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-(K1, . . . ,KN ) 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 fourthorder cumulants enables to remove the Gaussian components of an additive noise. In the presented method the estimation of the n-mode projector on the n-mode signal subspace is built from the eigenvectors associated with the largest eigenvalues of a fourthorder cumulant slice matrix instead of a covariance matrix. Each projector is applied by means of the n-mode product operator on the n-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.