Sequential unfolding SVD for tensors with applications in array signal processing

Authors:
Jussi Salmi;Andreas Richter;Visa Koivunen
Affiliations:
Department of Signal Processing and Acoustics, Helsinki University of Technology, SMARAD CoE, Espoo, Finland;Nokia Research Center, Helsinki, Finland and Department of Signal Processing and Acoustics, Helsinki University of Technology, SMARAD CoE, Espoo, Finland;Department of Signal Processing and Acoustics, Helsinki University of Technology, SMARAD CoE, Espoo, Finland
Venue:
IEEE Transactions on Signal Processing
Year:
2009

Citing 13
Cited 1

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A Counterexample to the Possibility of an Extension of the Eckart-Young Low-Rank Approximation Theorem for the Orthogonal Rank Tensor Decomposition

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Tensor Decompositions and Applications

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Higher-Order SVD-Based Subspace Estimation to Improve the Parameter Estimation Accuracy in Multidimensional Harmonic Retrieval Problems

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Parallel factor analysis in sensor array processing

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Hierarchical Singular Value Decomposition of Tensors

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Abstract

This paper contributes to the field of higher order (N2) 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 PARA-TREE 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.