A novel structure-preserving algorithm for the singular value decomposition of biquaternion matrices

In this paper, we study the singular value decomposition of biquaternion matrices. We prove that the singular value decomposition of biquaternion matrices can be equivalently converted to the singular value decomposition of quaternion adjoint matrices. By means of the Cheng product, we propose a novel representation called Q-representation and design a Q structure-preserving algorithm to deal with the singular value decomposition of quaternion matrices, which makes use of high-level operations. The algorithm is more efficient than that in quaternion toolbox for matlab using quaternion arithmetics and real structure-preserving algorithm. The Q structure-preserving algorithm for singular value decomposition of biquaternion matrices is presented through the application of the Q structure-preserving algorithm for singular value decomposition of quaternion matrices. Numerical experiments are provided to demonstrate the efficiency of the Q structure-preserving algorithm. We apply the Q structure-preserving algorithm of quaternion singular value decomposition to improve the image denoising process.