Two approaches to adaptation of sample myriad to characteristics of SalphaS distribution data

This paper deals with theoretical and numerical simulation based analysis of sample myriad properties for a family of symmetric @a-stable (S@aS) distributions often used for modeling noise in natural environments. The theoretically optimal values of a sample myriad tunable parameter k in the sense of minimal asymptotic variance are obtained. Two practical approaches are proposed to adapt the parameter k to S@aS distribution characteristics for data samples of a limited size. Statistical properties of the developed approaches are studied for cases of a priori unknown parameters of S@aS distribution. A practical application where the proposed approaches can be useful is considered.

[1]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .

[2]  P. Rayner,et al.  A near-optimal receiver for detection in /spl alpha/-stable distributed noise , 1998, Ninth IEEE Signal Processing Workshop on Statistical Signal and Array Processing (Cat. No.98TH8381).

[3]  Vladimir V. Lukin,et al.  Adaptive combined bispectrum-filtering signal processing in radar systems with low SNR , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[4]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[5]  D. Middleton,et al.  Optimum Reception in an Impulsive Interference Environment - Part II: Incoherent Reception , 1977, IEEE Transactions on Communications.

[6]  Gonzalo R. Arce,et al.  Adaptive weighted myriad filter algorithms for robust signal processing in α-stable noise environments , 1998, IEEE Trans. Signal Process..

[7]  D.B. Williams,et al.  On the characterization of impulsive noise with /spl alpha/-stable distributions using Fourier techniques , 1995, Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers.

[8]  Hean-Teik Chuah,et al.  On the Optimal Alpha- $k$ Curve of the Sample Myriad , 2007, IEEE Signal Processing Letters.

[9]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[10]  Panayiotis G. Georgiou,et al.  Alpha-Stable Modeling of Noise and Robust Time-Delay Estimation in the Presence of Impulsive Noise , 1999, IEEE Trans. Multim..

[11]  J. McCulloch,et al.  Simple consistent estimators of stable distribution parameters , 1986 .

[12]  Vladimir V. Lukin,et al.  Myriad based shift parameter estimation method and its application to image filtering and processing , 2005, SPIE Optics + Photonics.

[13]  Gonzalo R. Arce,et al.  Optimality of the myriad filter in practical impulsive-noise environments , 2001, IEEE Trans. Signal Process..

[14]  Gonzalo R. Arce,et al.  Robust techniques for wireless communications in non-gaussian environments , 1997 .

[15]  Aslihan D. Spaulding,et al.  Optimum reception in an impulsive interference environment. I - Coherent detection. II - Incoherent reception , 1977 .

[16]  Vladimir V. Lukin,et al.  Bootstrap based adaptation of sample myriad to characteristics of SαS distribution data , 2009, 2009 IEEE International Symposium on Circuits and Systems.

[17]  Steve McLaughlin,et al.  The estimation of stable distribution parameters from teletraffic data , 2000, IEEE Trans. Signal Process..

[18]  Akira Taguchi.  Adaptive /spl alpha/-trimmed mean filters with excellent detail-preserving , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[19]  Igor Djurovic,et al.  Robust L-estimation based forms of signal transforms and time-frequency representations , 2003, IEEE Trans. Signal Process..

[20]  Gonzalo R. Arce,et al.  Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad Filters , 2002, EURASIP J. Adv. Signal Process..

[21]  Peter A. Stark.  Introduction to Numerical Methods , 1970 .

[22]  S. Abramov,et al.  Adaptation of sample myriad tunable parameter to characteristics of SαS distribution , 2008, 2008 12th International Conference on Mathematical Methods in Electromagnetic Theory.

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

[24]  J. Astola,et al.  Fundamentals of Nonlinear Digital Filtering , 1997 .

[25]  James F. Epperson,et al.  An Introduction to Numerical Methods and Analysis , 2001 .

[26]  Chrysostomos L. Nikias,et al.  Parameter estimation and blind channel identification in impulsive signal environments , 1995, IEEE Trans. Signal Process..

[27]  Gonzalo R. Arce,et al.  A general weighted median filter structure admitting negative weights , 1998, IEEE Trans. Signal Process..

[28]  S. Janson.  Stable distributions , 2011, 1112.0220.

[29]  M. Melamed.  Detection , 2021, SETI: Astronomy as a Contact Sport.

[30]  Chrysostomos L. Nikias,et al.  Fast estimation of the parameters of alpha-stable impulsive interference using asymptotic extreme value theory , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[31]  V. Lukin,et al.  Filtering of frequency modulated signals embedded in α-stable noise using robust DFT forms , 2006, 2006 International Conference - Modern Problems of Radio Engineering, Telecommunications, and Computer Science.

[32]  Vladimir V. Lukin,et al.  Blind evaluation of noise variance in images using myriad operation , 2002, IS&T/SPIE Electronic Imaging.

[33]  Gonzalo R. Arce,et al.  Nonlinear Signal Processing - A Statistical Approach , 2004 .

[34]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[35]  R. Suoranta.  Amplitude Domain Approach to Digital Filtering: Theory and Applicatons of L-filters , 1995 .