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Statistical Analysis of Hyper-Spectral Data: A Non-Gaussian Approach


We investigate the statistical modeling of hyper-spectral data. The accurate modeling of experimental data is critical in target detection and classification applications. In fact, having a statistical model that is capable of properly describing data variability leads to the derivation of the best decision strategies together with a reliable assessment of algorithm performance. Most existing classification and target detection algorithms are based on the multivariate Gaussian model which, in many cases, deviates from the true statistical behavior of hyper-spectral data. This motivated us to investigate the capability of non-Gaussian models to represent data variability in each background class. In particular, we refer to models based on elliptically contoured (EC) distributions. We consider multivariate EC-t distribution and two distinct mixture models based on EC distributions. We describe the methodology adopted for the statistical analysis and we propose a technique to automatically estimate the unknown parameters of statistical models. Finally, we discuss the results obtained by analyzing data gathered by the multispectral infrared and visible imaging spectrometer (MIVIS) sensor.


  1. 1.

    Stein DWJ, Beaven SG, Hoff LE, Winter EM, Schaum AP, Stocker AD: Anomaly detection from hyperspectral imagery. IEEE Signal Processing Magazine 2002,19(1):58–69. 10.1109/79.974730

    Article  Google Scholar 

  2. 2.

    Manolakis D, Shaw G: Detection algorithms for hyperspectral imaging applications. IEEE Signal Processing Magazine 2002,19(1):29–43. 10.1109/79.974724

    Article  Google Scholar 

  3. 3.

    Landgrebe DA: Signal Theory Methods in Multispectral Remote Sensing. John Wiley & Sons, Hoboken, NJ, USA; 2003.

    Google Scholar 

  4. 4.

    Manolakis D, Marden D, Kerekes J, Shaw G: Statistics of hyperspectral imaging data. Algorithms for Multispectral, Hyperspectral, and Ultraspectral Imagery VII, April 2001, Orlando, Fla, USA, Proceedings of SPIE 4381: 308–316.

    Article  Google Scholar 

  5. 5.

    Manolakis D, Marden D: Non Gaussian models for hyperspectral algorithm design and assessment. Proceedings of IEEE International Geosciences and Remote Sensing Symposium (IGARSS '02), June 2002, Toronto, Canada 3: 1664–1666.

    Article  Google Scholar 

  6. 6.

    Marden D, Manolakis D: Modeling hyperspectral imaging data. Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery IX, April 2003, Orlando, Fla, USA, Proceedings of SPIE 5093: 253–262.

    Article  Google Scholar 

  7. 7.

    Yao K: A representation theorem and its applications to spherically-invariant random processes. IEEE Transactions on Information Theory 1973,19(5):600–608. 10.1109/TIT.1973.1055076

    MathSciNet  Article  Google Scholar 

  8. 8.

    Rangaswamy M, Weiner DD, Ozturk A: Non-Gaussian random vector identification using spherically invariant random processes. IEEE Transactions on Aerospace and Electronic Systems 1993,29(1):111–124. 10.1109/7.249117

    Article  Google Scholar 

  9. 9.

    Rangaswamy M, Weiner DD, Ozturk A: Computer generation of correlated non-Gaussian radar clutter. IEEE Transactions on Aerospace and Electronic Systems 1995,31(1):106–116.

    Article  Google Scholar 

  10. 10.

    Beaven SG, Stein DWJ, Hoff LE: Comparison of Gaussian mixture and linear mixture models for classification of hyperspectral data. Proceedings of IEEE International Geosciense and Remote Sensing Symposium (IGARSS '00), July 2000, Honolulu, Hawaii, USA 4: 1597–1599.

    Google Scholar 

  11. 11.

  12. 12.

    Kay SM: Fundamental of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Upper Saddle River, NJ, USA; 1993.

    Google Scholar 

  13. 13.

    Lagarias JC, Reeds JA, Wright MH, Wright PE: Convergence properties of the nelder-mead simplex method in low dimensions. SIAM Journal of Optimization 1998,9(1):112–147. 10.1137/S1052623496303470

    MathSciNet  Article  Google Scholar 

  14. 14.

    Moon TK: The expectation-maximization algorithm. IEEE Signal Processing Magazine 1996,13(6):47–60. 10.1109/79.543975

    Article  Google Scholar 

  15. 15.

    Acito N, Corsini G, Diani M: An unsupervised algorithm for hyper-spectral image segmentation based on the Gaussian mixture model. Proceedings of IEEE International Geoscience and Remote Sensing Symposium (IGARSS '03), July 2003, Toulouse, France 6: 3745–3747.

    Google Scholar 

  16. 16.

    Reed IS, Yu X: Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution. IEEE Transactions on Acoustics Speech and Signal Processing 1990,38(10):1760–1770. 10.1109/29.60107

    Article  Google Scholar 

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Correspondence to N. Acito.

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Acito, N., Corsini, G. & Diani, M. Statistical Analysis of Hyper-Spectral Data: A Non-Gaussian Approach. EURASIP J. Adv. Signal Process. 2007, 027673 (2006).

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  • Mixture Model
  • Visible Imaging
  • Target Detection
  • Gaussian Model
  • Reliable Assessment