@Article{NMTMA-17-727,
author = {Li , GenTu , ZhihuiLu , JianWang , Chao and Shen , Lixin},
title = {Multi-Dimensional Image Recovery via Self-Supervised Nonlinear Transform Based a Three-Directional Tensor Nuclear Norm},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2024},
volume = {17},
number = {3},
pages = {727--750},
abstract = {<p style="text-align: justify;">Recently, the tensor nuclear norm, based on self-supervised nonlinear
transformations, has gained significant attention in multidimensional image restoration. However, its primary concept involves solely nonlinear transformations along
the third mode of a three-order tensor, which limits its flexibility in dealing with
correlations in various modes of high-dimensional data. This paper makes three
main contributions. Firstly, we introduce a novel approach called three-directional
self-supervised nonlinear transform tensor nuclear norm (3DSTNN), which takes
into account nonlinear transformations in all modes and can better represent the
global structure of the tensor. Secondly, we suggest a model for multidimensional
picture recovery that minimizes ranks by modeling the underlying tensor data as
low-rank components subjected to nonlinear transformations. Thirdly, to solve the
suggested model, we create an effective algorithm based on the alternating direction
method of multipliers (ADMM). In low-rank tensor approximation for image restoration, our approach performs better than the state-of-the-art, according to extensive
experimental results on both synthetic and actual datasets.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2023-0158},
url = {http://global-sci.org/intro/article_detail/nmtma/23372.html}
}