Multidimensional filtering based on a tensor approach

A new multidimensional modelling of data has recently been suggested, which can be applied in a wide range of signal processing fields. Many studies have proposed new tensorial mathematical tools in order to process multidimensional data. With a view of perfecting this multidimensional model, this paper presents a new tensor approach for multidimensional data filtering. 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 an extension of the well-known Wiener filter in a particular mode. An alternating least square algorithm is proposed to determine each n-mode Wiener filter. This new multimode Wiener filtering method is tested for noise reduction in multicomponent seismic data. A comparative study with classical bidimensional filtering methods based on principal component analysis is also proposed and presents encouraging results.