Tensor Conjugate-Gradient methods for tensor linear discrete ill-posed problems-Reference-Cited by-同舟云学术

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

Published:2023 Issue:11 Volume:8 Page:26782-26800
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Song Hong-Mei¹²,Wang Shi-Wei¹²,Huang Guang-Xin²³

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference18 articles.

1. M. E. Kilmer, C. D. Martin, Factorization strategies for third order tensors, Linear Algebra Appl., 435 (2011), 641–658. https://doi.org/10.1016/j.laa.2010.09.020

2. N. Hao, M. E. Kilmer, K. Braman, R. C. Hoover, Facial recognition using tensor-tensor decompositions, SIAM J. Imaging Sci., 6 (2013), 437–463. https://doi.org/10.1137/110842570

3. M. E. Guide, A. E. Ichi, K. Jbilou, R. Sadaka, On tensor GMRES and Golub-Kahan methods via the T-product for color image processing, Electron. J. Linear Algebra, 37 (2021), 524–543. https://doi.org/10.13001/ela.2021.5471

4. L. Reichel, U. O. Ugwu, The tensor Golub–Kahan–Tikhonov method applied to the solution of ill-posed problems with a t-product structure, Numer. Linear Algebra Appl., 29 (2021), e2412. https://doi.org/10.1002/nla.2412

5. L. Reichel, U. O. Ugwu, Tensor Arnoldi–Tikhonov and GMRES-type methods for ill-posed problems with a t-product structure, J. Sci. Comput., 90 (2022), 59. https://doi.org/10.1007/s10915-021-01719-1

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