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一种利用单通道母体腹部心电信号提取胎儿心电信号的新技术

2021-09-14王文波钱龙

湖南大学学报·自然科学版 2021年10期
关键词:奇异值分解

王文波 钱龙

摘   要:针对母体腹部混合心电信号中胎儿心电信号微弱、包含诸多噪声,难以清晰提取的问题,本文提出了一种基于奇异值分解(SVD)、平滑窗(SW)技术和最小二乘支持向量机(LSSVM)的胎儿心电提取新方法. 首先,利用SVD从单通道母体腹部心电信号中重构分解矩阵,估计出母体心电参考信号,并利用SW方法对估计出的母体心电参考信号进行平滑处理;然后,利用LSSVM建立非线性估计模型,通过该模型和平滑后的母体心电参考信号估计出腹部信号中的母体心电成分,并采用布谷鸟搜索算法(CS)优化LSSVM的超参数;最后,将腹部混合信号与CS-LSSVM模型估计出的母体心电成分相减,即可获得初步胎儿心电信号,为了进一步消除干扰,对初步获取的胎儿心电信号再进行SW-SVD操作,从而获得较为清晰的胎儿心电信号. 采用Daisy数据集进行实验,结果表明,本文所提出的方法在可视化对比分析和四个统计评价指标上均优于其他三种经典方法,可从腹部混合信号中提取出更清晰的胎儿心电信号.

關键词:胎儿心电信号;奇异值分解;平滑窗;最小二乘支持向量机;布谷鸟搜索算法

中图分类号:R331                              文献标志码:A

A New Technology for Extracting Fetal ECG Signals

from Single-channel Maternal Abdominal ECG Signals

WANG Wenbo QIAN long

(College of Science,Wuhan University of Science and Technology,Wuhan 430065,China)

Abstract:Aiming at the problems that the fetal electrocareliogram(ECG) signal in the mixed ECG signal of the mother's abdomen is weak,contains a lot of noise,and is difficult to be extracted clearly,this paper proposes a method based on singular value decomposition (SVD),smooth window (SW) technology and least square support vector machine (LSSVM) new method of fetal ECG extraction. Firstly,SVD is used to reconstruct the decomposition matrix from the single-channel maternal abdominal ECG signal in order to estimate the maternal ECG reference signal,and the SW method is used to smooth the estimated maternal ECG reference signal;then,LSSVM is used to establish a non-linear estimation model,the maternal ECG component in the abdominal signal is estimated through the model and the smoothed maternal ECG reference signal,and the cuckoo search algorithm(CS) is used to optimize the hyperparameters of LSSVM. Finally,the mixed abdominal signal is subtracted from the maternal ECG component estimated by the CS-LSSVM model so as to obtain the preliminary fetal ECG signal. To further eliminate the interference,the SW-SVD operation is performed on the initially obtained fetal ECG signal,thereby obtaining a clearer fetal ECG signal. Experiments with Daisy data set show that the method proposed in this paper is superior to the other three classic methods in visual comparative analysis and four statistical evaluation indicators,and can extract clearer fetal ECG signals from the mixed abdominal signals.

Key words:fetal ECG signal;singular value decomposition;smooth window;least squares support vector machine;cuckoo search algorithm

据统计,全世界每年发生260多万例死产,其中45%以上病例发生于孕妇分娩期间,因此产前胎儿健康检测具有重要的生理学意义[1]. 通过在孕妇分娩前对胎儿心电信号进行检测,并分析其波形,可以高效评估胎儿在子宫内的生长发育情况,从而降低围产儿的死亡率和发病率[2-3]. 目前,多采用无创的非入侵式检测方法对胎儿健康进行检查[4-5].

非入侵式检测方法是使用多导联置电极技术分别记录孕妇胸部和腹壁混合信号,然后将胎儿心电信号从孕妇腹壁混合信号中分离出来. 然而由腹壁电极所采集的信号普遍包含较多的噪声:导联电极干扰、母体心电活动干扰、基线漂移[6]等,因此,如何有效抑制各种噪声从而分离出纯净的胎儿心电信号成为一个国内外学者研究的热点问题.

