@article{Song2023, 
author = {Hong-Mei Song and Shi-Wei Wang and Guang-Xin Huang},
title = {Tensor Conjugate-Gradient methods for tensor linear discrete ill-posed problems},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {26782-26800},
keywords = {linear discrete ill-posed problems, Conjugate-Gradient method, t-product, regularization parameter, discrepancy principle, Tikhonov regularization},
url = {https://www.sciopen.com/article/10.3934/math.20231371},
doi = {10.3934/math.20231371},
abstract = {This paper presents three types of tensor Conjugate-Gradient (tCG) methods for solving large-scale linear discrete ill-posed problems based on the t-product between third-order tensors. An automatic determination strategy of a suitable regularization parameter is proposed for the tCG method in the Fourier domain (A-tCG-FFT). An improved version and a preconditioned version of the tCG method are also presented. The discrepancy principle is employed to determine a suitable regularization parameter. Several numerical examples in image and video restoration are given to show the effectiveness of the proposed tCG methods.}
}