Multiway Filtering Applied on Hyperspectral Images

Abstract

A new multidimensional modeling of data has recently been introduced, which can be used a wide range of signals. This paper presents multiway filtering for denoising hyperspectral images. This approach is based on a tensorial modeling of the desired information. The optimization criterion used in this multiway 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. Using the ALS loop allows to take into account the mode interdependence. This algorithm requires the signal subspace estimation for each mode. In this study, we have extended the well-know Akaike Information Criterion (AIC) and the minimum description length (MDL) criterion to detect the number of dominant eigenvalues associated with the signal subspace. The performance of this new method is tested on hyperspectral images. Comparative studies with classical bidimensional filtering methods show that our algorithm presents good performances.