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Distributed Parameter Estimation for Univariate Generalized Gaussian Distribution over Sensor Networks

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Abstract

Generalized Gaussian distribution (GGD) is one of the most prominent and widely used parametric distributions to model the statistical properties of various phenomena. Parameter estimation for these distributions becomes a fundamental problem. However, most of the existing parameter estimation techniques are centralized. In this paper, we consider distributed parameter estimation for univariate GGD over sensor networks. Parameters among different nodes are estimated cooperatively for the proposed diffusion techniques. Numerical studies are carried out to evaluate the efficiency of the proposed methods, in terms of average root mean square error and convergence rate.

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References

  1. Q. Ahmed, K.H. Park, M.S. Alouini, Ultrawide bandwidth receiver based on a multivariate generalized Gaussian distribution. IEEE Trans. Wireless Commun. 14(4), 1800–1810 (2015)

    Article  Google Scholar 

  2. B. Aiazzi, L. Alparone, S. Baronti, Estimation based on entropy matching for generalized Gaussian PDF modeling. IEEE Signal Process. Lett. 6(6), 138–140 (1999)

    Article  Google Scholar 

  3. M. Allili, N. Baaziz, M. Mejri, Texture modeling using contourlets and finite mixtures of generalized Gaussian distributions and applications. IEEE Trans. Multimed. 16(3), 772–784 (2014)

    Article  Google Scholar 

  4. O. Besson, On false alarm rate of matched filter under distribution mismatch. IEEE Signal Process. Lett. 22(2), 167–171 (2015)

    Article  Google Scholar 

  5. F. Cattivelli, C. Lopes, A. Sayed, Diffusion recursive least-squares for distributed estimation over adaptive networks. IEEE Trans. Signal Process. 56(5), 1865–1877 (2008)

    Article  MathSciNet  Google Scholar 

  6. F. Cattivelli, A. Sayed, Diffusion LMS strategies for distributed estimation. IEEE Trans. Signal Process. 58(3), 1035–1048 (2010)

    Article  MathSciNet  Google Scholar 

  7. B. Chen, Y. Zhu, J. Hu, J.C. Principe, System parameter identification information criteria and algorithms, System Identification Under Minimum Error Entropy Criteria, vol. 4 (Elsevier, Oxford, 2013), pp. 61–165

    Google Scholar 

  8. Y. Chen, N.C. Beaulieu, Novel low-complexity estimators for the shape parameter of the generalized Gaussian distribution. IEEE Trans. Veh. Technol. 58(4), 2067–2071 (2009)

    Article  Google Scholar 

  9. M. Coban, R. Mersereau, Adaptive subband video coding using bivariate generalized Gaussian distribution model. in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 4, 1990–1993 (1996)

  10. M. Desai, R. Mangoubi, Robust Gaussian and non-Gaussian matched subspace detection. IEEE Trans. Signal Process. 51(12), 3115–3127 (2003)

    Article  MathSciNet  Google Scholar 

  11. G. Gonzalez-Farias, J. Molina, R. Rodriguez-Dagnino, Efficiency of the approximated shape parameter estimator in the generalized Gaussian distribution. IEEE Trans. Veh. Technol. 58(8), 4214–4223 (2009)

    Article  Google Scholar 

  12. J.M. Guo, H. Prasetyo, M. Farfoura, H. Lee, Vehicle verification using features from curvelet transform and generalized Gaussian distribution modeling. IEEE Trans. Intell. Transp. Syst. 16(4), 1989–1998 (2015)

    Article  Google Scholar 

  13. K. Kokkinakis, A.K. Nandi, Exponent parameter estimation for generalized Gaussian probability density functions with application to speech modeling. Signal Process. 85(9), 1852–1858 (2005)

    Article  MATH  Google Scholar 

  14. C. Lopes, A. Sayed, Incremental adaptive strategies over distributed networks. IEEE Trans. Signal Process. 55(8), 4064–4077 (2007)

    Article  MathSciNet  Google Scholar 

  15. R. Mabrouk, F. Dubeau, L. Bentabet, Dynamic cardiac PET imaging: Extraction of time-activity curves using ICA and a generalized Gaussian distribution model. IEEE Trans. Biomed. Eng. 60(1), 63–71 (2013)

