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  • Research Article
  • Open Access

Multiway Filtering Based on Fourth-Order Cumulants

EURASIP Journal on Advances in Signal Processing20052005:708571

  • Received: 31 March 2004
  • Published:


We propose a new multiway filtering based on fourth-order cumulants for the denoising of noisy data tensor with correlated Gaussian noise. The classical multiway filtering is based on the TUCKALS3 algorithm that computes a lower-rank tensor approximation. The presented method relies on the statistics of the analyzed multicomponent signal. We first recall how the well-known lower rank- tensor approximation processed by TUCKALS3 alternating least square algorithm exploits second-order statistics. Then, we propose to introduce the fourth-order statistics in the TUCKALS3-based method. Indeed, the use of fourth-order cumulants enables to remove the Gaussian components of an additive noise. In the presented method the estimation of the -mode projector on the -mode signal subspace are built from the eigenvectors associated with the largest eigenvalues of a fourth-order cumulant slice matrix instead of a covariance matrix. Each projector is applied by means of the -mode product operator on the -mode of the data tensor. The qualitative results of the improved multiway TUCKALS3-based filterings are shown for the case of noise reduction in a color image and multicomponent seismic data.

Keywords and phrases

  • Multicomponent signals
  • tensors
  • Tucker3 decomposition
  • cumulant slice matrix
  • subspace methods

Authors’ Affiliations

Groupe GSM, Institut Fresnel (UMR CNRS 6133), EGIM, Université Aix-Marseille III, D.U. de Saint Jérôme, Marseille Cedex 20, 13397, France


© Muti and Bourennane 2005