为了消除各种背景干扰和母体心电成分,国内外学者已经提出了一系列从腹壁混合信号中获取胎儿心电信号的方法:盲源提取技术[7-8]是假设各个源信号未知的情况下,只提取出胎儿心电信号,但该技术对时间延迟周期的依赖性较大,其性能具有局限性;独立成分分析(Independent Component Analysis,ICA)技术[9]在假定各信号成分统计独立的基础上建立ICA模型,该算法一般采用梯度法对分离矩阵自适应寻优,且需要严格设定初始分离矩阵和步长,使得该技术容易陷入局部最优,导致分离的胎儿心电信号精度不高[10];自适应滤波法[11]计算量小且易于收敛,但该算法不能有效提取出母体心电和胎儿心电重合部分的胎儿心电信号;小波分解技术[12]涉及到小波基和其他参数的选择,对于不同的数据,参数选择较为困难,因此该方法适用性较低,不能用于实时提取;匹配滤波法[13]需要保持信号之间同一波形形态,对滤波器的选择较为困难;支持向量机技术[14]和人工神经网络[15-16]技术在胎儿心电提取方法中得到了较多的应用,这些方法将传统统计学作为基础,以经验风险最小化原则进行学习,存在着泛化能力弱、结构设计较难、易陷入局部最优等问题. 以上这些方法都是建立在复杂导联多通道信号采集的基础上,然而多通道记录数据会要求在孕妇体表放置更多的电极,这可能会引起孕妇的身体不适从,并间接影响心电信号的提取效果. 因此这些方法的临床使用价值非常有限.

随着胎儿心电提取方法的不断深入研究,采用单通道腹壁混合心电信号进行胎儿心电提取的方法成为主流. 这些方法以自适应噪声消除技术[17]、奇异值分解技术[18]、模板去除技术[19]和卡尔曼滤波技术[20]等为基础,从单通道腹壁混合心电信号中分离出胎儿心电信号. 但现有的单通道胎儿心电提取方法仍存在一定的不足:模板去除技术很难从腹壁混合心电信号中消除噪声和母体心电成分[21],导致提取效果较差;奇异值分解技术分解出来的矩阵往往解释性较弱且分解矩阵随时间越来越大,对存贮空间有较大的需求[22];卡尔曼滤波技术的计算复杂度较高,并且在胎儿心电与母体心电重叠的部分,该技术将失去其提取作用[23];自适应噪声消除技术通常需要训练特定的滤波器参数[24],该方法的临床实用性较低.

为了解决上述问题并提取更为清晰的胎儿心电信号,本文提出了一种利用单通道腹壁混合信号进行胎儿心电信号分离的新方法,该方法只需记录一次孕妇腹壁混合信号,极大降低了信号的电极干扰且可以进行长期监测. 该方法的具体思路为:首先,将平滑窗(Smooth Window,SW)技术与SVD技术相结合(SW-SVD),用来估计孕妇腹壁混合信号中的母体心电成分,采用估计的母体心电信号代替母体胸部信号;然后,将SW-SVD方法估计的母体心电信号作为输入信号,利用最小二乘支持向量机(Least squares support vector machine,LSSVM)构造输入信号和腹壁混合信号中母体心电成分的最佳映射模型,并采用布谷鸟优化算法(cuckoo search,CS)优化LSSVM的关键超参数;最后,将CS-LSSVM映射模型得到最佳母体心电信号与腹壁混合信号相减,即可分离出初步的胎儿心电信号,对初步获取的胎儿心电信号再次使用SW-SVD技术进一步消除母体心电的干扰,最终得到更为纯净的胎儿心电信号. 实验结果表明,与传统的归一化最小均方误差(Normalized least mean squares,NLMS)、长短时记忆(Long short term memory,LSTM)网络以及LSSVM方法相比,文中所提出的方法具有更强的抗噪声能力和泛化能力,可以得到更为清晰的胎儿心电信号.

1   胎儿心电信号提取原理

2   SW-SVD技术

2.1   SVD原理

2.2   SVD提取母体心电参考信号

2.3   均值滤波

3   基于CS优化的LSSVM

3.1   LSSVM原理

3.2   CS算法

3.3   CS优化的LSSVM母体心电信号估计模型

4   实验与结果

4.1   模型評价标准

4.2   实验数据和实验方法

本文实验数据选取DaISy数据集进行研究,并与NLMS[43]、LSTM方法[44]和LSSVM方法进行对比实验. DaISy数据库(Database for the Identification of Systems)由Lieven De Lathauwer提供[45],心电数据采样频率为250 Hz,记录时长为10 s,各通道心电数据长度为2 500,采用电极放置法从孕妇体表获取的八导联(ch1~ch8)心电信号,ch1~ch5导联记录孕妇腹部混合信号,ch6~ch8 导联记录孕妇胸部信号. 考虑模型运算复杂度、计算时长和提取性能,选择前1 500点数据作为训练数据集,剩余1 000点数据作为测试数据集. NLMS方法中,迭代步长设为0.005,迭代次数设为 1 000. LSTM方法中隐藏层神经元选为30个,迭代次数设为400,学习率取为r = 0.01. 传统LSSVM方法中选择径向基函数作为核函数,核函数参数σ和惩罚系数C的取值分别为σ2= 3,C = 50.

