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Singular value decomposition of quaternion matrices: A new tool for vector-sensor signal processing. Augmented second-order statistics of quaternion random signals. Elements of Quaternions Longmans Green and Co.: London, UK, 1866. Moore-Penrose inverse of tensors via Einstein product. Interpolatory Methods for Model Reduction SIAM: Philadelphia, PA, USA, 2020. A simultaneous decomposition for seven matrices with applications. Some new results on a system of Sylvester-type quaternion matrix equations. Pure PSVD approach to Sylvester-type quaternion matrix equations. Decomposition for a quaternion tensor triplet with applications. Eigenvalues of quaternion tensors with applications to color video processing. A Study on Eigenvalues of Higher-Order Tensors and Related Polynomial Optimization Problems Science Press: Beijing, China, 2015. A simultaneous decomposition for three quaternion tensors with applications in color video signal processing.

Further results for Perron Frobenius theorem for nonnegative tensors II. Solving multilinear systems via tensor inversion. Generalized Singular Value Decompositions for Tensors and Their Applications. Some applications of a decomposition for five quaternion matrices in control system and color image processing. The authors declare no conflict of interest. This paper and future research content will provide new ideas and bring great improvements to video signal processing and high-dimensional signal processing. Due to the computational difficulty of quaternion and the high dimensionality of tensors, the design of a fast and effective quaternion tensor algorithm is a very meaningful research topic. In the future, implementation algorithms based on quaternion tensors need to receive more attention. Finally, numerical experiments show that the proposed blind color video watermarking scheme has reliable security.

We plug three color video watermarks simultaneously into one host by the blind color video watermarking scheme, and extract the three watermarks by using two keys. As an application of RSVD, we present a blind color video watermarking scheme under the forth-order RSVD over the quaternion algebra.

In this paper, we have derived the restricted singular value decomposition for three quaternion tensors ( A, B, C ) based on the isomorphic group structures and the Einstein product.

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