A New Tensor Factorization Based on the Dis-crete Simplified Fractional Fourier Transform

Tensor analysis approaches are of great importance in various fields such as computa-tion vision and signal processing. Thereinto, the definitions of tensor-tensor product (t-product) and tensor singular value decomposition (t-SVD) are significant in practice. This work presents new t-product and t-SVD definitions based on the discrete simplified fractional Fourier transform (DSFRFT). The proposed definitions can effectively deal with special complex tenors, which fur-ther motivates the transform based tensor analysis approaches. Then, we define a new tensor nucle-ar norm induced by the DSFRFT based t-SVD. In addition, we analyze the computational complex-ity of the proposed t-SVD, which indicates that the proposed t-SVD can improve the computation-al efficiency.