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<p>In this paper, we propose the dual complex representation of a dual quaternion matrix and give some important properties. Using the dual complex representation and its properties, we find the relation of the compact singular value decomposition of a dual quaternion matrix and the singular value decomposition of its corresponding dual complex representation matrix. Based on this relation, we propose a fast construction algorithm for the compact singular value decomposition of a dual quaternion matrix and apply it to multispectral image compression, encryption and decryption. Numerical experiments show that, compared with the existing algorithms for the singular value decomposition of a dual quaternion matrix, this fast construction algorithm has great advantages in computational efficiency on the premise of ensuring computational accuracy and a good performance in multispectral image compression, encryption and decryption.</p>

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A fast construction algorithm for compact singular value decomposition of dual quaternion matrix and its application

  • 期刊论文

  • 发表日期：

    2025年3月5日

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  • Tao Wang,
  • Ying Li,
  • Mingcui Zhang,
  • Musheng Wei,
  • Wenbin Guo

摘要

In this paper, we propose the dual complex representation of a dual quaternion matrix and give some important properties. Using the dual complex representation and its properties, we find the relation of the compact singular value decomposition of a dual quaternion matrix and the singular value decomposition of its corresponding dual complex representation matrix. Based on this relation, we propose a fast construction algorithm for the compact singular value decomposition of a dual quaternion matrix and apply it to multispectral image compression, encryption and decryption. Numerical experiments show that, compared with the existing algorithms for the singular value decomposition of a dual quaternion matrix, this fast construction algorithm has great advantages in computational efficiency on the premise of ensuring computational accuracy and a good performance in multispectral image compression, encryption and decryption.