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

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.

Automated summary

This paper presents three types of tensor Conjugate-Gradient methods based on the t-product between third-order tensors, for solving large-scale linear discrete ill-posed problems. An automatic determination strategy and the discrepancy principle are proposed for determining suitable regularization parameters for the methods. Numerical examples in image and video restoration demonstrate the effectiveness of the proposed methods.