Wang, S.-W.; Huang, G.-X.; Yin, F. Tensor Conjugate Gradient Methods with Automatically Determination of Regularization Parameters for Ill-Posed Problems with t-Product. Mathematics2024, 12, 159.
Wang, S.-W.; Huang, G.-X.; Yin, F. Tensor Conjugate Gradient Methods with Automatically Determination of Regularization Parameters for Ill-Posed Problems with t-Product. Mathematics 2024, 12, 159.
Wang, S.-W.; Huang, G.-X.; Yin, F. Tensor Conjugate Gradient Methods with Automatically Determination of Regularization Parameters for Ill-Posed Problems with t-Product. Mathematics2024, 12, 159.
Wang, S.-W.; Huang, G.-X.; Yin, F. Tensor Conjugate Gradient Methods with Automatically Determination of Regularization Parameters for Ill-Posed Problems with t-Product. Mathematics 2024, 12, 159.
Abstract
This paper presents three types of tensor Conjugate-Gradient methods for solving large-scale linear discrete ill-posed problems based on the t-product between third-order tensors. An automatical determination strategy of a suitable regularization parameter is proposed for the tensor conjugate gradient (tCG) method. A truncated version and a preprocessed verion of the tCG method are further presented. The discrepancy principle is employed to determine a suitable regularization parameter. Several numerical examples are given to show the effectiveness of the proposed tCG methods in image and video restoration.
Computer Science and Mathematics, Computational Mathematics
Copyright:
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