Elliptic Quaternion Matrices: A MATLAB Toolbox and Applications for Image Processing

Abstract

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.

Keywords

• elliptic quaternion matrices
• MATLAB toolbox
• optimal p-value
• singular value decomposition
• least minimum error
• image processing