trans. Multimed., 2015, 17, (1), pp. 5063.
    5. 5)
      • 16. Harshman, R.: ‘Foundations of the parafac procedure: model and conditions for an ‘explanatory’ multi-mode factor analysis’, UCLA Work. Pap. Phonetics, 1970, 16, pp. 184.
    6. 6)
      • 5. Jiang, T.-X., Huang, T.-Z., Zhao, X.-L, et al: ‘Matrix factorization for low-rank tensor completion using framelet prior’, Inf. Sci., 2018, 436, pp. 403417.
    7. 7)
      • 13. Romera-Paredes, B., Pontil, M.: ‘A new convex relaxation for tensor completion’, Proc. Conf. Neutral Information Processing Systems, Lake Tahoe, USA, 2013, pp. 29672975.
    8. 8)
      • 30. Yokota, T., Hontani, H.: ‘Simultaneous visual data completion and denoising based on tensor rank and total variation minimization and its primal-dual splitting algorithm’. IEEE Conf. on Computer Vision and Pattern Recognition, Honolulu, USA, 2017, pp. 37323740.
    9. 9)
      • 29. Li, X., Ye, Y., Xu, X.: ‘Low-rank tensor completion with total variation for visual data inpainting’. 31st AAAI Conf. on Artificial Intelligence, San Francisco, USA, 2017, pp. 22102216.
    10. 10)
      • 32. Osher, S., Burger, M., Goldfarb, D., et al: ‘An iterative regularization method for total variation-based image restoration’, Multiscale Model. Simul., 2006, 4, (2), pp. 460489.
    11. 11)
      • 44. Gu, K., Li, L., Lu, H., et al: ‘A fast reliable image quality predictor by fusing micro- and macro-structures’, IEEE Trans. Ind. Electron., 2017, 64, (5), pp. 39033912.
    12. 12)
      • 18. Oseledets, I.: ‘Tensor-train decomposition’, SIAM J. Sci. Comput., 2011, 33, pp. 22952317.
    13. 13)
      • 26. Chen, Y.-L., Hsu, C.-T., Liao, H.-Y.: ‘Simultaneous tensor decomposition and completion using factor priors’, IEEE Trans. Pattern Anal. Mach. Intell., 2014, 36, (3), pp. 577591.
    14. 14)
      • 27. Filipovic, M., Jukic, A.: ‘Tucker factorization with missing data with application to low-n-rank tensor completion’, Multidim. Syst. Sign. Process., 2015, 26, (3), pp. 116.
    15. 15)
      • 37. Guo, X.-J., Ma, Y.: ‘Generalized tensor total variation minimization for visual data recovery?’. IEEE Conf. on Computer Vision and Pattern Recognition, Boston, USA, 2015, pp. 36033611.
    16. 16)
      • 31. Yang, L., Huang, Z.-H., Shi, X.-A.: ‘Fixed point iterative method for low n-rank tensor pursuit’, IEEE Trans. Signal Process., 2013, 61, (11), pp. 29522962.
    17. 17)
      • 24. Yokota, T., Zhao, Q., Cichocki, A.: ‘Smooth PARAFAC decomposition for tensor completion’, IEEE Trans. Signal Process., 2015, 64, (20), pp. 54235436.
    18. 18)
      • 21. Zhang, Z., Ely, G., Aeron, S., et al: ‘Novel methods for multilinear data completion and denoising based on tensor-SVD’. IEEE Conf. on Computer Vision and Pattern Recognition, Columbus, USA, 2014, pp. 38423849.
    19. 19)
      • 14. Wang, H., Nie, F., Huang, H.: ‘Low-rank tensor completion with spatio-temporal consistency’. 28th AAAI Conf. on Artificial Intelligence, Québec, Canada, 2014, pp. 28462852.
    20. 20)
      • 10. Liu, J., Musialski, P., Wonka, P., et al: ‘Tensor completion for estimating missing values in visual data’. 12th IEEE Int. Conf. on Computer Vision, Kyoto, Japan, 2009, pp. 21142121.
    21. 21)
      • 47. Maolin, C., Yimin, W.: ‘Randomized algorithms for the approximations of Tucker and the tensor train decompositions’, Adv. Comput. Math., 2019, 45, (1), pp. 395428.
    22. 22)
      • 9. Madathil, B., George, S.N.: ‘Twist tensor total variation regularized-reweighted nuclear norm based tensor completion for video missing area recovery’, Inf. Sci., 2018, 423, pp. 376397.
    23. 23)
      • 7. Yokota, T., Zdunek, R., Cichocki, A., et al: ‘Smooth nonnegative matrix and tensor factorizations for robust multi-way data analysis’, Signal Process., 2015, 113, pp. 234249.
    24. 24)
      • 40. Batselier, K., Liu, H., Wong, N.: ‘A constructive algorithm for decomposing a tensor into a finite sum of orthonormal rank-1 terms’, SIAM J. Matrix Anal. Appl., 2015, 36, (3), pp. 13151337.
    25. 25)
      • 1. Li, N., Li, B.: ‘Tensor completion for on-board compression of hyperspectral images’. 2010 17th IEEE Int. Conf. on Image Processing, Hong Kong, China, 2010, pp. 517520.
