Kernel RX-algorithm: a nonlinear anomaly detector for hyperspectral imagery

• Published in: IEEE transactions on geoscience and remote sensing Vol. 43; no. 2; pp. 388 - 397
• Main Authors: Heesung Kwon, Nasrabadi, N.M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Anomalies; Anomaly detection; Applied geophysics; Detection algorithms; Detectors; Earth sciences; Earth, ocean, space; Exact sciences and technology; Gaussian distribution; hyperspectral images; Hyperspectral imaging; Hyperspectral sensors; Imagery; Internal geophysics; Kernel; kernel-based learning; Kernels; Layout; Mapping; Mathematical analysis; Mathematical models; Military; Military computing; Nonlinearity; Object detection; target detection; Testing; algorithms; mines; detection; target detection; hyper-spectral images; testing; imagery; kernels; cartography; anomalies; Anomaly detection; kernel- based learning
• ISSN: 0196-2892; 1558-0644
• DOI: 10.1109/TGRS.2004.841487

We present a nonlinear version of the well-known anomaly detection method referred to as the RX-algorithm. Extending this algorithm to a feature space associated with the original input space via a certain nonlinear mapping function can provide a nonlinear version of the RX-algorithm. This nonlinear RX-algorithm, referred to as the kernel RX-algorithm, is basically intractable mainly due to the high dimensionality of the feature space produced by the nonlinear mapping function. However, in this paper it is shown that the kernel RX-algorithm can easily be implemented by kernelizing the RX-algorithm in the feature space in terms of kernels that implicitly compute dot products in the feature space. Improved performance of the kernel RX-algorithm over the conventional RX-algorithm is shown by testing several hyperspectral imagery for military target and mine detection.