Complex-valued filtering based on the minimization of complex-error entropy

IEEE Transactions on Neural Networks and Learning Systems

Volumn 24, Issue 5, 2013, Pages 695-708

  Huang, Songyan ^a   Li, Chunguang ^a   Liu, Yiguang ^b  

^a ZHEJIANG UNIVERSITY   (China)

^b SICHUAN UNIVERSITY   (China)

Author keywords

Complex valued filtering; Entropy bound minimization; Minimization of complex error entropy; Neural network

Indexed keywords

COMPLEX DOMAINS; COMPLEX GRADIENT; COMPLEX-VALUED; ENTROPY BOUND; ERROR ENTROPY; INFORMATION-THEORETIC METHODS; LINEAR FILTERING; NONLINEAR CHANNEL;

ALGORITHMS; ESTIMATION; NEURAL NETWORKS;

ENTROPY;

EID: 84884944295     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2013.2241788     Document Type: Article

References (45)

1. S. Haykin, Adaptive Filter Theory. Englewood Cliffs, NJ, USA: Prentice-Hall, 1996.
2. N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series with Engineering Applications. Cambridge, MA, USA: MIT Press, 1949.
3. C. E. Shannon, "A mathematical theory of communications," Bell Syst. Tech. J., vol. 27, no. 3, pp. 379-423, 1948.
4. D. Erdogmus and J. C. Principe, "An error-entropy minimization algorithm for supervised training of nonlinear adaptive systems," IEEE Trans. Signal Process., vol. 50, no. 7, pp. 1780-1786, Jul. 2002. (Pubitemid 34882696)
5. A. Renyi, Probability Theory. New York, USA: Elsevier, 1970.
6. I. Santamaria, D. Erdogmus, and J. C. Principe, "Entropy minimization for supervised digital communications channel equalization," IEEE Trans. Signal Process., vol. 50, no. 5, pp. 1184-1192, May 2002. (Pubitemid 34515278)
7. J. M. Santos, L. A. Alexandre, and J. M. De Sá, "The error entropy minimization algorithm for neural network classification," in Proc. Int. Conf. Recent Adv. Soft Comput., Dec. 2004, pp. 92-97.
8. D. T. Pham, F. Vrins, and M. Verleysen, "On the risk of using Renyi's entropy for blind source separation," IEEE Trans. Signal Process., vol. 56, no. 10, pp. 4611-4620, Oct. 2008.
9. F. Vrins, D. T. Pham, and M. Verleysen, "Is the general form of Renyi's entropy a contrast for source separation?" in Proc. 7th Int. Conf. Independ. Compon. Anal. Signal Separat., vol. 4666. Sep. 2007, pp. 129-136.
10. X. L. Li and T. Adali, "Flexible adaptive filtering by minimization of error entropy bound and its application to system identification," in Proc. IEEE Int. Conf. Acoust., Speech Signal Proc., Dallas, TX, USA, Mar. 2010, pp. 1886-1889.
11. X. L. Li and T. Adali, "Independent component analysis by entropy bound minimization," IEEE Trans. Signal Process., vol. 58, no. 10, pp. 5151-5164, Oct. 2010.
12. H. L. Li, X. L. Li, M. Anderson, and T. Adali, "A class of adaptive algorithms based on entropy estimation achieving CRLB for linear non-Gaussian filtering," IEEE Trans. Signal Process., vol. 60, no. 4, pp. 2049-2055, Apr. 2012.
13. X. L. Li and T. Adali, "Complex independent component analysis by entropy bound minimization," IEEE Trans. Circuits Syst. I, Regular Papers, vol. 57, no. 7, pp. 1417-1430, Jul. 2010.
14. T. Adali and S. Haykin, Adaptive Signal Processing: Next Genaration Solutions. Piscataway, NJ, USA: IEEE Press, 2010.
15. H. Leung and S. Haykin, "The complex backpropagation algorithm," IEEE Trans. Signal Process., vol. 39, no. 9, pp. 2101-2104, Sep. 1991.
16. C. You and D. Hong, "Nonlinear blind equalization schemes using complex-valued multilayer feedforward neural networks," IEEE Trans. Neural Netw., vol. 9, no. 6, pp. 1442-1455, Nov. 1998. (Pubitemid 128742421)
17. X. L. Li and T. Adali, "Complex-valued linear and widely linear filtering using MSE and Gaussian entropy," IEEE Trans. Signal Process., vol. 60, no. 11, pp. 5672-5684, Nov. 2012.
18. X. L. Li and T. Adali, "Complex-valued Gaussian signal processing: Optimality of MSE, incorporation of full statistics, and a unified view," in Proc. 45th Annu. Conf. Inf. Sci. Syst., Mar. 2011, pp. 1-5.
19. S. Kullback, Information Theory and Statistics. New York, USA: Dover, 1968.
20. T. Adali, P. J. Schreier, and L. L. Scharf, "Complex-valued signal processing: The proper way to deal with impropriety," IEEE Trans. Signal Process., vol. 59, no. 11, pp. 5101-5125, Nov. 2011.
