Tensor Conjugate Gradient Methods with Automatically Determination of Regularization Parameters for Ill-Posed Problems with t-Product

Abstract

Ill-posed problems arise in many areas of science and engineering. Tikhonov is a usual regularization which replaces the original problem by a minimization problem with a fidelity term and a regularization term. In this paper, a tensor t-production structure preserved Conjugate-Gradient (tCG) method is presented to solve the regularization minimization problem. We provide a truncated version of regularization parameters for the tCG method and a preprocessed version of the tCG method. The discrepancy principle is used to automatically determine the regularization parameter. Several examples on image and video recover are given to show the effectiveness of the proposed methods by comparing them with some previous algorithms.

Keywords

• linear discrete ill-posed problems
• tensor Conjugate Gradient method
• t-product
• discrepancy principle
• Tikhonov regularization