基于广义合成分析和深度神经网络的自回归系数估计方法

doi:10.12263/DZXB.20200644

摘要/Abstract

摘要： 自回归（AR）模型是一类描述时序序列相关性的有效方法，经典的AR系数估计方法对残差信号做了简单的假设，在噪声干扰等复杂场景中难以准确估计AR系数，而基于深度神经网络（DNN）的AR （DNN-AR）系数估计方法在训练中容易受到莱文逊-杜宾迭代（LDR）解法的数值稳定性的影响.为改善DNN-AR系数训练的稳定性和整体性能，在保证系统稳定性的前提下，本文利用精度转化提高系统运算速度的思路，提出了基于广义合成分析（GABS）模型的深度网络结构改善方法，提高了AR系数在含噪环境下估计的准确性和网络训练的稳定性.组合DNN的GABS （GABS-DNN）的模型由三个主要部分组成：修正器的谱增强网络、编码器的DNN预处理及LDR参数估计和解码器的AR系数到功率谱的转换.在优化目标函数的过程中，引入了增强谱和观测谱的误差，减少了反向传播时LDR的梯度对增强网络的影响，实现了稳定估计含噪语音的AR系数.

关键词: AR系数, 广义合成分析, 深度神经网络, 莱文逊-杜宾迭代解

Abstract: The auto-regressive (AR) model is an effective method to describe the correlation of time series.The classic AR coefficient estimation method utilizes a simple assumption about residual signal.It is a challenge to accurately estimate the auto-regressive coefficients in a complex environment such as noise or interference.Even though Deep Neural Networks (DNN)based AR (DNN-AR) coefficient estimation method can estimate the AR coefficients in a complex environment,the DNN-AR method is easily affected by the numerical stability of Levinson-Durbin recursion (LDR) approach during the training stage.The main target is to improve the stability and overall performance of the DNN-AR based method.In this paper,the precision transform method is utilized to improve computational efficiency while keeping system stability,and the generalized analysis-by-synthesis combing DNN (GABS-DNN) model is proposed for improving the accuracy of AR coefficient estimation and stability of the DNN training in the noisy environment.The GABS-DNN model consists of three main parts:spectrum enhancement network in the modifier,DNN preprocessing and LDR parameter estimation at the encoder,and the conversion from autoregressive coefficient to power spectrum at the decoder.In the process of optimizing the objective function,the error between the enhanced spectrum and the observed spectrum is added for reducing the influence of the gradient of the LDR on the enhanced network during back-propagation,which results in a stable estimation of the AR coefficients of noisy speech.

Key words: auto-regressive (AR) coefficients, generalized analysis-by-synthesis (GABS), deep neural networks (DNN), Levinson-Durbin recursion (LDR)

中图分类号:

TN912.35

崔子豪, 鲍长春. 基于广义合成分析和深度神经网络的自回归系数估计方法[J]. 电子学报, 2021, 49(1): 29-39.

CUI Zi-hao, BAO Chang-chun. Auto-Regressive Coefficient Estimation Based on the GABS and DNN[J]. Acta Electronica Sinica, 2021, 49(1): 29-39.

