\begin{thebibliography}{34}
\providecommand{\natexlab}[1]{#1}
\providecommand{\url}[1]{\texttt{#1}}
\expandafter\ifx\csname urlstyle\endcsname\relax
  \providecommand{\doi}[1]{doi: #1}\else
  \providecommand{\doi}{doi: \begingroup \urlstyle{rm}\Url}\fi

\bibitem[Agustsson and Timofte(2017)]{Agustsson_2017_CVPR_Workshops}
Eirikur Agustsson and Radu Timofte.
\newblock {NTIRE} 2017 challenge on single image super-resolution: Dataset and
  study.
\newblock In \emph{The IEEE Conference on Computer Vision and Pattern
  Recognition (CVPR) Workshops}, July 2017.

\bibitem[Ahmadi-Asl et~al.(2020)Ahmadi-Asl, Cichocki, Phan, Asante-Mensah,
  Ghazani, Tanaka, and Oseledets]{ahmadi2020randomized}
Salman Ahmadi-Asl, Andrzej Cichocki, Anh~Huy Phan, Maame~G Asante-Mensah,
  Mirfarid~Musavian Ghazani, Toshihisa Tanaka, and Ivan Oseledets.
\newblock Randomized algorithms for fast computation of low rank tensor ring
  model.
\newblock \emph{Machine Learning: Science and Technology}, 2\penalty0
  (1):\penalty0 011001, 2020.

\bibitem[Carroll and Chang(1970)]{carroll1970analysis}
J~Douglas Carroll and Jih-Jie Chang.
\newblock Analysis of individual differences in multidimensional scaling via an
  {N-way} generalization of {“Eckart-Young”} decomposition.
\newblock \emph{Psychometrika}, 35\penalty0 (3):\penalty0 283--319, 1970.

\bibitem[Chen et~al.(2013)Chen, Hsu, and Liao]{chen2013simultaneous}
Yi-Lei Chen, Chiou-Ting Hsu, and Hong-Yuan~Mark Liao.
\newblock Simultaneous tensor decomposition and completion using factor priors.
\newblock \emph{IEEE Transactions on Pattern Analysis and Machine
  Intelligence}, 36\penalty0 (3):\penalty0 577--591, 2013.

\bibitem[Goldfarb and Qin(2014)]{goldfarb2014robust}
Donald Goldfarb and Zhiwei Qin.
\newblock Robust low-rank tensor recovery: Models and algorithms.
\newblock \emph{SIAM Journal on Matrix Analysis and Applications}, 35\penalty0
  (1):\penalty0 225--253, 2014.

\bibitem[Gu et~al.(2014)Gu, Gui, and Han]{gu2014robust}
Quanquan Gu, Huan Gui, and Jiawei Han.
\newblock Robust tensor decomposition with gross corruption.
\newblock \emph{Advances in Neural Information Processing Systems}, 27, 2014.

\bibitem[He et~al.(2011)He, Hu, Zheng, and Kong]{he2011robust}
Ran He, Bao-Gang Hu, Wei-Shi Zheng, and Xiang-Wei Kong.
\newblock Robust principal component analysis based on maximum correntropy
  criterion.
\newblock \emph{IEEE Transactions on Image Processing}, 20\penalty0
  (6):\penalty0 1485--1494, 2011.

\bibitem[He et~al.(2014)He, Hu, Yuan, Wang, et~al.]{he2014robust}
Ran He, Baogang Hu, Xiaotong Yuan, Liang Wang, et~al.
\newblock \emph{Robust recognition via information theoretic learning}.
\newblock SpringerBriefs in Computer Science. Springer Cham, 2014.

\bibitem[He et~al.(2019)He, Wang, Li, Qin, and Chen]{he2019robust}
Yicong He, Fei Wang, Yingsong Li, Jing Qin, and Badong Chen.
\newblock Robust matrix completion via maximum correntropy criterion and
  half-quadratic optimization.
\newblock \emph{IEEE Transactions on Signal Processing}, 68:\penalty0 181--195,
  2019.

\bibitem[Huang et~al.(2020)Huang, Liu, Long, and Zhu]{huang2020robust}
Huyan Huang, Yipeng Liu, Zhen Long, and Ce~Zhu.
\newblock Robust low-rank tensor ring completion.
\newblock \emph{IEEE Transactions on Computational Imaging}, 6:\penalty0
  1117--1126, 2020.

