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- Title
Solving the least squares (anti)-Hermitian solution for quaternion linear systems.
- Authors
Fan, Xueling; Li, Ying; Zhang, Mingcui; Zhao, Jianli
- Abstract
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.
- Subjects
QUATERNIONS; LEAST squares; IMAGE reconstruction; SYLVESTER matrix equations; MATRIX multiplications
- Publication
Computational & Applied Mathematics, 2022, Vol 41, Issue 8, p1
- ISSN
0101-8205
- Publication type
Article
- DOI
10.1007/s40314-022-02087-8