A novel L0 minimization framework of tensor tubal rank and its multi-dimensional image completion application

Jin-Liang Xiao, Ting-Zhu Huang*, Liang-Jian Deng*, Hong-Xia Dou

Inverse Problems and Imaging

My Homepage: https://jin-liangxiao.github.io/

Main results

• Constraint comparison of different approaches

• The sparsity of singular values of X is effectively enhanced by the adaptive transformation.

How to use?

• Directly run: Demo.m

Parameters

Parameters	Meaning	Adjustment scope
mu_1	Penalty parameter	[1e-6,1e-2]
alpha, beta	Parameters of L0 minimization	[1e-4,1e-1], [1e1,1e4]
rho	Control the extent of mu_1 increase	[1,1.4]
mu_2	Parameter of the proximal term of adaptive transformation	[1,1e4]
r	Parameter of adaptive transformation	[10,n3]

Note that n3 is the third dimention of the image.

Please adjust the above parameters for better results

Citation

@article{xiao2024ipi,
title = {A novel $ \ell_{0} $ minimization framework of tensor tubal rank and its multi-dimensional image completion application},
author = {Xiao, Jin-Liang and Huang, Ting-Zhu and Deng, Liang-Jian and Dou, Hong-Xia},
journal = {Inverse Problems and Imaging},
pages = {},
year = {2024},
issn = {1930-8337},
doi = {10.3934/ipi.2024018},
}