TY - JOUR
T1 - Tensor denoising using low-rank tensor train decomposition
AU - Gong, Xiao
AU - Chen, Wei
AU - Chen, Jie
AU - Ai, Bo
N1 - Publisher Copyright:
© 1994-2012 IEEE.
PY - 2020
Y1 - 2020
N2 - Exploiting the latent low-rankness of tensors is crucial in tensor denoising. Classically, many methods use the Tucker model to find the low-rank structure of a tensor. Recently, the tensor train (TT) model has drawn wide attention owing to its powerful representation ability, and well-balanced matricization scheme for a tensor, and it has been successfully applied to various problems in signal processing, and machine learning applications. In this letter, we propose a tensor denoising method using the TT singular value decomposition, and information criteria, where we leverage the minimum description length to automatically estimate the TT rank. Furthermore, we establish the relationship between Tucker decomposition, and TT decomposition. In specific, the low Tucker rank of a tensor is the sufficient but unnecessary condition to the low TT rank. It unveils in theory the potential advantages of the TT model in characterizing the latent low-rankness of tensor. Denoising experiments on both synthetic data, and real HSI dataset demonstrate its superiority against Tucker-based methods.
AB - Exploiting the latent low-rankness of tensors is crucial in tensor denoising. Classically, many methods use the Tucker model to find the low-rank structure of a tensor. Recently, the tensor train (TT) model has drawn wide attention owing to its powerful representation ability, and well-balanced matricization scheme for a tensor, and it has been successfully applied to various problems in signal processing, and machine learning applications. In this letter, we propose a tensor denoising method using the TT singular value decomposition, and information criteria, where we leverage the minimum description length to automatically estimate the TT rank. Furthermore, we establish the relationship between Tucker decomposition, and TT decomposition. In specific, the low Tucker rank of a tensor is the sufficient but unnecessary condition to the low TT rank. It unveils in theory the potential advantages of the TT model in characterizing the latent low-rankness of tensor. Denoising experiments on both synthetic data, and real HSI dataset demonstrate its superiority against Tucker-based methods.
KW - Denoising
KW - low rank
KW - tensor decomposition
UR - http://www.scopus.com/inward/record.url?scp=85092697154&partnerID=8YFLogxK
U2 - 10.1109/LSP.2020.3025038
DO - 10.1109/LSP.2020.3025038
M3 - 文章
AN - SCOPUS:85092697154
SN - 1070-9908
VL - 27
SP - 1685
EP - 1689
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
M1 - 9200561
ER -