A low complexity robust detector in impulsive noise

This paper demonstrates the effectiveness of a nonlinear extension to the matched filter for signal detection in certain kinds of non-Gaussian noise. The decision statistic is based on a new measure of similarity that can be considered as an extension of the correlation statistic used in the matched filter. The optimality of the matched filter is predicated on second order statistics and hence leaves room for improvement, especially when the assumption of Gaussianity is not applicable. The proposed method incorporates higher order moments in the decision statistic and shows an improvement in the receiver operating characteristics (ROC) for non-Gaussian noise, in particular, those that are impulsive distributed. The performance of the proposed method is demonstrated for detection in two types of widely used impulsive noise models, the alpha-stable model and the two-term Gaussian mixture model. Moreover, unlike other kernel based approaches, and those using the characteristic functions directly, this method is still computationally tractable and can easily be implemented in real-time.

[1]  John Shawe-Taylor,et al.  Canonical Correlation Analysis: An Overview with Application to Learning Methods , 2004, Neural Computation.

[2]  Heesung Kwon,et al.  Hyperspectral target detection using kernel matched subspace detector , 2004, 2004 International Conference on Image Processing, 2004. ICIP '04..

[3]  Luc Devroye,et al.  Combinatorial methods in density estimation , 2001, Springer series in statistics.

[4]  R. Weron.  Correction to: "On the Chambers–Mallows–Stuck Method for Simulating Skewed Stable Random Variables" , 1996 .

[5]  Deniz Erdogmus,et al.  Robust matched filtering in the feature space , 2005, 2005 13th European Signal Processing Conference.

[6]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[7]  Arnt-Børre Salberg,et al.  Robust Multidimensional Matched Subspace Classifiers Based on Weighted Least-Squares , 2007, IEEE Transactions on Signal Processing.

[8]  L. Scharf,et al.  Statistical Signal Processing: Detection, Estimation, and Time Series Analysis , 1991 .

[9]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[10]  N. Aronszajn.  Theory of Reproducing Kernels. , 1950 .

[11]  Carl W. Helstrom,et al.  Elements of signal detection and estimation , 1994 .

[12]  V. Zolotarev.  One-dimensional stable distributions , 1986 .

[13]  J. Príncipe,et al.  The Correntropy Mace Filter for Image Recognition , 2006, 2006 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing.

[14]  John G. Proakis,et al.  Digital Communications , 1983 .

[15]  H. Vincent Poor,et al.  Multiuser detection in flat fading non-Gaussian channels , 2002, IEEE Trans. Commun..

[16]  C. L. Brown.  Score functions for locally subptimum and locally suboptimum rank detection in alpha-stable interference , 2001, Proceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing (Cat. No.01TH8563).

[17]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

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

[19]  José Carlos Príncipe,et al.  Generalized correlation function: definition, properties, and application to blind equalization , 2006, IEEE Transactions on Signal Processing.

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

[21]  Deniz Erdogmus,et al.  Information Theoretic Learning , 2005, Encyclopedia of Artificial Intelligence.

[22]  H. Vincent Poor,et al.  Efficient estimation of Class A noise parameters via the EM algorithm , 1991, IEEE Trans. Inf. Theory.

[23]  Deniz Erdogmus,et al.  A mutual information extension to the matched filter , 2005, Signal Process..

[24]  Tom E. Bishop,et al.  Blind Image Restoration Using a Block-Stationary Signal Model , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[25]  P. Laguna,et al.  Signal Processing , 2002, Yearbook of Medical Informatics.

[26]  Thomas Kailath,et al.  RKHS approach to detection and estimation problems-IV: Non-Gaussian detection , 1973, IEEE Trans. Inf. Theory.

[27]  S. Kassam.  Signal Detection in Non-Gaussian Noise , 1987 .

[28]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[29]  Michael I. Jordan,et al.  Kernel independent component analysis , 2003 .

[30]  Deniz Erdogmus,et al.  A Closed Form Solution for a Nonlinear Wiener Filter , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[31]  Robert P. W. Duin,et al.  On the Choice of Smoothing Parameters for Parzen Estimators of Probability Density Functions , 1976, IEEE Transactions on Computers.

[32]  J. Huston McCulloch,et al.  13 Financial applications of stable distributions , 1996 .

[33]  G. Turin,et al.  An introduction to matched filters , 1960, IRE Trans. Inf. Theory.

[34]  C. L. Nikias,et al.  Signal processing with alpha-stable distributions and applications , 1995 .

[35]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.