TY - JOUR
T1 - Augmented Lagrangian method for tensor low-rank and sparsity models in multi-dimensional image recovery
AU - Zhu, Hong
AU - Liu, Xiaoxia
AU - Huang, Lin
AU - Lu, Zhaosong
AU - Lu, Jian
AU - Ng, Michael K.
N1 - We would like to thank Mr. Jiawei Mao from the School of Mathematical Sciences at Shenzhen University for running the source codes of STTN for the case study in Section 6.4. This work was funded by the National Natural Science Foundation of China under grants U21A20455, 61972265, 11871348, 61872429, 11701383, 11701227 and 11971149, by the Natural Science Foundation of Guangdong Province of China under grant 2020B1515310008, by the Educational Commission of Guangdong Province of China under grant 2019KZDZX1007, by the PolyU internal grant P0040271, by the HKRGC GRF 12306616, 12200317, 12300218, 12300519 and 17201020. Also, X. Liu was supported by the School of Mathematical Sciences, Shenzhen University, Shenzhen 518060, China.
Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
PY - 2024/7/16
Y1 - 2024/7/16
N2 - Multi-dimensional images can be viewed as tensors and have often embedded a low-rankness property that can be evaluated by tensor low-rank measures. In this paper, we first introduce a tensor low-rank and sparsity measure and then propose low-rank and sparsity models for tensor completion, tensor robust principal component analysis, and tensor denoising. The resulting tensor recovery models are further solved by the augmented Lagrangian method with a convergence guarantee. And its augmented Lagrangian subproblem is computed by the proximal alternative method, in which each variable has a closed-form solution. Numerical experiments on several multi-dimensional image recovery applications show the superiority of the proposed methods over the state-of-the-art methods in terms of several quantitative quality indices and visual quality.
AB - Multi-dimensional images can be viewed as tensors and have often embedded a low-rankness property that can be evaluated by tensor low-rank measures. In this paper, we first introduce a tensor low-rank and sparsity measure and then propose low-rank and sparsity models for tensor completion, tensor robust principal component analysis, and tensor denoising. The resulting tensor recovery models are further solved by the augmented Lagrangian method with a convergence guarantee. And its augmented Lagrangian subproblem is computed by the proximal alternative method, in which each variable has a closed-form solution. Numerical experiments on several multi-dimensional image recovery applications show the superiority of the proposed methods over the state-of-the-art methods in terms of several quantitative quality indices and visual quality.
KW - Augmented Lagrangian method
KW - Image recovery
KW - Low-rank regularization
KW - Sparsity
UR - http://www.scopus.com/inward/record.url?scp=85198665842&partnerID=8YFLogxK
U2 - 10.1007/s10444-024-10170-3
DO - 10.1007/s10444-024-10170-3
M3 - Journal article
AN - SCOPUS:85198665842
SN - 1019-7168
VL - 50
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
M1 - 75
ER -
