Generalized Singular Value Decompositions for Tensors and Their Applications

Abstract

In this paper, we consider the generalized singular value decompositions for two tensors via the T-product. We investigate and discuss in detail the structures of the quotient singular value decomposition (T-QSVD) and product singular value decomposition (T-PSVD) for two tensors. The algorithms are presented with numerical examples illustrating the results. For applications, we consider color image watermarking processing with T-QSVD and T-PSVD. There are two advantages to T-QSVD and T-PSVD approaches on color watermark processing: two color watermarks can be processed simultaneously and only one key needs to be saved.