Journal
AIMS MATHEMATICS
Volume 8, Issue 11, Pages 26782-26800Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.20231371
Keywords
linear discrete ill-posed problems; Conjugate-Gradient method; t-product; regularization parameter; discrepancy principle; Tikhonov regularization
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This paper presents three types of tensor Conjugate-Gradient (tCG) methods based on the t-product between third-order tensors for solving large-scale linear discrete ill-posed problems. An automatic determination strategy of a suitable regularization parameter is proposed in the Fourier domain for the tCG method (A-tCG-FFT). Improved and preconditioned versions of the tCG method are also introduced. The effectiveness of the proposed tCG methods is demonstrated with several numerical examples in image and video restoration.
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.
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