sensors Article
Single-Lead Fetal ECG Extraction Based on a Parallel Marginalized Particle Filter Zhidong Zhao 1, *, Huiling Tong 2 , Yanjun Deng 2 , Wen Xu 2 , Yefei Zhang 2 and Haihui Ye 3 1 2
3
*
College of Electronics and Information, Hangzhou Dianzi University; Hangdian Smart City Research Center of Zhejiang Province, Hangzhou 310018, China School of Communication Engineering, Hangzhou Dianzi University, Hangzhou 310018, China;
[email protected] (H.T.);
[email protected] (Y.D.);
[email protected] (W.X.);
[email protected] (Y.Z.) Women’s Hospital School of Medicine Zhejiang University, Hangzhou 310006, China;
[email protected] Correspondence:
[email protected]; Tel.: +86-135-8804-5453
Received: 2 May 2017; Accepted: 17 June 2017; Published: 21 June 2017
Abstract: This paper presents a novel method for extracting the fetal ECG (FECG) from a single-lead abdominal signal. A dynamical model for a modified abdominal signal is proposed, in which both the maternal ECG (MECG) and the FECG are modeled, and then a parallel marginalized particle filter (par-MPF) is used for tracking the abdominal signal. Finally, the FECG and MECG are simultaneously separated. Several experiments are conducted using both simulated and clinical signals. The results indicate that the method proposed in this paper effectively extracts the FECG and outperforms other Bayesian filtering algorithms. Keywords: Fetal ECG; marginalized particle filter; ECG dynamical model; extended Kalman filter
1. Introduction Fetal ECG (FECG) reflects changes in fetal heart activity and is used as a primary method for evaluating fetal heart status. However, there is no uniform, effective, non-invasive FECG signal elicitation and processing technique, partly because the FECG obtained with an abdominal sensor has a low signal-to-noise ratio and is contaminated by strong interference [1], including from the maternal ECG (MECG), fetal brain activity, and movement artifacts. An additional problem is the lack of a standard FECG database as well as a lack of knowledge of fetal cardiac function. Hence, the analysis of FECG is still in its infancy. Currently, sophisticated and precise biomedical amplifiers can be used to obtain ECG signals. Accordingly, extracting the FECG from these recordings has gained considerable attention [2]. A number of effective algorithms have been proposed for FECG extraction, and most of these techniques require a multi-lead input. However, the number of leads affects the performance of the algorithm. Extracting the FECG with a single lead would both be more convenient and have a lower cost. For this purpose, many methods have been examined. Adaptive filtering [3,4] is a simple and fast approach for FECG extraction, and conventional adaptive filtering is based on training an adaptive filter to remove the MECG using a maternal reference signal. However, the fetal ECG extracted using this algorithm is still influenced by the maternal ECG and other disturbances. An adaptive comb filter [5] is used for the FECG estimation from the abdominal signal, and the filter can adjust itself to the temporal variations in the fundamental frequency, which makes it qualified for the estimation of a quasi-periodic component from the abdominal signal. An important advantage of the adaptive comb filter over conventional adaptive filters is its ability to separate the MECG and FECG with a temporal overlap; additionally, it requires only one sensor. Sensors 2017, 17, 1456; doi:10.3390/s17061456
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Wavelet-based [6–8] methods have shown promising results. The properties of the wavelet transformation allow the extraction of the ECG waveforms from noise and artifact cancellation. These methods require the proper selection of the mother wavelet and scale to identify the frequency components in the signal. However, the selection of the mother wavelet is extremely important for the FECG and MECG delineation. An optimal wavelet should consider the edge variation of the ECG waveforms, which may be adapted to the signal morphology because a different mother wavelet can provide