An Adaptive Wavelet-Based Signal Denoising Schem
Subject Areas : electrical and computer engineeringM. nasri 1 , H. Nezamabadi-pour 2 , S. Saryazdi 3
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Abstract :
In this paper, a new class of nonlinear thresholding functions with a tunable shape parameter for wavelet-based signal denoising is presented. In addition, a new learning technique for training of thresholding neural network is introduced. Unlike to existing methods, both the shape and the threshold parameters are tuned simultaneously using LMS rule. This permits us to consider the effects of both the threshold and the shape parameters on denoising. The proposed functions are tested in both universal-threshold and subband-adaptive denoising and compared with conventional functions. In addition, to evaluate the proposed training method, several numerical examples are performed. The experimental results obtained from denoising of several standard benchmark signals confirm the efficiency and effectiveness of the proposed methods.
[1] D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation by wavelet shrinkage," Biometrika, vol. 81, no. 3, pp. 425-455, Sep. 1994.
[2] D. L. Donoho, "De - noising by soft - thresholding," IEEE Trans.Inform. Theory, vol. 41, no. 3, pp. 613-627, May 1995.
[3] D. L. Donoho and I. M. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," J. Amer. Statist. Assoc., vol. 90, no. 432, pp. 1200-1224, Dec. 1995.
[4] M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, "Wavelet – based signal processing using hidden Markov models," IEEE Trans. Signal Processing, vol. 46, no. 4, pp. 886-902, Apr. 1998.
[5] N. P. Subramaniam, M. S. Sudhakar, and K. B. Bagan, "A modified approach for denoising of power line signals using stein’s unbiased risk estimator incorporated with phaselet transform," Iranian J. of Elec. and Comp. Eng., vol. 5, no. 1, pp. 51-56, Winter-Spring 2006.
[6] X. P. Zhang and M. D. Desai, "Adaptive denoising based on SURE risk," IEEE Signal Processing Letters, vol. 5, no. 10, pp. 265-267, Oct. 1998.
[7] X. P. Zhang, "A new time-scale adaptive denoising method based on wavelet shrinkage," in Proc. ICASSP’99, vol. 3, pp. 1629-1632, Phoenix, Arizona, Mar. 1999.
[8] H. Y. Gao and A. G. Bruce, "Waveshrink with firm shrinkage," Statistica Sinica, vol. 7, no. 4, pp. 855-874, 1997.
[9] H. Gao, "Wavelet shrinkage denoising using the nonnegative garrote," J. Comput. Graph. Stat., vol. 7, no. 4, pp. 469-488, Dec. 1998.
[10] W. Q. Zhang and G. Song, "A translation-invariant wavelet de-noising method based on a new thresholding function," in Proc. Second Int. Conf. on Machine Learning and Cyber, vol. 4, pp. 2341-2345, Nov. 2003.
[11] B. J. Yoon and P. P. Vaidyanathan, "Wavelet-based denoising bycustomized thresholding," in Proc. ICASSP’04, vol. 2, pp. 925-928, May 2004.
[12] Z. D. Zhao, "Wavelet shrinkage denoising by generalized thresholding function," in Proc. Fourth Int. Conf. on Machine Learning and Cybernetic, vol. 9, pp. 5501-5506, Aug. 2005.
[13 ] م. نصري، ح. نظام آبادي پور و س. سريزدي، "حذف وفقي نويز از سيگنال در حوزه موجك،" دوازدهمين كنفرانس بي نالمللي انجمن كامپيوتر ايران،صص1932-1927 ، تهران، ايران، اسفند 1385.
[14] M. A. Kavchak and H. M. Budman, "Adaptive neural network architectures for nonlinear function estimation," in Proc. American Control Conf., vol. 1, pp. 63-67, Jun. 1998.
[15] Q. Zhang and A. Beveniste, "Wavelet networks," IEEE Trans. On Neural Networks, vol. 3, no. 6, pp. 889-898, Nov. 1992.
[16] X. L. Chen, M. Tian, and W. B. Yao, "GPR signal de-noising by using wavelet networks," in Proc. 4th Int. Conf. on Machine Learning and Cybernetics, vol. 8, pp. 4690-4693, Aug. 2005.
[17] U. Lotric, "Wavelet based denoising integrated into multilayered perceptron," Neurocomputing, vol. 62, pp. 179-196, Dec. 2004.
[18] X. P. Zhang, "Thresholding neural network for adaptive noise reduction," IEEE Tran. on Neural Networks, vol. 12, no. 3, pp. 567-584, May 2001.
[19] S. Haykin, Neural Network: A Comprehensive Foundation, Prentice-Hall, NJ, 2nd ed., 1999.
[20] S. Haykin, Adaptive Filter Theory, Prentice-Hall, Englewood Cliffs ,New Jersey, 1996.
[21] C. Stein, "Estimation of the mean of a multivariate normal distribution," Ann. Stat., vol. 9, no. 6, pp. 1135-1151, 1981.
[22] V. P. Oikonomou and D. I. Fotiadis, "A Bayesian approach for biomedical signal denoising," presented at IEEE ITAB 2006 Conf.,Ioannina, Greece, Oct. 2006.