Dual complex structure-preserving algorithm of dual quaternion singular value decomposition and its applications

Innovative dual complex structure-preserving algorithms are introduced to develop efficient and resilient algorithms for singular value decomposition of dual quaternion matrices. Under the framework of dual complex matrices, a novel dual complex structure-preserving algorithm is introduced for dual quaternion Householder transformations and dual complex unitary matrices derived from dual quaternion unitization. This algorithm is initially proposed and subsequently applied to compute the bidiagonal form of dual quaternion matrices. Drawing on the correlation between the singular values of the dual quaternion matrix and its bidiagonal dual number matrix, the dual complex structure-preserving algorithm for dual quaternion singular value decomposition is presented. Numerical experiments are conducted to showcase the efficiency and accuracy of the newly proposed algorithms. Additionally, we leverage dual complex matrices for representing color images, utilizing the proposed algorithms for singular value decomposition of these matrices. The singular value decomposition of dual complex matrices enables the compression of color images. Experimental results demonstrate the effectiveness of this method, showcasing its utility in image compression tasks.