The solution of the equation AX = B using commutative elliptic octonion matrix analysis and its applications in colour image restoration
Arzu Sürekçi, Mehmet Ali̇ Güngör · Journal of Modern Optics · 2024
In this study, the algebraic properties of commutative elliptic octonions and their relations with the base d1−d2 are examined. Then, the matrix structure is analyzed based on these properties and an algorithm for solving the equation AX = B is presented. In image processing, the Octonion Elliptic Linear Shift Invariant (OELSI) method for enhancing images is defined and applied represented by commutative elliptic octonion matrices. Finally, the obtained results are supported by examples and compared with other image restoration techniques in the literature.