[1] Bai, Z.-Z., Pan, J.-Y.: Matrix Analysis and Computations. SIAM, Philadelphia (2021)
[2] Cai, S.-T., Luo, Q.-L., Yang, M., Li, W., Xiao, M.-Q.: Tensor robust principal component analysis via non-convex low rank approximation. Appl. Sci. 9(7), 1411 (2019)
[3] Chan, S.H., Khoshabeh, R., Gibson, K.B., Gill, P.E., Nguyen, T.Q.: An augmented Lagrangian method for total variation video restoration. IEEE Trans. Image Process. 20(11), 3097-3111 (2011)
[4] Cichocki, A., Mandic, D., De Lathauwer, L., Zhou, G.-X., Zhao, Q.-B., Caiafa, C., Phan, H.A.: Tensor decompositions for signal processing applications: from two-way to multiway component analysis. IEEE Signal Process. Mag. 32(2), 145-163 (2015)
[5] De Silva, V., Lim, L.H.: Tensor rank and the ill-posedness of the best low-rank approximation problem. SIAM J. Matrix Anal. Appl. 30(3), 1084-1127 (2008)
[6] Deisenroth, M.P., Faisal, A.A., Ong, C.S.: Mathematics for Machine Learning. Cambridge University Press, Cambridge (2020)
[7] Donoho, D.L.: De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41(3), 613-627 (1995)
[8] Gandy, S., Recht, B., Yamada, I.: Tensor completion and low-n-rank tensor recovery via convex optimization. Inverse Probl. 27(2), 025010 (2011)
[9] Gao, K.-X, Huang, Z.-H.: Tensor robust principal component analysis via tensor fibered rank and minimization. SIAM J. Imaging Sci. 16(1), 423-460 (2023)
[10] Gao, S.-Q., Zhuang, X.-H.: Robust approximations of low-rank minimization for tensor completion. Neurocomputing 379, 319-333 (2020)
[11] Georghiades, A.S., Belhumeur, P.N., Kriegman, D.J.: From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans. Pattern Anal. Mach. Intell. 23(6), 643-660 (2001)
[12] Golub, G.H., Van Loan, C.F.: Matrix Computations, 4th edn. Johns Hopkins University Press, Baltimore (2013)
[13] Gu, S.-H., Xie, Q., Meng, D.-Y., Zuo, W.-M., Feng, X.-C., Zhang, L.: Weighted nuclear norm minimization and its applications to low level vision. Int. J. Comput. Vis. 121, 183-208 (2017)
[14] Huang, L.-T., De Almeida, A.L., So, H.C.: Target estimation in bistatic MIMO radar via tensor completion. Signal Process. 120, 654-659 (2016)
[15] Jiang, T.-X., Huang, T.-Z., Zhao, X.-L., Deng, L.-J.: Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm. J. Comput. Appl. Math. 372, 112680 (2020)
[16] Jiang, T.-X., Huang, T.-Z., Zhao, X.-L., Deng, L.-J., Wang, Y.: Fastderain: a novel video rain streak removal method using directional gradient priors. IEEE Trans. Image Process. 28(4), 2089-2102 (2018)
[17] Kang, Z., Peng, C., Cheng, Q.: Robust PCA via nonconvex rank approximation. In: 2015 IEEE International Conference on Data Mining, pp. 211-220. IEEE (2015)
[18] Kiers, H.A.: Towards a standardized notation and terminology in multiway analysis. J. Chemom. A J. Chemom. Soc. 14(3), 105-122 (2000)
[19] Kilmer, M.E., Braman, K., Hao, N., Hoover, R.C.: Third-order tensors as operators on matrices: a theoretical and computational framework with applications in imaging. SIAM J. Matrix Anal. Appl. 34(1), 148-172 (2013)
[20] Kilmer, M.E., Martin, C.D.: Factorization strategies for third-order tensors. Linear Algebra Appl. 435(3), 641-658 (2011)
[21] Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51(3), 455-500 (2009)
[22] Komodakis, N. Image completion using global optimization. In: 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’06), vol. 1, pp. 442-452. IEEE (2006)
