Sequential unfolding SVD for low rank orthogonal tensor approximation

Abstract

This paper contributes to the field of N-way (N ges 3) tensor decompositions, which are increasingly popular in various signal processing applications. A novel PARATREE decomposition structure is introduced, accompanied with sequential unfolding SVD (SUSVD) algorithm. SUSVD applies a matrix SVD sequentially on the unfolded tensor, which is 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 decompositions, describing a tensor as a sum of rank-1 tensors. PARATREE is an efficient model to be used for orthogonal lower rank approximations, offering significant computational savings in algorithm implementations due to a hierarchical tree structure. The performance of the proposed algorithm is illustrated through an application of measurement noise suppression in wideband MIMO measurements.