This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Kernel Matched Subspace Detectors for Hyperspectral Target Detection
February 2006 (vol. 28 no. 2)
pp. 178-194
In this paper, we present a kernel realization of a matched subspace detector (MSD) that is based on a subspace mixture model defined in a high-dimensional feature space associated with a kernel function. The linear subspace mixture model for the MSD is first reformulated in a high-dimensional feature space and then the corresponding expression for the generalized likelihood ratio test (GLRT) is obtained for this model. The subspace mixture model in the feature space and its corresponding GLRT expression are equivalent to a nonlinear subspace mixture model with a corresponding nonlinear GLRT expression in the original input space. In order to address the intractability of the GLRT in the feature space, we kernelize the GLRT expression using the kernel eigenvector representations as well as the kernel trick where dot products in the feature space are implicitly computed by kernels. The proposed kernel-based nonlinear detector, so-called kernel matched subspace detector (KMSD), is applied to several hyperspectral images to detect targets of interest. KMSD showed superior detection performance over the conventional MSD when tested on several synthetic data and real hyperspectral imagery.

[1] D. Manolakis and G. Shaw, “Detection Algorithms for Hyperspectral Imaging Applications,” IEEE Signal Processing Magazine, vol. 19, no. 1, pp. 29-43, Jan. 2002.
[2] J.C. Harsanyi and C.-I. Chang, “Hyperspectral Image Classification and Dimensionality Reduction: An Orthogonal Subspace Projection Approach,” IEEE Trans. Geoscience and Remote Sensing, vol. 32, no. 4, pp. 779-785, July 1994.
[3] I.S. Reed and X. Yu, “Adaptive Multiple-Band CFAR Detection of an Optical Pattern with Unknown Spectral Distribution,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 38, no. 10, pp. 1760-1770, Oct. 1990.
[4] C.-I. Chang, X.-L. Zhao, M.L.G. Althouse, and J.J. Pan, “Least Squares Subspace Projection Approach to Mixed Pixel Classification for Hyperspectral Images,” IEEE Trans. Geoscience and Remote Sensing, vol. 36, no. 3, pp. 898-912, May 1998.
[5] G. Healey and D. Slater, “Models and Methods for Automated Material Identification in Hyperspectral Imagery Acquired under Unknown Illumination and Atmospheric Conditions,” IEEE Trans. Geoscience and Remote Sensing, vol. 37, no. 6, pp. 2706-2717, Nov. 1999.
[6] L.L. Scharf and B. Friedlander, “Matched Subspace Detectors,” IEEE Trans. Signal Processing, vol. 42, no. 8, pp. 2146-2157, Aug. 1994.
[7] H.L. Van Trees, Detection, Estimation, and Modulation Theory. John Wiley and Sons, 1968.
[8] B. Thai and G. Healey, “Invariant Subpixel Material Detection in Hyperspectral Imagery,” IEEE Trans. Geoscience and Remote Sensing, vol. 40, no. 3, pp. 599-608, Mar. 2002.
[9] V.N. Vapnik, The Nature of Statistical Learning Theory. Springer, 1999.
[10] B. Schölkopf and A.J. Smola, Learning with Kernels. MIT Press, 2002.
[11] K.R. Müller, S. Mika, G. Rätsch, K. Tsuda, and B. Schölkopf, “A Introduction to Kernel-Based Learning Algorithms,” IEEE Trans. Neural Networks, no. 2, pp. 181-202, 2001.
[12] G. Baudat and F. Anouar, “Generalized Discriminant Analysis Using a Kernel Approach,” Neural Computation, no. 12, pp. 2385-2404, 2000.
[13] A. Ruiz and P. López de Teruel, “Nonlinear Kernel-Based Statistical Pattern Analysis,” IEEE Trans. Neural Networks, vol. 12, no. 1, pp. 16-32, 2001.
[14] H. Kwon and N.M. Nasrabadi, “Kernel RX-Algorithm: A NonLinear Anomaly Detector for Hyperspectral Imagery,” IEEE Trans. Geoscience and Remote Sensing, vol. 43, no. 2, pp. 388-397, Feb. 2005.
[15] B. Schölkopf, A.J. Smola, and K.-R. Müller, “Kernel Principal Component Analysis,” Neural Computation, no. 10, pp. 1299-1319, 1999.
[16] T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning. Springer, 2001.
[17] G. Strang, Linear Algebra and Its Applications. Harcourt Brace & Company, 1986.
[18] D. Cremers, T. Kohlberger, and C. Schörr, “Shape Statistics in Kernel Space for Variational Image Segmentation,” Pattern Recognition, vol. 36, pp. 1929-1943, 2003.
[19] R.C. Williamson, A.J. Smola, and B. Schölkopf, “Generalization Performance of Regularization Networks and Support Vector Machines via Entropy Numbers of Compact Operators,” IEEE Trans. Information Theory, vol. 47, no. 6, pp. 2516-2532, 2001.
[20] F.R. Bach and M.I. Jordan, “Kernel Independent Component Analysis,” J. Machine Learning Research, vol. 47, pp. 1-48, 2002.
[21] M. Girolami, “Mercer Kernel-Based Clustering in Feature Space,” IEEE Trans. Neural Networks, vol. 13, no. 3, pp. 780-784, 2002.
[22] H. Kwon and N.M. Nasrabadi, “A Comparative Study of Kernel Spectral Matched Signal Detectors for Hyperspectral Target Detection,” Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XI, Proc. SPIE, vol. 5806, pp. 827-838, 2004.

Index Terms:
Index Terms- Target detection, subspace detectors, matched signal detectors, kernel-based learning, hyperspectral data, spectral mixture models, nonlinear detection.
Citation:
Heesung Kwon, Nasser M. Nasrabadi, "Kernel Matched Subspace Detectors for Hyperspectral Target Detection," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 2, pp. 178-194, Feb. 2006, doi:10.1109/TPAMI.2006.39
Usage of this product signifies your acceptance of the Terms of Use.