RSVD for Three Quaternion Tensors with Applications in Color Video Watermark Processing

Abstract

In this paper, we study the restricted singular-value decomposition (RSVD) for three quaternion tensors under the Einstein product, and give higher-order RSVD over the quaternion algebra, which can achieve simultaneous singular value decomposition of three quaternion tensors. Moreover, we give the algorithm for computing the RSVD of for quaternion tensors. What is more, we present a new blind color video watermarking scheme based on the forth-order RSVD over the quaternion algebra, and our numerical example demonstrates the effectiveness of the framework.

Keywords

• tensor decomposition
• quaternion algebra