The LSQR method for solving tensor least-squares problems

Bentbib, Abdeslem Hafid; Khouia, A.; Sadok, H.

doi:10.1553/etna_vol55s92

Cited by 6 publications

(2 citation statements)

References 11 publications

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“…Tensors are high-dimensional arrays that have many applications in science and engineering, including in image, video and signal processing, computer vision, and network analysis [1][2][3][4][5][6][7][8]. A new t-product based on third-order tensors was proposed by Kilmer et al [9,10].…”

Section: Introductionmentioning

confidence: 99%

Tensor Conjugate Gradient Methods with Automatically Determination of Regularization Parameters for Ill-Posed Problems with t-Product

Wang,

Huang,

Yin

2024

Mathematics

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Ill-posed problems arise in many areas of science and engineering. Tikhonov is a usual regularization which replaces the original problem by a minimization problem with a fidelity term and a regularization term. In this paper, a tensor t-production structure preserved Conjugate-Gradient (tCG) method is presented to solve the regularization minimization problem. We provide a truncated version of regularization parameters for the tCG method and a preprocessed version of the tCG method. The discrepancy principle is used to automatically determine the regularization parameter. Several examples on image and video recover are given to show the effectiveness of the proposed methods by comparing them with some previous algorithms.

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Section: Introductionmentioning

confidence: 99%

Tensor Conjugate Gradient Methods with Automatically Determination of Regularization Parameters for Ill-Posed Problems with t-Product

Wang,

Huang,

Yin

2024

Mathematics

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“…Tensors are high-dimensional arrays that have many applications in science and engineering, including in image, video and signal processing, computer vision, and network analysis [11,12,[16][17][18][19][20]26]. A new t-product based on third-order tensors proposed by Kilmer et al [1,2].…”

Section: Introductionmentioning

confidence: 99%

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

Wang,

Huang,

Yin

2023

Preprint

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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.

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