Elliptic Quaternion Matrices: A MATLAB Toolbox and Applications for Image Processing
In this study, we developed a MATLAB 2024a toolbox that performs advanced algebraic calculations in the algebra of elliptic numbers and elliptic quaternions. Additionally, we introduce color image processing methods, such as principal component analysis, image compression, image restoration, and wat...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-11-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/13/11/771 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850149296278601728 |
|---|---|
| author | Hidayet Hüda Kösal Emre Kişi Mahmut Akyiğit Beyza Çelik |
| author_facet | Hidayet Hüda Kösal Emre Kişi Mahmut Akyiğit Beyza Çelik |
| author_sort | Hidayet Hüda Kösal |
| collection | DOAJ |
| description | In this study, we developed a MATLAB 2024a toolbox that performs advanced algebraic calculations in the algebra of elliptic numbers and elliptic quaternions. Additionally, we introduce color image processing methods, such as principal component analysis, image compression, image restoration, and watermarking, based on singular-value decomposition theory for elliptic quaternion matrices; we added these to the newly developed toolbox. The experimental results demonstrate that elliptic quaternionic methods yield better image analysis and processing performance compared to other hypercomplex number-based methods. |
| format | Article |
| id | doaj-art-30980bf20ad24ff2bd9a00de0fca72af |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-30980bf20ad24ff2bd9a00de0fca72af2025-08-20T02:26:59ZengMDPI AGAxioms2075-16802024-11-01131177110.3390/axioms13110771Elliptic Quaternion Matrices: A MATLAB Toolbox and Applications for Image ProcessingHidayet Hüda Kösal0Emre Kişi1Mahmut Akyiğit2Beyza Çelik3Faculty of Sciences, Department of Mathematics, Sakarya University, Sakarya TR-54050, TürkiyeFaculty of Sciences, Department of Mathematics, Sakarya University, Sakarya TR-54050, TürkiyeFaculty of Sciences, Department of Mathematics, Sakarya University, Sakarya TR-54050, TürkiyeFaculty of Sciences, Department of Mathematics, Sakarya University, Sakarya TR-54050, TürkiyeIn this study, we developed a MATLAB 2024a toolbox that performs advanced algebraic calculations in the algebra of elliptic numbers and elliptic quaternions. Additionally, we introduce color image processing methods, such as principal component analysis, image compression, image restoration, and watermarking, based on singular-value decomposition theory for elliptic quaternion matrices; we added these to the newly developed toolbox. The experimental results demonstrate that elliptic quaternionic methods yield better image analysis and processing performance compared to other hypercomplex number-based methods.https://www.mdpi.com/2075-1680/13/11/771elliptic quaternion matricesMATLAB toolboxoptimal p-valuesingular value decompositionleast minimum errorimage processing |
| spellingShingle | Hidayet Hüda Kösal Emre Kişi Mahmut Akyiğit Beyza Çelik Elliptic Quaternion Matrices: A MATLAB Toolbox and Applications for Image Processing Axioms elliptic quaternion matrices MATLAB toolbox optimal p-value singular value decomposition least minimum error image processing |
| title | Elliptic Quaternion Matrices: A MATLAB Toolbox and Applications for Image Processing |
| title_full | Elliptic Quaternion Matrices: A MATLAB Toolbox and Applications for Image Processing |
| title_fullStr | Elliptic Quaternion Matrices: A MATLAB Toolbox and Applications for Image Processing |
| title_full_unstemmed | Elliptic Quaternion Matrices: A MATLAB Toolbox and Applications for Image Processing |
| title_short | Elliptic Quaternion Matrices: A MATLAB Toolbox and Applications for Image Processing |
| title_sort | elliptic quaternion matrices a matlab toolbox and applications for image processing |
| topic | elliptic quaternion matrices MATLAB toolbox optimal p-value singular value decomposition least minimum error image processing |
| url | https://www.mdpi.com/2075-1680/13/11/771 |
| work_keys_str_mv | AT hidayethudakosal ellipticquaternionmatricesamatlabtoolboxandapplicationsforimageprocessing AT emrekisi ellipticquaternionmatricesamatlabtoolboxandapplicationsforimageprocessing AT mahmutakyigit ellipticquaternionmatricesamatlabtoolboxandapplicationsforimageprocessing AT beyzacelik ellipticquaternionmatricesamatlabtoolboxandapplicationsforimageprocessing |