Regularization for spectral matched filter and RX anomaly detector

This paper describes a new adaptive spectral matched filter and a modified RX-based anomaly detector that incorporates the idea of regularization (shrinkage). The regularization has the effect of restricting the possible matched filters (models) to a subset which are more stable and have better performance than the non-regularized adaptive spectral matched filters. The effect of regularization depends on the form of the regularization term and the amount of regularization is controlled by so called regularization coefficient. In this paper the sum-of-squares of the filter coefficients is used as the regularization term and several different values for the regularization coefficient are tested. A Bayesian-based derivation of the regularized matched filter is also provided. Experimental results for detecting and recognizing targets in hyperspectral imagery are presented for regularized and non-regularized spectral matched filters and RX algorithm.

[1]  Geoffrey E. Hinton,et al.  Learning distributed representations of concepts. , 1989 .

[2]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[3]  Daniel R. Fuhrmann,et al.  A CFAR adaptive matched filter detector , 1992 .

[4]  Andreas F. Hayden,et al.  Refinement and generalization of the extension method of covariance matrix inversion by regularization for spectral filtering optimization , 2004, SPIE Optics + Photonics.

[5]  Gary A. Shaw,et al.  Hyperspectral Image Processing for Automatic Target Detection Applications , 2003 .

[6]  D. Stein,et al.  Application of the normal compositional model to the analysis of hyperspectral imagery , 2003, IEEE Workshop on Advances in Techniques for Analysis of Remotely Sensed Data, 2003.

[7]  E. M. Winter,et al.  Anomaly detection from hyperspectral imagery , 2002, IEEE Signal Process. Mag..

[8]  Sailes K. Sengijpta.  Fundamentals of Statistical Signal Processing: Estimation Theory , 1995 .

[9]  Xiaoli Yu,et al.  Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution , 1990, IEEE Trans. Acoust. Speech Signal Process..

[10]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .

[11]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[12]  S. Kay.  Fundamentals of statistical signal processing: estimation theory , 1993 .

[13]  Edward J. Wegman,et al.  Statistical Signal Processing , 1985 .

[14]  James Theiler,et al.  Improved matched-filter detection techniques , 1999, Optics & Photonics.

[15]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[16]  Vic Barnett,et al.  Outliers in Statistical Data , 1980 .

[17]  Alan P. Schaum,et al.  Application of stochastic mixing models to hyperspectral detection problems , 1997, Defense, Security, and Sensing.

[18]  Dimitris G. Manolakis,et al.  Comparative analysis of hyperspectral adaptive matched filter detectors , 2000, SPIE Defense + Commercial Sensing.

[19]  David G. Stork,et al.  Pattern Classification , 1973 .

[20]  Irving S. Reed,et al.  A new CFAR detection test for radar , 1991, Digit. Signal Process..

[21]  Alan P. Schaum,et al.  Spectral subspace matched filtering , 2001, SPIE Defense + Commercial Sensing.

[22]  James Theiler,et al.  Sparse linear filters for detection and classification in hyperspectral imagery , 2006, SPIE Defense + Commercial Sensing.

[23]  Sameer Singh,et al.  Novelty detection: a review - part 1: statistical approaches , 2003, Signal Process..

[24]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .