TY - JOUR
T1 - Robust Tensor SVD and Recovery With Rank Estimation
AU - Shi, Qiquan
AU - Cheung, Yiu Ming
AU - Lou, Jian
N1 - Funding Information:
This work was supported in part by the National Natural Science Foundation of China under Grant 61672444; in part by the Hong Kong Baptist University (HKBU), Research Committee, Initiation Grant, Faculty Niche Research Areas (IGFNRA) 2018/19 under Grant RC-FNRA-IG/18-19/SCI/03
Publisher Copyright:
© 2013 IEEE.
PY - 2022/10
Y1 - 2022/10
N2 - Tensor singular value decomposition (t-SVD) has recently become increasingly popular for tensor recovery under partial and/or corrupted observations. However, the existing t-SVD-based methods neither make use of a rank prior nor provide an accurate rank estimation (RE), which would limit their recovery performance. From the practical perspective, the tensor RE problem is nontrivial and difficult to solve. In this article, we, therefore, aim to determine the correct rank of an intrinsic low-rank tensor from corrupted observations based on t-SVD and further improve recovery results with the estimated rank. Specifically, we first induce the equivalence of the tensor nuclear norm (TNN) of a tensor and its f-diagonal tensor. We then simultaneously minimize the reconstruction error and TNN of the f-diagonal tensor, leading to RE. Subsequently, we relax our model by removing the TNN regularizer to improve the recovery performance. Furthermore, we consider more general cases in the presence of missing data and/or gross corruptions by proposing robust tensor principal component analysis and robust tensor completion with RE. The robust methods can achieve successful recovery by refining the models with correct estimated ranks. Experimental results show that the proposed methods outperform the state-of-the-art methods with significant improvements.
AB - Tensor singular value decomposition (t-SVD) has recently become increasingly popular for tensor recovery under partial and/or corrupted observations. However, the existing t-SVD-based methods neither make use of a rank prior nor provide an accurate rank estimation (RE), which would limit their recovery performance. From the practical perspective, the tensor RE problem is nontrivial and difficult to solve. In this article, we, therefore, aim to determine the correct rank of an intrinsic low-rank tensor from corrupted observations based on t-SVD and further improve recovery results with the estimated rank. Specifically, we first induce the equivalence of the tensor nuclear norm (TNN) of a tensor and its f-diagonal tensor. We then simultaneously minimize the reconstruction error and TNN of the f-diagonal tensor, leading to RE. Subsequently, we relax our model by removing the TNN regularizer to improve the recovery performance. Furthermore, we consider more general cases in the presence of missing data and/or gross corruptions by proposing robust tensor principal component analysis and robust tensor completion with RE. The robust methods can achieve successful recovery by refining the models with correct estimated ranks. Experimental results show that the proposed methods outperform the state-of-the-art methods with significant improvements.
KW - Rank estimation (RE)
KW - robust tensor PCA (RTPCA)
KW - robust tensor recovery
KW - tensor completion (TC)
KW - tensor singular value decomposition (t-SVD)
UR - http://www.scopus.com/inward/record.url?scp=85104577860&partnerID=8YFLogxK
U2 - 10.1109/TCYB.2021.3067676
DO - 10.1109/TCYB.2021.3067676
M3 - Journal article
AN - SCOPUS:85104577860
SN - 2168-2267
VL - 52
SP - 10667
EP - 10682
JO - IEEE Transactions on Cybernetics
JF - IEEE Transactions on Cybernetics
IS - 10
ER -