A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
Multidimensional filtering based on a tensor approach
Signal Processing
Survey on tensor signal algebraic filtering
Signal Processing
ACIVS'07 Proceedings of the 9th international conference on Advanced concepts for intelligent vision systems
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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.