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

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...

Full description

Saved in:
Bibliographic Details
Published inMathematics (Basel) Vol. 12; no. 1; p. 159
Main Authors Wang, Shi-Wei, Huang, Guang-Xin, Yin, Feng
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2024
Subjects
Algorithms
Conjugate gradient method
Data compression
Decomposition
discrepancy principle
Fourier transforms
Ill posed problems
linear discrete ill-posed problems
Mathematical analysis
Methods
Optimization
Parameter estimation
Parameters
Regularization
Regularization methods
t-product
tensor Conjugate Gradient method
Tensors
Tikhonov regularization
Video compression
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12010159