21. M. Novey, T. Adali, and A. Roy, "A complex generalized Gaussian distribution-characterization, generation, and estimation," IEEE Trans. Signal Process., vol. 58, no. 3, pp. 1427-1433, Mar. 2010.
22. B. Picinbono, "On circularity," IEEE Trans. Signal Process., vol. 42, no. 12, pp. 3473-3482, Dec. 1994.
23. A. Zerguine, C. Cowan, and M. Bettayeb, "Adaptive echo cancellation using least mean mixed-norm algorithm," IEEE Trans. Signal Process., vol. 45, no. 5, pp. 1340-1343, May 1997. (Pubitemid 127766079)
24. P. Bouboulis, K. Slavakis, and S. Theodoridis, "Adaptive learning in complex reproducing kernel Hilbert spaces employing Wirtinger's subgradients," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 3, pp. 425-438, Mar. 2012.
25. J. C. Principe, Information Theoretic Learning. New York, USA: Springer-Verlag, 2010.
26. L. M. Silva, J. M. Sa, and L. A. Alexandre, "Neural network classification using Shannon's entropy," in Proc. Eur. Symp. Arif. Neural Netw., Apr. 2005, pp. 217-222.
27. A. van den Bos, "Complex gradient and Hessian," IEEE Proc. Vis. Image Signal Process., vol. 141, no. 6, pp. 380-382, Dec. 1994.
28. D. H. Brandwood, "A complex gradient operator and its application in adaptive array theory," IEEE Proc. F Commun. Radar Signal Process., vol. 130, no. 1, pp. 11-16, Feb. 1983.
29. W. Wirtinger, "Zur formalen theorie der funktionen von mehr komplexen veränderlichen," Math. Ann., vol. 97, no. 1, pp. 357-375, Dec. 1927.
30. K. Kreutz-Delgado, "The complex gradient operator and the CR-calculus," Dept. Elect. Comput. Eng., Univ. California, San Diego, USA, Tech. Rep. ECE275A, 2006.
31. T. Adali, H. L. Li, M. Novey, and J. F. Cardoso, "Complex ICA using nonlinear functions," IEEE Trans. Signal Process., vol. 56, no. 9, pp. 4536-4544, Sep. 2008.
32. B. Picinbono and P. Chevalier, "Widely linear estimation with complex data," IEEE Trans. Signal Process., vol. 43, no. 8, pp. 2030-2033, Aug. 1995.
33. C. C. Took and D. P. Mandic, "A quaternion widely linear adaptive filter," IEEE Trans. Signal Process., vol. 58, no. 8, pp. 4427-4431, Aug. 2010.
34. D. Mandic and V. S. L. Goh, Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models. New York, USA: Wiley, 2009.
35. G. M. Georgiou and C. Koutsougeras, "Complex domain backpropagation," IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 39, no. 5, pp. 330-334, May 1992.
36. N. Benvenuto and F. Piazza, "On the complex backpropagation algorithm," IEEE Trans. Signal Process., vol. 40, no. 4, pp. 967-968, Apr. 1992.
37. S. Chen, S. McLaughlin, and B. Mulgrew, "Complex-valued radial basic function network, part I: Network architecture and learning algorithms," Signal Process., vol. 35, no. 1, pp. 19-31, Jan. 1994.
38. Q. Gan, P. Saratchandran, N. Sundararajan, and K. R. Subramanian, "A complex valued radial basis function network for equalization of fast time varying channels," IEEE Trans. Neural Netw., vol. 10, no. 4, pp. 958-960, Jul. 1999.
39. J. P. Deng, N. Sundararajan, and P. Saratchandran, "Communication channel equalization using complex-valued minimal radial basis function neural networks," IEEE Trans. Neural Netw., vol. 13, no. 3, pp. 687-696, May 2002.
40. S. Chen, S. McLaughlin, and B. Mulgrew, "Complex-valued radial basis function network, part II: Application to digital communications channel equalisation," Signal Process., vol. 36, no. 2, pp. 175-188, Mar. 1994.
41. A. Uncini, L. Vecci, P. Campolucci, and F. Piazza, "Complex-valued neural networks with adaptive spline activation function for digital radio links nonlinear equalization," IEEE Trans. Signal Process., vol. 47, no. 2, pp. 505-514, Feb. 1999.
42. I. Cha and S. A. Kassam, "Channel equalization using adaptive complex radial basis function networks," IEEE J. Sel. Areas Commun., vol. 13, no. 1, pp. 122-131, Jan. 1995.
43. K. E. Hild, D. Erdogmus, K. Torkkola, and J. C. Principe, "Feature extraction using information-theoretic learning," IEEE Trans. Pattern Anal. Mach. Intell., vol. 28, no. 9, pp. 1385-1392, Sep. 2006. (Pubitemid 44132646)
44. C. C. Took, S. C. Douglas, and D. P. Mandic, "On approximate diagonalization of correlation matrices in widely linear signal processing," IEEE Trans. Signal Process., vol. 60, no. 3, pp. 1469-1473, Mar. 2012.
45. S. U. H. Qureshi, "Adaptive equalization," Proc. IEEE, vol. 73, no. 9, pp. 1349-1387, Sep. 1985.