    26. 26)
      • 28. Gandy, S., Recht, B., Yamada, I.: ‘Tensor completion and low-n-rank tensor recovery via convex optimization’, Inverse Probl., 2011, 27, (2), pp. 119.
    27. 27)
      • 25. Bengua, J.A., Phiem, H.N., Tuan, H.D., et al: ‘Efficient tensor completion for color image and video recovery: low-rank tensor train’, IEEE Trans. Image Process., 2017, 26, (5), pp. 24662479.
    28. 28)
      • 43. Zhang, L., Zhang, L., Mou, X., et al: ‘FSIM: A feature similarity index for image quality assessment’, IEEE Trans. Image Process., 2011, 20, (8), p. 2378.
    29. 29)
      • 12. Yao, Q., Kwok, J.T.: ‘Colorization by patch-based local low-rank matrix completion’. 29th AAAI Conf. on Artificial Intelligence, Austin, USA, 2015, pp. 19591965.
    30. 30)
      • 15. Kolda, T.G., Bader, B.W.: ‘Tensor decompositions and applications’, SIAM Rev.., 2009, 51, (3), pp. 455500.
    31. 31)
      • 36. Cai, J.-F., Candès, E. J., Shen, Z. A.: ‘Singular value thresholding algorithm for matrix completion’, SIAM J. Optim., 2010, 20, (4), pp. 19561982.
    32. 32)
      • 23. Wang, W., Aggarwal, V., Aeron, S.: ‘Efficient low rank tensor ring completion’. IEEE Int. Conf. on Computer Vision, Venice, Italy, 2017, pp. 56985706.
    33. 33)
      • 38. Feng, S., Jian, C., Li, W., et al: ‘LRTV: MR image super-resolution with low-rank and total variation regularizations’, IEEE Trans. Med. Imaging, 2015, 34, (12), pp. 24592466.
    34. 34)
      • 4. Wu, Z., Wang, Q., Jin, J., et al: ‘Structure tensor total variation-regularized weighted nuclear norm minimization for hyperspectral image mixed denoising’, Signal Process., 2017, 131, pp. 202219.
    35. 35)
      • 41. Condat, L.: ‘A primal–dual splitting method for convex optimization involving lipschitzian, proximable and linear composite terms’, J. Optim. Theory Appl., 2013, 158, (2), pp. 460479.
    36. 36)
      • 3. Shang, F., Liu, Y., Cheng, J.: ‘Generalized higher-order tensor decomposition via parallel admm’. 28th AAAI Conf. on Artificial Intelligence, Québec, Canada, 2014, pp. 12791285.
    37. 37)
      • 19. Kilmer, M.E., Martin, C.D.: ‘Factorization strategies for third-order tensors’, Linear Algebr. Appl., 2011, 435, (3), pp. 641658.
    38. 38)
      • 33. He, W., Zhang, H., Zhang, L., et al: ‘Total-variation-regularized low-rank matrix factorization for hyperspectral image restoration’, IEEE Trans. Geosci. Remote Sens., 2015, 54, (1), pp. 178188.
    39. 39)
      • 22. Zhang, Z., Aeron, S.: ‘Exact tensor completion using t-SVD’, IEEE Trans. Signal Process., 2017, 65, (6), pp. 15111526.
    40. 40)
      • 20. Zhao, Q., Zhou, G., Xie, S., et al: ‘Tensor ring decomposition’, preprint arXiv:1606.05535, 2016, pp. 114.
    41. 41)
      • 8. Ji, T.-Y., Huang, T.-Z., Zhao, X.-L., et al: ‘A non-convex tensor rank approximation for tensor completion’, Appl. Math. Model., 2017, 48, pp. 410422.
    42. 42)
      • 2. Du, B., Zhang, M., Zhang, L., et al: ‘PLTD: patch-based low-rank tensor decomposition for hyperspectral images’, IEEE Trans. Multimed., 2017, 19, (1), pp. 6779.
    43. 43)
      • 35. Kurucz, M., Benczúr, A.A., Csalogány, K.: ‘Methods for large scale SVD with missing values’. Proc. of KDD Cup and Workshop, San Jose, USA, 2007, pp. 3138.
    44. 44)
      • 45. Gu, K., Zhai, G., Lin, W., et al: ‘No-reference image sharpness assessment in autoregressive parameter space’, IEEE Trans. Image Process., 2015, 24, (10), pp. 32183231.
    45. 45)
      • 39. Rudin, L.I., Osher, S., Fatemi, E.: ‘Nonlinear total variation based noise removal algorithms’, Phys. D, Nonlinear Phenom., 1992, 60, (1), pp. 259268.
    46. 46)
      • 17. Tucker, L.: ‘Some mathematical notes on three-mode factor analysis’, Psychometrika, 1996, 31, pp. 279311.
    47. 47)
      • 11. Liu, J., Musialski, P., Wonka, P., et al: ‘Tensor completion for estimating missing values in visual data’, IEEE Trans. Pattern Anal. Mach. Intell., 2013, 35, (1), pp. 208220.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-ipr.2018.6594
Loading

Related content

content/journals/10.1049/iet-ipr.2018.6594
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address