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In this paper we propose a new multidimensional filtering method based on fourth order cumulants to denoise of data tensor impaired by correlated Gaussian noise. We overview the multidimensional Wiener filtering that overcomes the well known lower rank-(K1,..., KN) tensor approximation. But this method only exploits second order statistics. In some applications, it may be interesting to consider a correlated Gaussian noise. Then, we propose to introduce the fourth order statistics in the denoising algorithm. Indeed, the use of fourth order cumulants enables to remove the Gaussian components of an additive noise. Qualitative results of the improved multidimensional Wiener filtering are shown for the case of noise reduction in hyperspectral imagery.