different results. In the case of waveform reconstruction, EMD [9] for respiratory signal evaluation shows better performance. Extended Kalman filtering (EKF)/extended Kalman smoother (EKS) [10–12] has also been applied to extract FECG, which is a synthetic dynamic ECG model within an EKF framework that has been extended to jointly model several ECGs to extract the desired ECGs from an abdominal recording of maternal and fetal ECGs and noise. The results show that model can obtain the FECG and has a high signal-to-noise ratio. However, these methods should approximate the posterior density with a Gaussian density. If the assumption does not hold, the prevailing Bayesian filtering methods that are based on the Gaussian model [13] may fail to address the non-Gaussian and nonlinear FECG signals. Thus, another technique, referred to as MPF, is proposed in this paper. In this paper, a modified abdominal signal dynamical model containing MECG and FECG is proposed. Both of the new ECG dynamical models have 17 state variables that allow the artificial ECG to adapt to normal or abnormal morphologies. A parallel marginalized particle filter is then used for tracking the abdominal signal. Finally, the FECG and MECG are separated at the same time from an abdominal signal. To evaluate the proposed Bayesian method, both simulated signal experiments and clinical signal experiments were conducted in this paper. Additionally, the performance of the filter was compared with several other Bayesian algorithms. The rest of this paper is organized as follows: in Section 2, the previously developed synthetic ECG dynamical models are described. The proposed methodology is fully described in Section 3. In Section 4, a description of the performance indices that have been used to estimate the performance of the proposed methods is presented. The results and discussion of the different filtering methods are presented in Section 5; finally, in Section 6, some of the main conclusions are noted. 2. ECG Dynamical Model The ECG dynamical equations, which describe the states used in the KF, were proposed by McSharry in 2003 [14]. The dynamical model is used for generating a synthetic ECG with Cartesian coordinates and consists of three nonlinear dynamical state equations, as follows: . x = αx − ωy . y = αy + ωx . ∑ z=−
i ∈{ Q,P,R,S,T }
i ai ∆θi exp(− ∆θ 2b ) − (z − z0 )
(1)
i
p where α = 1 − x2 + y2 , ∆θi = (θ − ξ i )mod(2π ), θ = arctan2(y, x ), −π ≤ arctan2(y, x ) ≤ π, ω is the angular velocity of the trajectory as it moves around the limit cycle, and z0 is used for modeling the baseline wander of the ECG signal. Each of the P, Q, R, S, and T waves of the ECG waveform is modeled with a Gaussian function, and all are located at specific angular positions ξ i , and ai , bi in Equation (1), and they correspond to the amplitude and width parameters of the Gaussian function. Then, a simplified dynamic model in its discrete form was used, as proposed by Sameni [15], with the assumption of a small sampling period as follows: θk+1 = (θk + ωδ)mod(2π ) z k +1 = −
∑
i ∈{ Q,P,R,S,T }
δ αbi 2ω ∆θi,k exp(− i
2 ∆θi,k
2bi2
) + z k + ηk
where θ is the phase, z is the amplitude of the ECG, and η is a random additive noise.
(2)
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3. Proposed Methodology for FECG Extraction 3.1. Modified Abdominal Signal Dynamical Model It is well understood that the abdominal electrocardiogram (AECG) is a mixture of the MECG, FECG and noise. Thus, we consider the amplitude z and phase θ in Equation (3) of the FECG and the amplitude z and phase θ in Equation (4) of the MECG as state variables so that the new dynamic model can be used to estimate the MECG and FECG simultaneously: f f f θk+1 = (θk + ω δ)mod(2π ) f
5
f
α ω f f zk+1 = − ∑ δ i f 2 ∆θi,k exp(−
( bi )
i =1
m m m θk+1 = (θk + ω δ)mod(2π ) 5
f z k +1 = − ∑ δ i =1
f
αi ω f f ( bi )
f
2 ∆θi,k exp(−
f
(∆θi,k )
2
f 2 2 ( bi )
f
(∆θi,k )
f
f
(3)
f
f
(4)
) + z k + ηk
2
f 2 2 ( bi )
) + z k + ηk
