Multiway Filtering Applied on Hyperspectral Images

  • N. Renard
  • S. Bourennane
  • J. Blanc-Talon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4179)


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.


Akaike Information Criterion Hyperspectral Image Noisy Image Minimum Description Length Signal Subspace 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Comon, P.: Tensor decompositions, state of the art and applications. In: IMA Conf. mathematics in Signal Processing, Warwick, UK (2000)Google Scholar
  2. 2.
    Muti, D., Bourennane, S.: Multidimensional filtering based on a tensor approach. Signal Proceesing Journal 85, 2338–2353 (2005)MATHCrossRefGoogle Scholar
  3. 3.
    Muti, D., Bourennane, S.: Multiway filtering based on fourth order cumulants. Applied Signal Processing, EURASIP 7, 1147–1159 (2005)CrossRefGoogle Scholar
  4. 4.
    Tucker, L.: Some mathematical notes on three-mode factor analysis. Psychometrika 31, 279–311 (1966)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Muti, D., Bourennane, S.: Survey on tensor signal algebraic filtering. Signal Proceesing Journal (to be published) (2006) Google Scholar
  6. 6.
    Le Bihan, N.: Traitement algébrique des signaux vectoriels: Application á la séparation d’ondes sismiques. Phd thesis, INPG, Grenoble, France (2001)Google Scholar
  7. 7.
    Muti, D., Bourennane, S.: Multidimensional signal processing using lower rank tensor approximation. In: IEEE Int. Conf. on Accoustics, Systems and Signal Processing, Hong Kong, China (2003)Google Scholar
  8. 8.
    Wax, M., Kailath, T.: Detection of signals information theoretic criteria. In: IEEE International Conference on Acoustics Speech and Signal Processing, vol. 33, pp. 387–392 (1985)Google Scholar
  9. 9.
    De Lathauwer, L., De Moor, B., Vandewalle, J.: A multilinear singular value decomposition. SIAM Journal on Matrix Analysis and Applications 21, 1253–1278 (2000)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • N. Renard
    • 1
  • S. Bourennane
    • 1
  • J. Blanc-Talon
    • 2
  1. 1.Univ. Paul Cézanne, EGIM, Institut Fresnel (CNRS UMR 6133), Dom. Univ. de Saint JérômeMarseilleFrance
  2. 2.DGA/D4S/MRISArcueilFrance

Personalised recommendations