{"title":"Color image restoration based on reduced biquaternion matrix singular value decomposition","authors":"Xiao-Min Cai , Yi-Fen Ke , Lin-Jie Chen","doi":"10.1016/j.cam.2024.116428","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, the singular value decomposition of reduced biquaternion matrix is studied and its expression is obtained based on the complex representation of reduced biquaternion matrix. In addition, the expression of the minimal norm least squares solution for the reduced biquaternion matrix equation is derived by the generalized inverse. The proposed algorithms are very simple and convenient, because they only involve operations on the field of complex numbers. Finally, in order to prove the authenticity of our algorithms, some numerical examples are presented including color image restoration and comparison with existing results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116428"},"PeriodicalIF":2.6000,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724006769","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/12/9 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the singular value decomposition of reduced biquaternion matrix is studied and its expression is obtained based on the complex representation of reduced biquaternion matrix. In addition, the expression of the minimal norm least squares solution for the reduced biquaternion matrix equation is derived by the generalized inverse. The proposed algorithms are very simple and convenient, because they only involve operations on the field of complex numbers. Finally, in order to prove the authenticity of our algorithms, some numerical examples are presented including color image restoration and comparison with existing results.
期刊介绍：
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.
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