In addition, most previous Bayesian ECG analyses directly use Equation (2) as the state space representation instead of the basic parameters of the Gaussian wave. As a result, occasional morphologic disturbances from random muscle artifacts have considerable effects on the performance of the filter. In these cases, the filter does not have sufficient time to adapt the Gaussian parameters, and a slight phase error of the model can lead to large errors in the Gaussian parameters [16]. The morphology of the ECG is determined by the Gauss parameters αi , bi , and ξ i ; therefore, αi , bi , and ξ i are also considered state variables following the random noise ε as follows: f f αk+1 = αk + ηα,k f f bk+1 = bk + ηb,k f f ξk+1 = ξk + ηξ,k
(5)
m m αk+1 = αk + ηα,k m bm k +1 = bk + ηb,k ξm = ξm + η ξ,k k +1 k
(6)
where the superscripts f and m in Equations (5) and (6) denote the fetus and mother, respectively. The modified abdominal ECG dynamical model is shown in Equation (7), xk represents state variables, and ηk represents process noise. The initial values of the dynamical model parameters can be obtained using the automatic off-line parameter selection procedure proposed in [15]: T f f f T f T f T m m m T m T m T xk = [ θ k , z k , (αk ) , (bk ) , (ξk ) , θ k , z k , (αk ) , (bk ) , (ξk ) ] f
f
f
T
f
T
f
T
m , η m , (ηm )T , (ηm )T , (ηm )T ] ηk = [ηθ,k , ηz,k , (ηα,k ) , (ηb,k ) , (ηξ,k ) , ηθ,k z,k α,k b,k ξ,k x = x + η k +1 k k
T
(7)
3.2. Observation Equation of the Dynamical Model The phase observation and the noise ECG measurements are related to the measurement vectors described by Sameni [15]. The MECGs can be between five and 10 times greater in intensity than the FECGs, and thus, the extracted FECG signals will be distorted when only the abdominal signal is considered an observation. Thus, in this paper, two auxiliary observation equations are added as
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observations. These equations are derived from Equation (2), and both are deformation formulas of Equation (2): f s k − z k −1
2 f (∆θi,k−1 ) f + δ ∆θi,k−1 exp(− ) f 2 f 2 i =1 ( b ) 2 ( b ) i i 5
∑
f
αi ω f
5
αim ω m
2 m (∆θi,k −1 )
i =1
(bim )
2(bim )2
sk − zm k −1 + ∑ δ
m ∆θi,k −1 exp(− 2
m = zm k + vk
f
f
) = zk + vk
(8)
(9)
where Equation (8) is the auxiliary FECG observation equation, and Equation (9) is the auxiliary MECG observation equation. Both equations can be used to estimate the MECG and FECG more accurately. The corresponding observation equations are as follows: f f f ϕk = θk + uk 2 m 5 (∆θi,k αim ω m f f −1 ) m m sk − zk−1 + ∑ δ (bm )2 ∆θi,k−1 exp(− 2(bm )2 ) = zk + vk i =1
i
i =1
( bi )
i
m m ϕm k = θk + uk 2 f f 5 (∆θi,k−1 ) αi ω f f f m sk − zk−1 + ∑ δ f 2 ∆θi,k−1 exp(− ) = zm k + vk f 2 f
(10)
2 ( bi )
f
m where uk , vk , um k , and vk are observation noise. The advantage of MPF is that it can approximate non-Gaussian filtering problems; however, to compare it with the Kalman filter, we assumed that the observation noise is Gaussian white noise.
3.3. Parallel-Marginalized Particle Filter The basic idea of a marginalized particle filter (Rao-Blackwellized particle filter) divides the state vector into linear components and nonlinear components [13]. Using the Rao-Blackwell theorem, we marginalized out the linear state variables and estimated them using the Kalman filter, while the particle filter was used to estimate the nonlinear state variables [17]. Thus, the optimal estimation of the state variables was obtained in the linear condition by the Kalman filter, while the dimension of the state variables was reduced in the nonlinear condition by the particle filter. Therefore, the marginalized particle filter algorithm greatly improves the accuracy when using the same number of particles. In this paper, the par-MPF algorithm is proposed based on the improved AECG dynamic model, which was used to estimate the abdominal signal. Finally, the FECG and MECG can be obtained f in parallel. We consider Gaussian amplitude parameters αk , αm k as linear variables and the other parameters as the nonlinear variables [17]. Therefore, the state variable xk can be split into xkL and xkNL , which are referred to as linear state and nonlinear variables, respectively: T x L = [(α f )T , (αm )T ] k k k T NL f f f T f T m )T , (ξm )T ] xk = [θk , zk , (bk ) , (ξk ) , θkm , zm , ( b k k k
