Sequential Unfolding SVD for Tensors With Applications in Array Signal Processing

This paper contributes to the field of higher order $(N>2)$ tensor decompositions in signal processing. A novel PARATREE tensor model is introduced, accompanied with Sequential Unfolding SVD (SUSVD) algorithm. SUSVD, as the name indicates, applies a matrix singular value decomposition sequentially on the unfolded tensor reshaped from the right hand basis vectors of the SVD of the previous mode. The consequent PARATREE model is related to the well known family of PARAFAC tensor decomposition models. Both of them describe a tensor as a sum of rank-1 tensors, but PARATREE has several advantages over PARAFAC, when it is applied as a lower rank approximation technique. PARATREE is orthogonal (due to SUSVD), fast and reliable to compute, and the order (or rank) of the decomposition can be adaptively adjusted. The low rank PARATREE approximation can be applied for, e.g., reducing computational complexity in inverse problems, measurement noise suppression as well as data compression. The benefits of the proposed algorithm are illustrated through application examples in signal processing in comparison to PARAFAC and HOSVD.