Solving the least squares (anti)-Hermitian solution for quaternion linear systems

In this paper, based on semi-tensor product of quaternion matrices, we explore the operation conclusion of quaternion matrices under vector representation, which can realize the transformation from quaternion matrix equation to quaternion vector matrix equation. Then using complex representation of...

Full description

Saved in:
Bibliographic Details
Published in:Computational & applied mathematics 2022-12, Vol.41 (8), Article 371
Main Authors: Fan, Xueling, Li, Ying, Zhang, Mingcui, Zhao, Jianli
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Digital imaging
Generalized inverse
Image restoration
Least squares
Linear systems
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Quaternions
Representations
Tensors
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, based on semi-tensor product of quaternion matrices, we explore the operation conclusion of quaternion matrices under vector representation, which can realize the transformation from quaternion matrix equation to quaternion vector matrix equation. Then using complex representation of quaternion matrix and Moore–Penrose generalized inverse, we obtain the expression of the minimal norm least squares (anti)-Hermitian solution of the system of quaternion generalized Sylvester matrix Eq.  ( 1.1 ). We compare the algorithm in this paper with the other algorithms, and the corresponding numerical experiments reflect the feasibility and advantage of the algorithm in this paper. At the same time, we apply the algorithm in this paper to the symmetric color digital image restoration model.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-022-02087-8