(11)
Using the Bayesian theorem, we can calculate the following: p(xkNL , xkL Yk ) = p(xkL xkNL , Yk ) p(xkNL , Yk )
(12)
where p(xkL xkNL , Yk ) is estimated by the Kalman filter, and p(xkNL , Yk ) is estimated by the particle filter. In summary, the par-MPF algorithm presented in this paper includes the following steps:
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Step 1: Initialize the M particles: n oM x NL,(i) ∼ p(x0NL ) 0|−1 , o Mi=1 n L) x L,(i) ∼ p ( x 0 0|−1
(13)
NL,(i) (i ) wk = p(Yk xk|k−1 ) i = 1, 2, · · · , M;
(14)
i =1
and set k = 0. Step 2: Calculate the importance: weight:
normalization:
M
wk = wk / ∑ wk . (i )
(i )
(i )
(15)
i =1
Step 3: Resample the M particles: NL,(i )
p (xk | k
NL,( j)
( j)
= xk | k −1 ) = w k
(16)
Step 4: Update the Kalman filter measurement: f /m,(i) f /m,(i) α e k|k e k | k −1 =α , P f /m = P f /m k|k
(17)
k | k −1
where the superscript f /m means that there are two cases, i.e., the fetal ECG and the maternal ECG estimates. Step 5: Update the particle filter time:
f /mNL,(i ) f /mNL,(i ) ) xk|k
p (xk +1| k
f /m
= N (µk
f /m
, Σk
)
(18)
where: f /m f /m,(i ) f /mNL,(i ) f /m,(i ) f /m,(i ) f /m,(i ) f /m,(i ) T µk = [θk + w f /m δ, −gT ( xk )αk + zk , bk , ξk ] f /m 2 2 2 2 Σk = diag(σθ f /m , σz f /m , σb f /m , σ f /m ) ξ
NL ), g (x NL ), g (x NL ), g (x NL ), g (x NL )] g(xkNL ) = [ g(xk,1 k,2 k,3 k,4 k,5 ∆θ 2j,k α j,k ω NL g(xk,j ) = δ 2 ∆θ j,k exp(− 2 ) b 2b j,k
(19)
j,k
Step 6: Update the Kalman filter time: f /m,(i)
f /m,(i)
e k +1| k = α e k|k α where:
f /m
+ Lk
f /m,(i )
f /m,(i )
(e z k +1| k − z k
f /mNL,(i )
− g T ( x k +1| k
f /mNL,(i ) f /m,(i ) f /mNL,(i ) f /mNL F f /m = gT (e xk +1| k ) Pk|k g(e xk +1| k ) + Qk k f /mNL,(i ) f /m −1 L f /m = P f /m,(i) g(e xk +1| k )( Fk ) k k|k
f /m,(i)
e k|k )α
)
,
P is the process noise covariance matrix, and Q is the observation noise covariance matrix.
(20)
(21)
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Step 7: k = k + 1,
(22)
and iterate from step 2. 4. Performance Index of the FECG Extraction 4.1. Performance Index of the Simulated Data For the simulated data, the percentage root mean-square difference (PRD) and the signal-to-noise ratio enhancement (SNRenh ) were used to estimate the performance of filtering algorithms. The percentage root mean-square difference is defined as follows [18]: PRD =
∑n ( f (n) − fˆ(n)) 2 ∑n ( f (n))
2
(23)
where f (n) is the original FECG signal, fˆ(n) denotes the extracted FECG, and PRD is the most frequently used interference measurement tool that enumerates the error between the original signal and the reconstructed signal. The nearer the PRD is to zero, the more it indicates the similarity between the two signals and, hence, indicates the signal quality. The signal-to-noise ratio enhancement is defined as follows [19]: SNRenh = 10 log
2 ∑n ( a(n) − f (n)) 2 ∑n ( f (n) − fˆ(n))
(24)
where a(n) is the abdominal signal, f (n) is the original FECG signal, and fˆ(n) denotes the extracted FECG. SNRenh denotes the difference between the SNR before and after filtering. A larger SNRenh indicates a better performance of the algorithm. 4.2. Performance Index of the Clinical Data For the clinical data, the signal-to-noise ratio is based on an eigenvalue analysis and a cross correlation can be used to estimate the performance of filtering algorithms. Jagannath D.J. et al. [18], used SNR, including SNRsvd , the quotient between the first singular value (fetus signal energy) and the sum of the rest of the singular values (noise energy), and SNRcor , as an indicator of the goodness of the extraction method. For a square matrix, similarly, the eigenvalue was used to represent signal energy instead. Both of the SNR values can be calculated by the following steps [6]: Step 1: The extracted FECG is divided into N pieces crossing to the R peak, and each piece includes M samples and one QRS complex. Step 2: All of the pieces are stored in columns of an M by N matrix U, and the vectors u(k ) are the zero mean and are normalized to the unit length; that is, uT (k)u(k ) = 1.
