Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Tensor Conjugate-Gradient Methods With Automatically Determination of Regularization Parameters for Ill-Posed Problems With T-product

Version 1 : Received: 26 October 2023 / Approved: 26 October 2023 / Online: 26 October 2023 (11:09:51 CEST)

A peer-reviewed article of this Preprint also exists.

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. 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.

Keywords

linear discrete ill-posed problems; tensor Conjugate-Gradient method; t-product; discrepancy principle; Tikhonov regularization

Subject

Computer Science and Mathematics, Computational Mathematics

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