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A Comparative Analysis of Kernel Subspace Target Detectors for Hyperspectral Imagery

Abstract

Several linear and nonlinear detection algorithms that are based on spectral matched (subspace) filters are compared. Nonlinear (kernel) versions of these spectral matched detectors are also given and their performance is compared with linear versions. Several well-known matched detectors such as matched subspace detector, orthogonal subspace detector, spectral matched filter, and adaptive subspace detector are extended to their corresponding kernel versions by using the idea of kernel-based learning theory. In kernel-based detection algorithms the data is assumed to be implicitly mapped into a high-dimensional kernel feature space by a nonlinear mapping, which is associated with a kernel function. The expression for each detection algorithm is then derived in the feature space, which is kernelized in terms of the kernel functions in order to avoid explicit computation in the high-dimensional feature space. Experimental results based on simulated toy examples and real hyperspectral imagery show that the kernel versions of these detectors outperform the conventional linear detectors.

References

  1. 1.

    Scharf LL, Friedlander B: Matched subspace detectors. IEEE Transactions on Signal Processing 1994,42(8):2146-2156. 10.1109/78.301849

    Article  Google Scholar 

  2. 2.

    Harsanyi JC, Chang C-I: Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach. IEEE Transactions on Geoscience and Remote Sensing 1994,32(4):779-785. 10.1109/36.298007

    Article  Google Scholar 

  3. 3.

    Manolakis D, Shaw G, Keshava N: Comparative analysis of hyperspectral adaptive matched filter detectors. Algorithms for Multispectral, Hyperspectral, and Ultraspectral Imagery VI, April 2000, Orlando, Fla, USA, Proceedings of SPIE 4049: 2–17.

    Article  Google Scholar 

  4. 4.

    Robey FC, Fuhrmann DR, Kelly EJ, Nitzberg R: A CFAR adaptive matched filter detector. IEEE Transactions on Aerospace and Electronic Systems 1992,28(1):208-216. 10.1109/7.135446

    Article  Google Scholar 

  5. 5.

    Kraut S, Scharf LL: The CFAR adaptive subspace detector is a scale-invariant GLRT. IEEE Transactions on Signal Processing 1999,47(9):2538-2541. 10.1109/78.782198

    Article  Google Scholar 

  6. 6.

    Kraut S, Scharf LL, McWhorter LT: Adaptive subspace detectors. IEEE Transactions on Signal Processing 2001,49(1):1-16. 10.1109/78.890324

    Article  Google Scholar 

  7. 7.

    Kwon H, Nasrabadi NM: Kernel matched subspace detectors for hyperspectral target detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 2006,28(2):178-194.

    Article  Google Scholar 

  8. 8.

    Kwon H, Nasrabadi NM: Kernel orthogonal subspace projection for hyperspectral signal classification. IEEE Transactions on Geoscience and Remote Sensing 2005,43(12):2952-2962.

    Article  Google Scholar 

  9. 9.

    Kwon H, Nasrabadi NM: Kernel adaptive subspace detector for hyperspectral imagery. IEEE Transactions on Geoscience and Remote Sensing 2006,3(2):271-275. 10.1109/LGRS.2006.869985

    Article  Google Scholar 

  10. 10.

    Kwon H, Nasrabadi NM: Kernel spectral matched filter for hyperspectral target detection. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 4: 665–668.

    Google Scholar 

  11. 11.

    Vapnik VN: The Nature of Statistical Learning Theory. Springer, New York, NY, USA; 1999.

    Google Scholar 

  12. 12.

    Schölkopf B, Smola AJ: Learning with Kernels. MIT Press, Cambridge, Mass, USA; 2002.

    Google Scholar 

  13. 13.

    Schölkopf B, Smola AJ, Müller K-R: Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 1998,10(5):1299-1319. 10.1162/089976698300017467

    Article  Google Scholar 

  14. 14.

    Baudat G, Anouar F: Generalized discriminant analysis using a kernel approach. Neural Computation 2000,12(10):2385-2404. 10.1162/089976600300014980

    Article  Google Scholar 

  15. 15.