\bibitem[Jiang and Ng(2019)]{jiang2019robust}
Qiang Jiang and Michael Ng.
\newblock Robust low-tubal-rank tensor completion via convex optimization.
\newblock In \emph{IJCAI}, pages 2649--2655, 2019.

\bibitem[Kolda and Bader(2009)]{kolda2009tensor}
Tamara~G Kolda and Brett~W Bader.
\newblock Tensor decompositions and applications.
\newblock \emph{SIAM review}, 51\penalty0 (3):\penalty0 455--500, 2009.

\bibitem[Koren et~al.(2009)Koren, Bell, and Volinsky]{koren2009matrix}
Yehuda Koren, Robert Bell, and Chris Volinsky.
\newblock Matrix factorization techniques for recommender systems.
\newblock \emph{Computer}, 42\penalty0 (8):\penalty0 30--37, 2009.

\bibitem[Li et~al.(2017)Li, Feng, Jin, Zhang, Xu, and Yan]{li2017online}
Ping Li, Jiashi Feng, Xiaojie Jin, Luming Zhang, Xianghua Xu, and Shuicheng
  Yan.
\newblock Online robust low-rank tensor learning.
\newblock In \emph{Proceedings of the 26th International Joint Conference on
  Artificial Intelligence}, pages 2180--2186, 2017.

\bibitem[Li and So(2021)]{li2021robust}
Xiao~Peng Li and Hing~Cheung So.
\newblock Robust low-rank tensor completion based on tensor ring rank via
  $\ell_{p,\epsilon}$-norm.
\newblock \emph{IEEE Transactions on Signal Processing}, 69:\penalty0
  3685--3698, 2021.

\bibitem[Li et~al.(2023)Li, Wang, Shi, So, and Sidiropoulos]{li2023robust}
Xiao~Peng Li, Zhi-Yong Wang, Zhang-Lei Shi, Hing~Cheung So, and Nicholas~D
  Sidiropoulos.
\newblock Robust tensor completion via capped {Frobenius} norm.
\newblock \emph{IEEE Transactions on Neural Networks and Learning Systems},
  2023.

\bibitem[Liu et~al.(2007)Liu, Pokharel, and Pr{\'\i}ncipe]{liu2007correntropy}
Weifeng Liu, Puskal~P Pokharel, and Jos{\'e}~C Pr{\'\i}ncipe.
\newblock Correntropy: Properties and applications in {non-Gaussian} signal
  processing.
\newblock \emph{IEEE Transactions on Signal Processing}, 55\penalty0
  (11):\penalty0 5286--5298, 2007.

\bibitem[Malik and Becker(2021)]{malik2021sampling}
Osman~Asif Malik and Stephen Becker.
\newblock A sampling-based method for tensor ring decomposition.
\newblock In \emph{International Conference on Machine Learning}, pages
  7400--7411. PMLR, 2021.

\bibitem[Nikolova and Ng(2005)]{nikolova2005analysis}
Mila Nikolova and Michael~K Ng.
\newblock Analysis of half-quadratic minimization methods for signal and image
  recovery.
\newblock \emph{SIAM Journal on Scientific computing}, 27\penalty0
  (3):\penalty0 937--966, 2005.

\bibitem[Oseledets(2011)]{oseledets2011tensor}
Ivan~V Oseledets.
\newblock Tensor-train decomposition.
\newblock \emph{SIAM Journal on Scientific Computing}, 33\penalty0
  (5):\penalty0 2295--2317, 2011.

\bibitem[Qiu et~al.(2021)Qiu, Bai, Ng, and Zhang]{qiu2021robust}
Duo Qiu, Minru Bai, Michael~K Ng, and Xiongjun Zhang.
\newblock Robust low-rank tensor completion via transformed tensor nuclear norm
  with total variation regularization.
\newblock \emph{Neurocomputing}, 435:\penalty0 197--215, 2021.

\bibitem[Sidiropoulos et~al.(2017)Sidiropoulos, De~Lathauwer, Fu, Huang,
  Papalexakis, and Faloutsos]{sidiropoulos2017tensor}
Nicholas~D Sidiropoulos, Lieven De~Lathauwer, Xiao Fu, Kejun Huang, Evangelos~E
  Papalexakis, and Christos Faloutsos.
\newblock Tensor decomposition for signal processing and machine learning.
\newblock \emph{IEEE Transactions on Signal Processing}, 65\penalty0
  (13):\penalty0 3551--3582, 2017.

