Tensor Conjugate-Gradient methods for tensor linear discrete ill-posed problems

Hong-Mei Song; Shi-Wei Wang; Guang-Xin Huang; Hong-Mei Song; Shi-Wei Wang; Guang-Xin Huang

doi:10.3934/math.20231371

AIMS Mathematics

2023, Volume 8, Issue 11: 26782-26800. doi: 10.3934/math.20231371

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Tensor Conjugate-Gradient methods for tensor linear discrete ill-posed problems

1.
College of Mathematical and physics, Chengdu University of Technology, Chengdu, China
2.
Sichuan Geomathematics Key Laboratory, Chengdu University of Technology, Chengdu, China
3.
College of Computer Science and Cyber Security, Chengdu University of Technology, Chengdu, China

Received: 09 July 2023 Revised: 02 September 2023 Accepted: 05 September 2023 Published: 20 September 2023
MSC : 15A69, 65F05, 65J20

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.
- linear discrete ill-posed problems,
- Conjugate-Gradient method,
- t-product,
- regularization parameter,
- discrepancy principle,
- Tikhonov regularization
Citation: Hong-Mei Song, Shi-Wei Wang, Guang-Xin Huang. Tensor Conjugate-Gradient methods for tensor linear discrete ill-posed problems[J]. AIMS Mathematics, 2023, 8(11): 26782-26800. doi: 10.3934/math.20231371

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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.

References

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