    Girolami M: Mercer kernel-based clustering in feature space. IEEE Transactions on Neural Networks 2002,13(3):780-784. 10.1109/TNN.2002.1000150

    Article  Google Scholar 

  16. 16.

    Ruiz A, Lopez-de-Teruel PE: Nonlinear kernel-based statistical pattern analysis. IEEE Transactions on Neural Networks 2001,12(1):16-32. 10.1109/72.896793

    Article  Google Scholar 

  17. 17.

    Park CH, Park H: Nonlinear feature extraction based on centroids and kernel functions. Pattern Recognition 2004,37(4):801-810. 10.1016/j.patcog.2003.07.011

    MathSciNet  Article  Google Scholar 

  18. 18.

    Kwon H, Nasrabadi NM: Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery. IEEE Transactions on Geoscience and Remote Sensing 2005,43(2):388-397.

    Article  Google Scholar 

  19. 19.

    Maeda E, Murase H: Multi-category classification by kernel based nonlinear subspace method. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '99), March 1999, Phoenix, Ariz, USA 2: 1025–1028.

    Google Scholar 

  20. 20.

    Dundar MM, Landgrebe DA: Toward an optimal supervised classifier for the analysis of hyperspectral data. IEEE Transactions on Geoscience and Remote Sensing 2004,42(1):271-277. 10.1109/TGRS.2003.817813

    Article  Google Scholar 

  21. 21.

    Pekalska E, Paclik P, Duin RPW: A generalized kernel approach to dissimilarity based classification. Journal of Machine Learning Research 2001, 2: 175–211.

    MathSciNet  MATH  Google Scholar 

  22. 22.

    Lu J, Plataniotis KN, Venetsanopoulos AN: Face recognition using kernel direct discriminant analysis algorithms. IEEE Transactions on Neural Networks 2003,14(1):117-126. 10.1109/TNN.2002.806629

    Article  Google Scholar 

  23. 23.

    Settle JJ: On the relationship between spectral unmixing and subspace projection. IEEE Transactions on Geoscience and Remote Sensing 1996,34(4):1045-1046. 10.1109/36.508422

    Article  Google Scholar 

  24. 24.

    Van Veen BD, Buckley KM: Beamforming: a versatile approach to spatial filtering. IEEE ASSP Magazine 1988,5(2):4-24.

    Article  Google Scholar 

  25. 25.

    Harsanyi JC: Detection and classification of subpixel spectral signatures in hyperspectral image sequences, Ph.D. dissertation, Department of Computer Science & Electrical Engineering, University of Maryland, Baltimore, Md, USA, 1993.

    Google Scholar 

  26. 26.

    Chang C-I: Hyperspectral Imaging: Techniques for Spectral Detection and Classification. Kluwer Academic /Plenum, New York, NY, USA; 2003.

    Google Scholar 

  27. 27.

    Scharf LL: Statistical Signal Processing. Addison-Wesley, Reading, Mass, USA; 1991.

    Google Scholar 

  28. 28.

    Johnson DH, Dudgeon DE: Array Signal Processing. Prentice Hall, Englewood Cliffs, NJ, USA; 1993.

    Google Scholar 

  29. 29.

    Capon J: High resolution frequency-wavenumber spectrum analysis. Proceedings of the IEEE 1969,57(8):1408-1418.

    Article  Google Scholar 

  30. 30.

    Strang G: Linear Algebra and Its Applications. Harcourt Brace, Orlando, Fla, USA; 1986.

    Google Scholar 

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Correspondence to Heesung Kwon.

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Kwon, H., Nasrabadi, N.M. A Comparative Analysis of Kernel Subspace Target Detectors for Hyperspectral Imagery. EURASIP J. Adv. Signal Process. 2007, 029250 (2006). https://doi.org/10.1155/2007/29250

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Keywords

  • Kernel Function
  • Feature Space
  • Matched Filter
  • Orthogonal Subspace
  • Kernel Version