Efficient quaternion CUR method for low-rank approximation to quaternion matrix

The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix approximation is sometimes considerable due to the computation of t...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Numerical algorithms Ročník 99; číslo 3; s. 1531 - 1549
Hlavní autori: Wu, Pengling, Kou, Kit Ian, Cai, Hongmin, Yu, Zhaoyuan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.07.2025
Springer Nature B.V
Predmet:
Algebra
Algorithms
Approximation
Color imagery
Computer Science
Costs
Decomposition
Image processing
Methods
Numeric Computing
Numerical Analysis
Perturbation methods
Quaternions
Singular value decomposition
Theory of Computation
Quaternion matrix
low-rank approximation
65F55
quaternion CUR decomposition
color image processing
ISSN:1017-1398, 1572-9265
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix approximation is sometimes considerable due to the computation of the quaternion singular value decomposition (QSVD), which limits their application to real large-scale data. To address this deficiency, an efficient quaternion matrix CUR (QMCUR) method for low-rank approximation is suggested, which provides significant acceleration in color image processing. We first explore the QMCUR approximation method, which uses actual columns and rows of the given quaternion matrix, instead of the costly QSVD. Additionally, two different sampling strategies are used to sample the above-selected columns and rows. Then, the perturbation analysis is performed on the QMCUR approximation of noisy versions of low-rank quaternion matrices. And we also employ the proposed QMCUR method to color image recovery problem. Extensive experiments on both synthetic and real data further reveal the superiority of the proposed algorithm compared with other algorithms for getting low-rank approximation, in terms of both efficiency and accuracy.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01923-8