参考文献

[1] 舒新玲,周岱.风速时程AR模型及其快速实现[J].空间结构,2003,(04):27-32+46. SHU X-L,ZHOU D.AR model of wind speed time series and its rapid implementation[J].Spatial Structures,2003,(04):27-32+46.(in Chinese)
[2] 马秉伟,刘会金,周莉,崔福鑫.一种基于自回归模型的间谐波谱估计的改进算法[J].中国电机工程学报,2005,(15):79-83. MA B-W,LIU H-J,ZHOU L,CUI F-X.An improved algorithm of interharmonic spectral estimation based on AR model[J].Proceedings of the CSEE,2005,(15):79-83.(in Chinese)
[3] 李星秀,韦志辉.基于局部自回归模型的压缩感知视频图像递归重建算法[J].电子学报,2012,40(9):1795-1800. LI Xing-xiu,WEI Zhi-hu.Compressed sensing video images recursive reconstruction algorithm based on local autoregressive model[J].Acta Electronica Sinica,2012,40(9):1795-1800.(in Chinese)
[4] 吴桐雨,王健.中国物流业、经济增长与技术创新——基于2002~2017年向量自回归模型的实证研究[J].工业技术经济,2019,38(03):116-122.
[5] 陈辉,张博霞.自回归预测多级矢量量化线谱频率编码技术[J].西安科技大学学报,2017,37(05):736-741. CHEN H,ZHANG B-X.Technology of multi-stage vector quantization with autoregressive prediction for linear spectrum frequency[J].Journal of Xi'an University of Science and Technology,2017,37(05):736-741.(in Chinese)
[6] SCHROEDER M,ATAL B S.Code-excited linear prediction (CELP):High-quality speech at very low bit rates[A].IEEE International Conference on Acoustics,Speech,and Signal Processing[C].USA:IEEE,1985.937-940.
[7] GIACOBELLO D,CHRISTENSEN M G,MURTHI M N,et al.Sparse linear prediction and its applications to speech processing[J].IEEE Transactions on Audio,Speech,and Language Processing,2012,20(5):1644-1657.
[8] 刘敬伟,王作英,肖熙.基于自回归模型的加性噪声环境稳健语音识别[J].清华大学学报(自然科学版),2006,(01):50-53. LIU J-W,WANG Z-Y,XIAO X.Autoregressive model-based robust speech recognition in additive noise environment[J].Journal of Tsinghua University(Science and Technology),2006,(01):50-53.(in Chinese)
[9] ROE D.Speech recognition with a noise-adapting codebook[A].IEEE International Conference on Acoustics,Speech,and Signal Processing[C].USA:IEEE,1987.1139-1142.
[10] EPHRAIM Y,MALAH D.Speech enhancement using a minimum mean-square error log-spectral amplitude estimator[J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1985,33(2):443-445.
[11] CUI Z H,BAO C C.Linear prediction-based part-defined auto-encoder used for speech enhancement[A].IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP)[C].USA:IEEE,2019.6880-6884.
[12] 何玉文,鲍长春,夏丙寅.基于AR-HMM在线能量调整的语音增强方法[J].电子学报,2014,42(10):1991-1997. HE Yu-wen,BAO Chang-chun,XIA Bing-yin.Online energy adjustment using AR-HMM for speech enhancement[J].Acta Electronica Sinica,2014,42(10):1991-1997.(in Chinese)
[13] 孟宪波,鲍长春.基于最小控制GARCH模型的噪声估计算法[J].电子学报,2016,44(3):747-752. MENG Xian-bo,BAO Cang-chun.Noise estimate algorithm based on minima controlled GARCH model[J].Acta Electronica Sinica,2016,44(3):747-752.(in Chinese)
[14] WALKER G T.On periodicity in series of related terms[J].Proceedings of the Royal Society of London (Series A,Containing Papers of a Mathematical and Physical Character),1931,131(818):518-532.
[15] YULE G U.On a method of investigating periodicities disturbed series,with special reference to Wolfer's sunspot numbers[J].Philosophical Transactions of the Royal Society of London (Series A,Containing Papers of a Mathematical or Physical Character),1927,226(636-646):267-298.
[16] LEVINSON N.The Wiener (root mean square) error criterion in filter design and prediction[J].Journal of Mathematics and Physics,1946,25(1-4):261-278.
[17] DURBIN J.The fitting of time-series models[J].Revue de l'Institut International de Statistique,1960,28(3):233-244.
[18] SHI L M,JENSEN J R,CHRISTENSEN M G.Least 1-norm pole-zero modeling with sparse deconvolution for speech analysis[A].IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP)[C].USA:IEEE,2017.731-735.
[19] EL-JAROUDI A,MAKHOUL J.Discrete all-pole modeling[J].IEEE Transactions on Signal Processing,1991,39(2):411-423.
[20] MURTHI M N,RAO B D.All-pole modeling of speech based on the minimum variance distortionless response spectrum[J].IEEE Transactions on Speech and Audio Processing,2000,8(3):221-239.
