基于隐马尔可夫模型平滑估计的随机噪声压制方法
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摘要
以地震勘探记录去噪为目标,本文提出了一种隐马尔可夫模型平滑估计方法.它是在基本隐马尔可夫模型滤波基础之上,运用信号检测环节将带噪信号段和无信号段加以区分,构建带噪地震记录的状态转移模型,在贝叶斯框架下,利用平滑密度函数进行状态估计,从而达到压制噪声的目的.数值模拟表明,无论对信噪比还是均方误差,隐马尔可夫模型平滑估计处理后的重构信号优于常规的维纳滤波所恢复信号.我们可以期待这种方法会成为实际地震记录噪声压制的有效手段.
Aiming at denoising seismic prospecting records, this paper proposes a method of hidden Markov model smoothing estimate(HMM-S). Based on the basic Hidden Markov Model filter, it plots the whole seismic records into noisy signal segment and no signal segment by signal detection, establishes the state transition model of noisy seismic records, and under Bayesian framework, implements state estimate using smoothing density function to suppress noise. Simulation shows that for SNR and MSE, the status of the recovered signal processed by hidden Markov model smoothing estimate(HMM-S) excels those of Wiener filter.
Aiming at denoising seismic prospecting records, this paper proposes a method of hidden Markov model smoothing estimate(HMM-S). Based on the basic Hidden Markov Model filter, it plots the whole seismic records into noisy signal segment and no signal segment by signal detection, establishes the state transition model of noisy seismic records, and under Bayesian framework, implements state estimate using smoothing density function to suppress noise. Simulation shows that for SNR and MSE, the status of the recovered signal processed by hidden Markov model smoothing estimate(HMM-S) excels those of Wiener filter.
引文
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[15] De Jong P, Shephard N. The simulation smoother for time series models[J]. Biometrika, 1995,82:339-350．
[16] Shepard N, Pitt M K. Likelihood analyis of non-Gaussian measurement time series[J]. Biometrika, 1997, 84 :653-667．
[17] Mayne D Q. A solution of the smoothing problem for linear dynamic systems[J]. Automatica, 1966,4:73-92．
[18] Kim S, Shephard N, Chib S. Stochastic volatility: Likelihood inference and comparison with ARCH models[J]. Review of Economics Studies, 1998,65:361-393．
[19] Russel S, Norvig P. Artificial intelligence: A modern approach [M]. 2nd ed. New York: Pearson Education, 2003．
[20] Baum L E, Petrie T, Soules G, et al. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains[J]. Ann. Math. Statist., 1970, 41(1) :164-171．
[21] Viterbi A J. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm [J]. IEEE Transactions on Information Theory, 1967,13(2) :260-269．
[22] Forney G D. The Viterbi algorithm[J]. Proceedings of the IEEE, 1973,61(3) :268-278．
[2] 薛亚茹,陆文凯,陈小宏,等.基于正交多项式变换的CMP动 校正道集随机噪声压制[J].地球物理学进展,2009,24(1) :159-163． Xue Y R , Lu W K, Chen X H, et al. Random noise attenuation based on orthogonal polynomials transform for CMP gathers[J]. Progress in Geophysics. 2009,24(1) :159-163．
[3] 张军华,吕宁,田连玉,等.地震资料去噪方法、技术综合评述[J].地球物理学进展,2005,20(4) :1083-1091． Zhang J H, Lu N, Tian L Y, et al. An overview of the methods and techniques for seismic data noise attenuation[J]. Progress in Geophysics, 2005,20(4) :1083-1091．
[4] 高静怀,毛剑,满蔚仕,等.叠前地震资料噪声衰减的小波域方法研究.地球物理学报,2006,49(4) :1155-1163． Gao J H , Mao J , Man W S , et al. On the denoising method of prestack seismic data in wavelet domain[J]. Chinese J .Geophys. (in Chinese) ,2006,49(4) :1155-1163．
[5] Rabiner L R. A tutorial on hidden Markov models and selected applications in speech recognition [J]. Proceedings of the IEEE, 1989, 77(2) :257-286．
[6] Rabiner L R, Juang B H. An introduction to hidden Markov models[J]. IEEE ASSP Magazine,1986,1:4-15．
[7] Kay S M, Fundamentals of statistical signal processing, volume Ⅰ: estimation theory [M]. New York: Pearson Education, 1993．
[8] Kay S M. Fundamentals of statistical signal processing. volume Ⅱ: detction theory [M]. New York: Pearson Education, 1993．
[9] Arulampalam M S, Maskell S, Gordon N, et al. A tutorial on particle filters for online nonlinear/Non-Gaussian Bayesian tracking[J]. IEEE Transactions on signal processing, 2002,50(2) :174-188．
[10] Kitagawa G. Non-Gaussian state-space modeling of nonstationary time series [J]. Journal of the American Statistical Association, 1987 ,82(400) : 1032-1041．
[11] Godsill S J, Doucet A, West M. Monte Carlo smoothing for nonlinear time series[J]. Journal of the American Statistical Association, 2004 ,99(465) :156-167．
[12] Vaseghi S V. Advanced digital signal processing and noise reduction[M]. 2nd ed. England: John Wiley&Sons, 2000．
[13] West M, Harrison J. Bayesian forecasting and dynamic models[M]. 2nd ed. New York: Springer-Verlag, 1997．
[14] Gilks W R, Berzuini C. Following a moving target-Monte Carlo inference for dynamic Bayesian models[J]. Journal of the Royal Statistical Society, Ser. B. 2000,63:1-20．
[15] De Jong P, Shephard N. The simulation smoother for time series models[J]. Biometrika, 1995,82:339-350．
[16] Shepard N, Pitt M K. Likelihood analyis of non-Gaussian measurement time series[J]. Biometrika, 1997, 84 :653-667．
[17] Mayne D Q. A solution of the smoothing problem for linear dynamic systems[J]. Automatica, 1966,4:73-92．
[18] Kim S, Shephard N, Chib S. Stochastic volatility: Likelihood inference and comparison with ARCH models[J]. Review of Economics Studies, 1998,65:361-393．
[19] Russel S, Norvig P. Artificial intelligence: A modern approach [M]. 2nd ed. New York: Pearson Education, 2003．
[20] Baum L E, Petrie T, Soules G, et al. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains[J]. Ann. Math. Statist., 1970, 41(1) :164-171．
[21] Viterbi A J. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm [J]. IEEE Transactions on Information Theory, 1967,13(2) :260-269．
[22] Forney G D. The Viterbi algorithm[J]. Proceedings of the IEEE, 1973,61(3) :268-278．
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