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Multiway Filtering Based on Fourth-Order Cumulants


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.

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Correspondence to Damien Muti.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Muti, D., Bourennane, S. Multiway Filtering Based on Fourth-Order Cumulants. EURASIP J. Adv. Signal Process. 2005, 708571 (2005).

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Keywords and phrases

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