[21] GRAY A,MARKEL J.Distance measures for speech processing[J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1976,24(5):380-391.
[22] KRIZHEVSKY A,Sutskever I,Hinton G E.Imagenet classification with deep convolutional neural networks[A].Advances in Neural Information Processing Systems[C].USA:Curran Associates,Inc,2012.1097-1105.
[23] JI Y,ZHU W P,CHAMPAGNE B.Recurrent neural network-based dictionary learning for compressive speech sensing[J].Circuits,Systems,and Signal Processing,2019,38(8):3616-3643.
[24] 袁文浩,胡少东,时云龙,等.一种用于语音增强的卷积门控循环网络[J].电子学报,2020,48(7):1276-1283. YUAN Wen-hao,HU Shao-dong,SHI Yun-long,et al.A convolutional gated recurrent network for speech enhancement[J].Acta Electronica Sinica,2020,48(7):1276-1283.(in Chinese)
[25] CUI Z H,BAO C C,Nielsen J K,et al.Autoregressive parameter estimation with DNN-based pre-processing[A].IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP)[C].USA:IEEE,2020.6759-6763.
[26] KRISHNA H,WANG Y.The split Levinson algorithm is weakly stable[J].SIAM Journal on Numerical Analysis,1993,30(5):1498-1508.
[27] BUNCH J R.The weak and strong stability of algorithms in numerical linear algebra[J].Linear Algebra and Its Applications,1987,88:49-66.
[28] KLEIJN W B,RAMACHANDRAN R P,KROON P.Generalized analysis-by-synthesis coding and its application to pitch prediction[A].IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP)[C].USA:IEEE,1992.337.
[29] MICHELSANTI D,TAN Z H,SIGURDSSON S,et al.On training targets and objective functions for deep-learning-based audio-visual speech enhancement[A].IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP)[C].USA:IEEE,2019.8077-8081.
[30] CYBENKO G.The numerical stability of the Levinson-Durbin algorithm for Toeplitz systems of equations[J].SIAM Journal on Scientific and Statistical Computing,1980,1(3):303-319.
[31] PLANCHEREL M,LEFFLER M.Contribution à l' étude de la représentation d'une fonction arbitraire par des intégrales définies[J].Rendicontidel Circolo Matematico di Palermo (1884-1940),1910,30(1):289-335.
[32] GAROFOLO J S,LAMEL L F,FISHER W M,et al.DARPA TIMIT acoustic-phonetic continous speech corpus CD-ROM NIST speech disc 1-1.1[J].STIN,1993,93:27403.
[33] PANAYOTOV V,GUOGUO C,DANIEL P,et al.Librispeech:An ASR corpus based on public domain audio books[A].IEEE International Conference on Acoustics,Speech and Signal Processing (ICASSP)[C].USA:IEEE,2015.5206-5210.
[34] VARGA A,STEENEKEN H J M.Assessment for automatic speech recognition:Ⅱ.NOISEX-92:A database and an experiment to study the effect of additive noise on speech recognition systems[J].Speech Communication,1993,12(3):247-251.
[35] THIEMANN J,NOBUTAKA I,EMMANUEL V.The diverse environments multi-channel acoustic noise database (DEMAND):A database of multichannel environmental noise recordings[J].The Journal of the Acoustical Society of America,2013,133(5):3591.
[36] BARKER J,MARXER R,VINCENT E,et al.The third ‘CHiME’ speech separation and recognition challenge:Dataset,task and baselines[A].IEEE Workshop on Automatic Speech Recognition and Understanding (ASRU)[C].USA:IEEE,2015.504-511.
[37] KAY S M.Modern Spectral Estimation:Theory and Application[M].India:Pearson Education India,1988.
[38] XU Y,DU J,DAI L R,et al.A regression approach to speech enhancement based on deep neural networks[J].IEEE/ACM Transactions on Audio,Speech,and Language Processing,2014,23(1):7-19.
[39] XU B,WANG N,CHEN T,et al.Empirical evaluation of rectified activations in convolutional network[J].arXiv Preprint,2015,arXiv:1505.00853.
[40] SRIVASTAVA N,HINTON G,KRIZHEVSKY A,et al.Dropout:A simple way to prevent neural networks from overfitting[J].The Journal of Machine Learning Research,2014,15(1):1929-1958.
[41] LIU L,JIANG H,HE P,et al.On the variance of the adaptive learning rate and beyond[J].arXiv Preprint,2019,arXiv:1908.03265.
[42] PASZKE A,GROSS S,MASSA F,et al.Pytorch:An imperative style,high-performance deep learning library[A].Conference on Neural Information Processing Systems (NIPS)[C].Vancouver,Canada:NIPS,2019.8026-8037.