\bibitem[Tanner and Wei(2016)]{tanner2016low}
Jared Tanner and Ke~Wei.
\newblock Low rank matrix completion by alternating steepest descent methods.
\newblock \emph{Applied and Computational Harmonic Analysis}, 40\penalty0
  (2):\penalty0 417--429, 2016.

\bibitem[Tucker(1966)]{tucker1966some}
Ledyard~R Tucker.
\newblock Some mathematical notes on three-mode factor analysis.
\newblock \emph{Psychometrika}, 31\penalty0 (3):\penalty0 279--311, 1966.

\bibitem[Vervliet and De~Lathauwer(2015)]{vervliet2015randomized}
Nico Vervliet and Lieven De~Lathauwer.
\newblock A randomized block sampling approach to canonical polyadic
  decomposition of large-scale tensors.
\newblock \emph{IEEE Journal of Selected Topics in Signal Processing},
  10\penalty0 (2):\penalty0 284--295, 2015.

\bibitem[Wang et~al.(2020)Wang, Jin, and Tang]{wang2020robust}
Andong Wang, Zhong Jin, and Guoqing Tang.
\newblock Robust tensor decomposition via t-{SVD}: Near-optimal statistical
  guarantee and scalable algorithms.
\newblock \emph{Signal Processing}, 167:\penalty0 107319, 2020.

\bibitem[Wang et~al.(2017)Wang, Aggarwal, and Aeron]{wang2017efficient}
Wenqi Wang, Vaneet Aggarwal, and Shuchin Aeron.
\newblock Efficient low rank tensor ring completion.
\newblock In \emph{Proceedings of the IEEE International Conference on Computer
  Vision}, pages 5697--5705, 2017.

\bibitem[Wang et~al.(2016)Wang, Tang, and Li]{wang2016correntropy}
Yulong Wang, Yuan~Yan Tang, and Luoqing Li.
\newblock Correntropy matching pursuit with application to robust digit and
  face recognition.
\newblock \emph{IEEE Transactions on Cybernetics}, 47\penalty0 (6):\penalty0
  1354--1366, 2016.

\bibitem[Yamaguchi and Hayashi(2017)]{yamaguchi2017tensor}
Yuto Yamaguchi and Kohei Hayashi.
\newblock Tensor decomposition with missing indices.
\newblock In \emph{International Joint Conferences on Artificial Intelligence
  (IJCAI)}, volume~17, pages 3217--3223, 2017.

\bibitem[Yang et~al.(2015)Yang, Feng, and Suykens]{yang2015robust}
Yuning Yang, Yunlong Feng, and Johan~AK Suykens.
\newblock Robust low-rank tensor recovery with regularized redescending
  {M-estimator}.
\newblock \emph{IEEE Transactions on Neural Networks and Learning Systems},
  27\penalty0 (9):\penalty0 1933--1946, 2015.

\bibitem[Yu et~al.(2019)Yu, Li, Zhao, and Zhao]{yu2019tensor}
Jinshi Yu, Chao Li, Qibin Zhao, and Guoxu Zhao.
\newblock Tensor-ring nuclear norm minimization and application for visual:
  Data completion.
\newblock In \emph{IEEE International Conference on Acoustics, Speech and
  Signal Processing (ICASSP)}, pages 3142--3146, 2019.

\bibitem[Yu et~al.(2020)Yu, Zhou, Li, Zhao, and Xie]{yu2020low}
Jinshi Yu, Guoxu Zhou, Chao Li, Qibin Zhao, and Shengli Xie.
\newblock Low tensor-ring rank completion by parallel matrix factorization.
\newblock \emph{IEEE Transactions on Neural Networks and Learning Systems},
  32\penalty0 (7):\penalty0 3020--3033, 2020.

\bibitem[Yuan et~al.(2019)Yuan, Li, Cao, and Zhao]{yuan2019randomized}
Longhao Yuan, Chao Li, Jianting Cao, and Qibin Zhao.
\newblock Randomized tensor ring decomposition and its application to
  large-scale data reconstruction.
\newblock In \emph{IEEE International Conference on Acoustics, Speech and
  Signal Processing (ICASSP)}, pages 2127--2131, 2019.

\bibitem[Zhao et~al.(2016)Zhao, Zhou, Xie, Zhang, and Cichocki]{zhao2016tensor}
Qibin Zhao, Guoxu Zhou, Shengli Xie, Liqing Zhang, and Andrzej Cichocki.
\newblock Tensor ring decomposition.
\newblock \emph{arXiv preprint arXiv:1606.05535}, 2016.

\end{thebibliography}