(25)
Step 3: A signal-to-noise ratio based on eigenvalues can be calculated as: SNReig =
λmax N − λmax
(26)
where λ contains the eigenvalues of U. Step 4: A signal-to-noise ratio based on the cross-correlation coefficients can be calculated as SNRcor =
η 1−η
(27)
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where η=
M −2 M −1 2 ∑ f ( i )T f ( k ), M( M − 1) i∑ =0 k = i +1
(28)
and f is the FECG. 5. Results and Analysis To verify the feasibility and reliability of the proposed algorithm, both simulated and clinical data were used to study the performance of the proposed method, and other methods were tested with the same signals, including EKS, EKF and the Bayesian adaptive neuro fuzzy inference system [18]. The main ideas of these algorithms are shown in Table 1. Table 1. Filtering algorithms used in the experiments. Filtering Algorithm
Main Idea
par-MPF EKS [10] EKF [11] ANFIS-EKS [12] ANFIS-EKF [12]
Marginalized particle filter Extended Kalman filter + Smooth Extended Kalman filter EKS + Adaptive neuro fuzzy inference system EKF + Adaptive neuro fuzzy inference system
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5.1. FECG 5.1. Extraction the on Simulated Data Sensors 2017,Extraction 17,on 1456 FECG the Simulated Data
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5.1. FECG Extraction the Simulated 5.1.1. Simulated Data without Noise 5.1.1. Simulated Data on without Noise Data
An artificial FECG-MECG mixture simulator, as by Behar [20], was used forused creating 5.1.1. Simulated Data without Noise An artificial FECG-MECG mixture simulator, asproposed proposed by Behar [20], was for creating the simulated data, where the MECG was simulated with a beat rate of 70 bpm, and the FECG was An artificial FECG-MECG mixture as proposed by Behar used for creating the simulated data, where the MECG was simulator, simulated with a beat rate[20], of was 70 bpm, and the FECG was simulated with a beat rate of 120 bpm. The sampling frequency was set to 250 Hz, and the the simulated data, of where MECG was simulated frequency with a beat rate of 70 bpm, and the FECG was 2 set to 250 Hz, and the acquisition simulated with a beat rate 120the bpm. The sampling was fecg (n) was set to 250 Hz, and the frequency simulated with a beat rate of 120 bpm. The sampling n f ecg(SNR n)2 fm = acquisition time was 10 s. The parameter = −10dB , and a synthetic time was 10 s. The parameter SNR f m = ∑n 10 dB, = − mecg fecgand ((nn))2 2a synthetic AECG signal is shown mecg(n)2 ∑ n n acquisition time was 10 s. The parameter SNR fm = = −10dB , and a synthetic in Figure 1.AECG Thesignal simulated FECG signal is simulated shown in Figure 2.is shown is shown in Figure 1. The FECG signal mecg (n) 2 in Figure 2. n
AECG signal is shown in Figure 1. The simulated FECG signal is shown in Figure 2. 1.5
AECG AECG
1.5 1
0.51 0.5 0 0 -0.5 -0.5 -1 0 -1 0
500 500
1000
1500
1000 1500 Figure 1. Simulated data.
2000
2500
2000
2500
2000 2000
2500 2500
Figure 1. Simulated data. Figure 1. Simulated data. 0.4 0.4 0.2 0.2 0 0 -0.2 -0.2 -0.4 -0.40 0
500 500
1000 1000
1500 1500
Figure 2. Simulated FECG. Figure 2. Simulated FECG.
Figure The FECG signals extracted are shown2.inSimulated Figure 3. ItFECG. is clear that all three algorithms correctly The FECG signals extracted are shown in Figure 3. Itwe is can clearsee that allunlike three algorithms separate the mixed signal, and from the extracted FECG, that par-MPF, itcorrectly does not separate the mixed signal, and from the extracted FECG, we can see that unlike par-MPF, it does not fail when the MECG and FECG overlap. This performance was particularly noted foralgorithms the samples The FECG signals extracted are shown in Figure 3. It is clear that all three correctly fail when the MECG andbetween FECG overlap. This performance particularly noted samples between 700 and 800 and 2200 and 2300 in Figure 3, was in which some parts offor thethe FECG signal separate the mixed700 signal, from the extracted we can see that unlike par-MPF, between and 800and and between 2200 and 2300 inFECG, Figure 3, in which some parts of the FECG signal it does not deteriorated during the MECG extraction by the EKS and EKF methods. In contrast, the proposed deteriorated during the MECG extraction by the EKS and EKF methods. In contrast, the proposed par-MPF jointly models the FECG and MECG, resulting in a better estimate of the FECG. The reason par-MPF jointly models the FECG and MECG, resulting in a better estimate of the FECG. The reason for this is that some parts of the FECG signal deteriorated during the MECG extraction by the EKS for this is that some parts of the FECG signal deteriorated during the MECG extraction by the EKS and EKF methods. In contrast, the proposed method obtains the MECG and FECG at the same time and EKF methods. In contrast, the proposed method obtains the MECG and FECG at the same time and results in a better estimate of the FECG. and results in a better estimate of the FECG.
