αβ- Tessarine工具箱：用于超复数张量代数的高性能MATLAB框架
$αβ$-Tessarine Toolbox: A high-performance MATLAB framework for hypercomplex tensor algebra
AI总结：
该研究推出αβ-Tessarine工具箱，这是一款用于超复数张量代数的高性能MATLAB框架，内置优化的超复数矩阵分解功能，可连接理论与应用，支持相关领域的新计算研究。
AI中文摘要：
本文介绍了αβ-Tessarine Toolbox，它是用于广义超复数张量代数的高性能MATLAB框架。通过实现αβ- tessarine数学结构，该工具箱提供了比现有四元数或有限tessarine包更通用的环境。这款开源软件连接了抽象理论模型与实验应用，让研究人员能高效解决多维问题。其内置功能包括精确的超复数矩阵分解，如针对大规模图像修复、去噪和数字水印优化的奇异值分解（SVD）与QR分解，可扩展的架构还为机器学习和多维信号处理领域的新计算研究提供支持。
英文摘要：
The \textit{$αβ$-Tessarine Toolbox} is introduced as a high-performance MATLAB framework for generalized hypercomplex tensor algebra. By implementing the $αβ$-tessarine mathematical structure, a strictly more general environment than existing quaternion or limited tessarine packages is provided. This open-source software bridges abstract theoretical models and experimental applications, allowing researchers to efficiently solve multidimensional problems. Built-in capabilities include exact hypercomplex matrix factorizations, such as Singular Value Decomposition (SVD) and QR, optimized for large-scale image in-painting, denoising, and digital watermarking. The scalable architecture facilitates new computational research in machine learning and multidimensional signal processing.
