Multidimensional estimation based on a tensor decomposition

This paper presents a new tensorial approach to multidimensional data filtering. In this approach, multidimensional data are considered as whole tensors. A theoretical expression of n-mode filters is established based on a specific modelling of the desired information. The optimization criterion used in this tensorial filtering is the minimization of the mean square error between the estimated signal and the desired signal. This minimization leads to some estimated n-mode filters which can be considered as the extension of the well known Wiener filter in a particular mode. An ALS algorithm is proposed to determine each n-mode Wiener filter. The performance of this new method is tested on simulated data for noise reduction in noisy color images. Comparative studies with classical bidimensional filtering methods are also proposed and present encouraging results.