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fail when the MECG and FECG overlap. This performance was particularly noted for the samples between 700 and 800 and between 2200 and 2300 in Figure 3, in which some parts of the FECG signal deteriorated during the MECG extraction by the EKS and EKF methods. In contrast, the proposed par-MPF jointly models the FECG and MECG, resulting in a better estimate of the FECG. The reason for this is that some parts of the FECG signal deteriorated during the MECG extraction by the EKS and EKF methods. In contrast, the proposed method obtains the MECG and FECG at the same time and Sensors 2017, 17, 1456 9 of 19 results in a better estimate of the FECG. Sensors 2017, 17, 1456
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Figure Figure3.3.FECG FECGestimation: estimation:(a)(a)FECG FECGextracted extractedbybypar-MPF; par-MPF;(b) (b)FECG FECGextracted extractedbybyEKS; EKS;(c) (c)FECG FECG Figure 3. FECG estimation: (a) FECG extracted by par-MPF; (b) FECG extracted by EKS; (c) FECG extracted extractedby byEKF. EKF. extracted by EKF.
Another 10 FECG datasets, in which S N R fm = − 2, − 4 , − 1 8, − 2 0 d B , were used to Another FECGdatasets, datasets, in in which usedused to to N R fmf m= = − 2,− −2, 4 2 0−d20dB, B , were Another 10 10 FECG which SSNR −4, ·−· 1· 8, , −−18, were further verify the proposed algorithm. Three filtering algorithms were imposed on these signals further verify the proposed algorithm. Three filtering algorithms were imposed on these signals further verify the proposed algorithm. Three filtering algorithms were imposed on these signals to to PRD of the extracted FECG shown in Figurein split the MECG and FECG, andand theand NNRReSNR to split the andFECG, FECG, the and PRD and the extracted FECG are shown PRD ofenh theofextracted FECG areare shown in Figure andS S split the MECG MECG and the ennhh Figure 4a,b, respectively. 4a,b, respectively. 4a,b, respectively. 0.4
0.4
0.35
0.35
7575
par-MPF par-MPF EKS EKS EKF EKF
60
60
0.25
S NR enh (dB )
S NR enh (dB )
P RD
P RD
0.25 0.2
0.2 0.15
0.15 0.1
0.1 0.05 0 -20
EKF
65
65
0.3
0.3
par-MPF par-MPF EKS EKS EKF
70
70
-18
50
50
45
45
40
4035
0.05 0 -20
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55
3530 -18
-16
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-12 -10 SNRfm(dB)
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-8
-8
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3025
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-12 -10 SNRfm(dB)
-8
-12 -10 SNRfm(dB)
-6
-8
-4
-6
-2
-4
-2
S NSNR R enh . Figure 4. Comparison of performance indices: (a) PRD; (b) enh Figure 4. Comparison of performance indices: (a) PRD; (b)
.