[23] Korah, T., Rasmussen, C.: Spatiotemporal inpainting for recovering texture maps of occluded building facades. IEEE Trans. Image Process. 16(9), 2262-2271 (2007)
[24] Li, M.-H., Li, W., Chen, Y.-N., Xiao, M.-Q.: The nonconvex tensor robust principal component analysis approximation model via the weighted \begin{document}$ \ell _p $\end{document}-norm regularization. J. Sci. Comput. 89(3), 67 (2021)
[25] Li, N., Li, B.-X.: Tensor completion for on-board compression of hyperspectral images. In: 2010 IEEE International Conference on Image Processing, pp. 517-520. IEEE (2010)
[26] Liu, G.-C., Lin, Z.-C., Yan, S.-C., Sun, J., Yu, Y., Ma, Y.: Robust recovery of subspace structures by low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 171-184 (2012)
[27] Liu, Y.-P., Long, Z., Zhu, C.: Image completion using low tensor tree rank and total variation minimization. IEEE Trans. Multimed. 21(2), 338-350 (2018)
[28] Lu, C.-Y., Feng, J.-S., Chen, Y.-D., Liu, W., Lin, Z.-C., Yan, S.-C.: Tensor robust principal component analysis with a new tensor nuclear norm. IEEE Trans. Pattern Anal. Mach. Intell. 42(4), 925-938 (2019)
[29] Lu, Z.-S.: Iterative reweighted minimization methods for \begin{document}$ \ell _p $\end{document} regularized unconstrained nonlinear programming. Math. Program. 147(1/2), 277-307 (2014)
[30] Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming. Springer, Switzerland (2016)
[31] Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001, vol. 2, pp. 416-423. IEEE (2001)
[32] Miao, Y., Qi, L.-Q., Wei, Y.-M.: Generalized tensor function via the tensor singular value decomposition based on the T-product. Linear Algebra Appl. 590, 258-303 (2020)
[33] Moreau, J.J.: Proximité et dualité dans un espace hilbertien. Bull Soc. Math. Fr. 93, 273-299 (1965)
[34] Oseledets, I.V.: Tensor-train decomposition. SIAM J. Sci. Comput. 33(5), 2295-2317 (2011)
[35] Sidiropoulos, N.D., De Lathauwer, L., Fu, X., Huang, K., Papalexakis, E.E., Faloutsos, C.: Tensor decomposition for signal processing and machine learning. IEEE Trans. Signal Process. 65(13), 3551-3582 (2017)
[36] Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600-612 (2004)
[37] Xu, W.-H., Zhao, X.-L., Ji, T.-Y., Miao, J.-Q., Ma, T.-H.: Laplace function based nonconvex surrogate for low-rank tensor completion. Signal Process. Image Commun. 73, 62-69 (2019)
[38] Xue, J.-Z., Zhao, Y.-Q., Liao, W.-Z., Chan, J.C.W.: Nonconvex tensor rank minimization and its applications to tensor recovery. Inf. Sci. 503, 109-128 (2019)
[39] Yang, M., Luo, Q.-L., Li, W., Xiao, M.-Q.: Nonconvex 3D array image data recovery and pattern recognition under tensor framework. Pattern Recogn. 122, 108311 (2022)
[40] Yang, M., Luo, Q.-L., Li, W., Xiao, M.-Q.: 3-D array image data completion by tensor decomposition and nonconvex regularization approach. IEEE Trans. Signal Process. 70, 4291-4304 (2022)
[41] Zhou, M.-Y., Liu, Y.-P., Long, Z., Chen, L.-X., Zhu, C.: Tensor rank learning in CP decomposition via convolutional neural network. Signal Process. Image Commun. 73, 12-21 (2019)
[42] Zuo, W.-M., Meng, D.-Y., Zhang, L., Feng, X.-C., Zhang, D.: A generalized iterated shrinkage algorithm for non-convex sparse coding. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 217-224. IEEE (2013)