4.3   實验结果比较

4.3.1   母体心电参考信号的可视化提取结果

选取Daisy数据集中的五个腹部心电信号进行单通道胎儿心电信号的提取,五个通道的信号波形如图4所示. 为了去除基线漂移对信号的影响,本文对母体心电参考信号做了Savitzky-Golay(S-G)平滑滤波操作;然后利用第二节中所提出的SW-SVD技术,提取母体心电参考信号,提取结果如图7所示. 通过对比图4和图5的五通道信号可知,利用SW和SVD结合的技术可以从腹壁混合心电信号中提取出清晰的母体心电参考信号.

4.3.2   胎儿心电信号提取结果的可视化对比分析

本文将ch1和ch2两个腹部通道信号作为可视化结果分析,并与目前传统的NLMS、LSTM和LSSVM方法进行对比实验,实验可视化对比结果如图6和图7所示.

图6和图7显示了四种胎儿心电信号提取方法在ch1和ch2两个通道上的可视化结果,可以看出本文提出的方法明显优于其他三种方法,基本上可以提取出所有的胎儿QRS波,且有效避免了母体心电和其他噪声的干扰.

4.3.3   胎儿心电信号提取结果的统计指标分析

为了定量研究CS-LSSVM方法的提取效果,本文采用Se、PPV、ACC和F1四个指标来分析[12,13]. 选择DaISy数据集中 ch1~ch5 共5个通道孕妇腹壁心电数据进行统计分析,该数据集中每个通道记录有22个胎儿心电QRS波,在测试集数据中每个通道有9个QRS波,本文统计5个通道共45个胎儿心电QRS波. 四种方法的统计分析结果如表1所示.

由表 1 可知,CS-LSSVM心电信号提取方法在五个导联上的胎儿心电信号提取效果最好,该方法可以提取到42个胎儿心电QRS波,误检和漏检的胎儿心电个数相对较少,只有4个QRS波被误检且漏检个数为3个,模型准确率ACC高达85.71%,灵敏度Se为93.33%,精确度PPV达到91.30%,且总体概率F1为 92.31%,四项统计指标均为最高. NLMS方法能够提取到40个胎儿心电QRS波,误检个数为12个,漏检的胎儿心电为5个,模型准确率ACC为70.18%,四项评价指标都不及本文提出的方法. 这是由于NLMS方法对胎儿心电信号适应性不强,尤其在母体心电与胎儿心电重叠部分,对胎儿心电的识别率较低. LSTM 方法可以提取到30个胎儿心电QRS波,在四项心电提取性能指标分析中,其ACC只有51.72%,四项评价指标均为最低,这是由于LSTM存在泛化能力弱,易陷入局部极值,导致该模型漏检和误检较多. LSSVM方法可以提取到40个胎儿心电QRS波,误检11个,漏检5个,并且ACC为71.43%,Se为88.89%,PPV为78.43%,F1为83.33%. 由于LSSVM方法的超参数很难人工取到最优值,导致该方法提取性能低于CS-LSSVM. 通过上述的对比可见,CS-LSSVM心电提取方法在四项指标上均优于其他三种心电提取方法. 可见利用CS算法先对LSSVM模型的关键超参数进行寻优处理,然后构建CS-LSSVM母体心电信号估计模型,并经过SW-SVD操作可以有效提高胎儿心电信号提取性能.

5   结   论

在本文的研究中,提出了一种利用单通道母体腹部混合心电信号提取胎儿心电信号的新方法. 该方法以LSSVM模型为基础构建CS-LSSVM母体心电信号提取模型,采用CS算法对LSSVM模型的超参数进行寻优处理,有效提高了模型的预测性能,减小了人为确定超参数的影响. 并且结合平滑窗口和奇异值分解技术,建立母体心电参考信号,有效避免了至少记录一个母体胸部心电信号的局限性. 文中选取DaISy数据集进行对比实验,实验表明,相比于传统的NLMS、LSTM 和 LSSVM方法,本文提出的CS-LSSVM心电提取方法表现出更优的性能,能够提取出42个清晰的胎儿心电信号QRS波,误检和漏检的胎儿心电较少,为产前胎儿健康检测提供了新思路,具有较好的临床应用价值.

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