Figure 4. Comparison of performance indices: (a) PRD; (b) S N R h . As shown in Figure 4, when the SNR fm increases, the PRD value of thee npar-MPF is smaller
than the EKS and EKF, while the S N R e n h is higher than the EKS and EKF. Overall, the proposed As shown in Figure 4, when the SNR fm algorithm increases,can thebePRD value of the par-MPF is smaller method has a stable performance; thus, the applied to the simulated data with noise. than the EKS and EKF, while the S N R e n h is higher than the EKS and EKF. Overall, the proposed
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10 of Figure 4, when the SNR f m increases, the PRD value of the par-MPF is smaller 10than of19 19 the EKS and EKF, while the SNRenh is higher than the EKS and EKF. Overall, the proposed method 5.1.2. Data Noise 5.1.2. Simulated Datawith withthus, Noise has a Simulated stable performance; the algorithm can be applied to the simulated data with noise. Sensors 2017, 17, As shown in Sensors 2017, 17,1456 1456
The artificial FECG-MECG mixture simulator was used again to generate the AECG with a artificial FECG-MECG 5.1.2.The Simulated Data with Noise mixture simulator was used again to generate the AECG with a motion artifact, as shown in Figure motion artifact, as shown in Figure5, 5,in inwhich which SNR and SNR keepingthe theother other SNRmnmn ==66dB dB,,keeping SNRfmfm==−−10 10dB dB,,and The artificial FECG-MECG mixture simulator was used again to generate the AECG with a motion conditions conditionsthe thesame: same: artifact, as shown in Figure 5, in which SNR f m = −10 dB, and SNRmn = 6 dB, keeping the other [ fecg (n) 22 + mecg (n) 22] conditions the same: nn [ fecg ( n )2 + mecg ( n2) ] SNR == ∑ [ f ecg(n) + mecg (29) (n) ] SNRmn (29) (29) SNRmnmn = n noise ((nn)2)22 noise n ∑nn noise(n)
33
AECG AECG
22 11 00 -1 -1 -2 -2 00
500 500
1000 1000
1500 1500
2000 2000
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Figure Figure5. 5.Simulated datawith withnoise. noise. Figure 5. Simulated data data with noise.
To Toverify verifythe thefeasibility feasibilityof of the theproposed proposedalgorithm, algorithm,the theAECG AECGin inFigure Figure555was wasprocessed processedby bythe the To verify the feasibility of the proposed algorithm, the AECG in Figure was processed by the three filtering methods. The extracted FECG is shown in Figure 6. The EKS and EKF also fail when three filtering filteringmethods. methods.The Theextracted extractedFECG FECGis is shown Figure 6. The EKS when three shown in in Figure 6. The EKS andand EKFEKF alsoalso fail fail when the the MECG and FECG overlap, while the par-MPF does not fail. This experiment shows that the the MECG and FECG overlap, while the par-MPF does not fail. This experiment shows that the MECG and FECG overlap, while the par-MPF does not fail. This experiment shows that the algorithm algorithm isisfeasible for the FECG separation of the clinical signal. algorithm feasible for the FECG separation of the clinical signal. is feasible for the FECG separation of the clinical signal.
Figure Figure 6. 6.FECG FECG estimation: estimation: (a) (a) FECG extracted by par-MPF; (b) FECG extracted by by EKS; EKS; (c) (c) FECG FECG Figure 6. FECG estimation: (a)FECG FECGextracted extractedby bypar-MPF; par-MPF;(b) (b)FECG FECG extracted extracted by EKS; (c) FECG extracted by EKF. extracted by by EKF. EKF. extracted
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We changed the values of S N R m n , after which the PRD and S N R e n h were calculated to We changed the values of SNRmn , after, after which the PRD PRD and SNR were calculated to evaluate We changed the valuesofofthese which theThe and enh were calculated S N Rfiltering S Nthe R e n PRD mn h and evaluate the performance methods. results of S N R to
enh the performance of these filtering methods. The results of the PRD and SNRenh calculations are shown evaluate the performance of these filtering methods. The results of the PRD and S N R e n h SN R = 2, 4, ,18, 20 dB calculations are shown in Figure 7a,b, respectively, when . in Figure 7a,b, respectively, when SNRmn = 2, 4, · · · , 18, 20 dB. m n SN R mthe 2, 4,PRD the ,18, 20 par-MPF dB .is smaller calculations shown in Figure 7a,b, respectively, n = PRD Figure 7 clearly demonstrates thatthat when SNRSmn of Figure 7areclearly demonstrates when increases, the ofpar-MPF the is Nwhen Rincreases, mn PRD Figure 7 clearly demonstrates that when increases, the of the par-MPF is S N R than smaller the EKS and EKF, while the SNR is higher than the EKS and EKF. In summary, when the AECG n than the EKS and EKF, while higher than the EKS and EKF. In summary, enh the S N R e n h is m is mixed with different the shows a perfect and the smaller than the EKS and EKF, while the algorithm is higher than thefiltering EKS andperformance, EKF. In summary, S N R ethe n h proposed algorithm shows a perfect filtering when the AECG is noise, mixed withproposed different noise, extracted FECG is high quality. Therefore, the application of the filtering algorithm to the clinical when the AECG mixed with FECG different noise,quality. the proposed algorithm shows a perfect filtering performance, and isthe extracted is high Therefore, the application of the filtering AECG should to bethe considered. performance, and the extracted FECGbeisconsidered. high quality. Therefore, the application of the filtering algorithm clinical AECG should