    Article  Google Scholar 

  16. S.G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11(7), 674–693 (1989)

    Article  MATH  Google Scholar 

  17. S. Meignen, H. Meignen, On the modeling of small sample distributions with generalized Gaussian density in a maximum likelihood framework. IEEE Trans. Image Process. 15(6), 1647–1652 (2006)

    Article  MathSciNet  Google Scholar 

  18. F. Pascal, L. Bombrun, J.Y. Tourneret, Y. Berthoumieu, Parameter estimation for multivariate generalized Gaussian distributions. IEEE Trans. Signal Process. 61(23), 5960–5971 (2013)

    Article  MathSciNet  Google Scholar 

  19. R. Prasad, H. Saruwatari, K. Shikano, Estimation of shape parameter of GGD function by negentropy matching. Neural Process. Lett. 22(3), 377–389 (2005)

    Article  Google Scholar 

  20. A. Sayed, S.Y. Tu, J. Chen, X. Zhao, Z. Towfic, Diffusion strategies for adaptation and learning over networks: an examination of distributed strategies and network behavior. IEEE Signal Process. Mag. 30(3), 155–171 (2013)

    Article  Google Scholar 

  21. I. Schizas, G. Mateos, G. Giannakis, Distributed LMS for consensus-based in-network adaptive processing. IEEE Trans. Signal Process. 57(6), 2365–2382 (2009)

    Article  MathSciNet  Google Scholar 

  22. H. Shu, H. Huang, S. Rahardja, Analysis of bit-plane probability for generalized Gaussian distribution and its application in audio coding. IEEE Trans. Audio Speech Lang. Process. 20(4), 1167–1176 (2012)

    Article  Google Scholar 

  23. K.S. Song, A globally convergent and consistent method for estimating the shape parameter of a generalized Gaussian distribution. IEEE Trans. Inf. Theory 52(2), 510–527 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  24. K.S. Song, Asymptotic relative efficiency and exact variance stabilizing transformation for the generalized Gaussian distribution. IEEE Trans. Inf. Theory 59(7), 4389–4396 (2013)

    Article  MathSciNet  Google Scholar 

  25. H. Soury, F. Yilmaz, M.S. Alouini, Error rates of m-PAM and m-QAM in generalized fading and generalized Gaussian noise environments. IEEE Commun. Lett. 17(10), 1932–1935 (2013)

    Article  Google Scholar 

  26. M.K. Varanasi, B. Aazhang, Parametric generalized Gaussian density estimation. J. Acoust. Soc. Am. 86(4), 1404–1415 (1989)

    Article  Google Scholar 

  27. L. Xiao, S. Boyd, S.J. Kim, Distributed average consensus with least-mean-square deviation. J. Parallel Distrib. Comput. 67(1), 33–46 (2007)

    Article  MATH  Google Scholar 

  28. J. Yang, Y. Wang, W. Xu, Q. Dai, Image and video denoising using adaptive dual-tree discrete wavelet packets. IEEE Trans. Circuits Syst. Video Technol. 19(5), 642–655 (2009)

    Article  Google Scholar 

  29. J. Yin, J. Sun, X. Jia, Sparse analysis based on generalized Gaussian model for spectrum recovery with compressed sensing theory. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 8(6), 2752–2759 (2015)

    Article  Google Scholar 

  30. S. Yu, A. Zhang, H. LI, A review of estimating the shape parameter of generalized Gaussian distribution. J. Comput. Inf. Syst. 8(21), 9055–9064 (2012)

    Google Scholar 

  31. T. Zhang, A. Wiesel, M. Greco, Multivariate generalized Gaussian distribution: convexity and graphical models. IEEE Trans. Signal Process. 61(16), 4141–4148 (2013)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Computer Science and Technology, Xi’an University of Posts and Telecommunications, Xi’an, Shaanxi, China

    Chen Liang & Zhongmin Wang

  2. Information Systems Technology and Design, Singapore University of Technology and Design, Singapore, Singapore

    Fuxi Wen

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  1. Chen Liang
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  2. Fuxi Wen
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  3. Zhongmin Wang
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Correspondence to Fuxi Wen.

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Liang, C., Wen, F. & Wang, Z. Distributed Parameter Estimation for Univariate Generalized Gaussian Distribution over Sensor Networks. Circuits Syst Signal Process 36, 1311–1321 (2017). https://doi.org/10.1007/s00034-016-0345-0

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  • DOI: https://doi.org/10.1007/s00034-016-0345-0

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