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This paper presents a new multidimensional filtering method for multidimensional images impaired by correlated Gaussian noise. Instead of matrices or vectors, multidimensional images are considered as multidimensional arrays also called tensors. Some noise removal techniques consist in vectorizing or matricizing multidimensional data. That could lead to the loss of inter-bands relations. The presented filtering method consider multidimensional data as whole entities. Such a method is based on multilinear algebra. Most of multidimensional noise removal techniques are based on second order statistics and are only efficient in the case of additive white noise. But in some cases, it can be interesting to consider additive correlated noise. Therefore, we introduce higher order statistics for tensor filtering to remove Gaussian components. Experiments on HYDICE hyperspectral images are presented to show the improvement using higher order statistics.