AIMS Mathematics (Sep 2023)

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

  • Hong-Mei Song,
  • Shi-Wei Wang ,
  • Guang-Xin Huang

DOI
https://doi.org/10.3934/math.20231371
Journal volume & issue
Vol. 8, no. 11
pp. 26782 – 26800

Abstract

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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.

Keywords