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5.2. FECG Extraction on the Different Database. 5.2. FECG Extraction on the Different Database. 5.2.1. Database for the Identification of Systems 5.2.1. Database for the Identification of Systems 5.2.1. Database for the Identification of Systems The clinical data are from the Database for the Identification of Systems (DaISy), which is a The The clinical datameasured areare from theaDatabase for the Identification Identification of Systems (DaISy), which clinical from Databasewoman. for the Systems (DaISy), which is a is well-known ECG data fromthe pregnant A total of eightofchannels are available, which a well-known ECG measured from a pregnant woman. A total of eight channels are available, which well-known ECG a pregnant woman. total of eight channels are available, which are sampled at 250measured Hz with a from duration of 10 s [21]. Five A abdominal signals are shown in Figure 8. The are sampled at 250 Hz with a duration of 10 s [21]. Five abdominal signals are shown in Figure are sampled at 250 Hz with awere duration of 10 obvious, s [21]. Five abdominal signals arehad shown in Figure 8. that The 8. FECG components in lead_1 the most while the lead_4 signal so much noise The FECG components lead_1 were the most obvious, while the lead_4 so noise muchthat noise FECG components ininlead_1 were the most obvious, while the lead_4 signalsignal had sohad much the FECG components could hardly be seen. that the componentscould could hardly seen. the FECG FECG components hardly be be seen.
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We ran algorithm and and the other threethree algorithms. Figure 9 presents thethe FECG Wethe ranproposed the proposed algorithm the other algorithms. Figure 9 presents FECG We ran the proposed algorithm and the other three algorithms. Figure 9 presents the FECG extracted usingusing the lead_1. The proposed method resulted in ainsuperior estimation of the FECG extracted the lead_1. The proposed method resulted a superior estimation of the FECG extracted themethods. lead_1. When The proposed method resulted in a superior of the FECG compared tousing theto other the MECG and and FECG completely overlap inestimation samples between compared the other methods. When the MECG FECG completely overlap in samples between compared to the other methods. When the MECG and FECG completely overlap in samples between 1600 and there there is a small effecteffect on the and and ANFIS-EKF outputs, while thethe FECGs 16001700, and 1700, is a small onANFIS-EKS the ANFIS-EKS ANFIS-EKF outputs, while FECGs 1600 and 1700, there is a small effect on the ANFIS-EKS and ANFIS-EKF outputs, while the suffersuffer a severe loss when extracted by the and and EKF.EKF. As described above, there areare twotwo steps inFECGs a severe loss when extracted byEKS the EKS As described above, there steps in suffer a severe loss when extracted by the and EKF. As described above, there are two extracting the FECG signal with the EKS and EKF algorithms. FECG is obtained from the in extracting the FECG signal with the EKS andEKS EKF algorithms. TheThe FECG is obtained from thesteps extracting the FECG signal withreduce the EKF algorithms. The FECG is obtained the residual residual signal, will theand QRS wave of the FECG component, while the par-MPF residual signal, whichwhich will reduce theEKS QRS wave of the FECG component, while thefrom par-MPF signal, which theimproved QRSAECG wave of the FECG component, while the par-MPF algorithm iswill based onimproved the AECG model and extracts MCG FECG aalgorithm parallel is algorithm is based onreduce the model and extracts the the MCG andand FECG in ainparallel manner. the FECG is model estimated accurately, the performance of the algorithm based on theThus, improved AECG andmore extracts the MCG and FECG in a parallel manner. Thus, manner. Thus, the FECG is estimated more accurately, and and the performance of the algorithm is is the greatly improved. greatly improved. FECG is estimated more accurately, and the performance of the algorithm is greatly improved.
Figure 9. Cont.
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Figure FECG estimation: (a)FECG FECGextracted extractedby bypar-MPF; par-MPF;(b) (b) FECG extracted by EKS; (c) FECG Figure FECG estimation:(a) (a) FECG extracted by par-MPF; FECG extracted byby EKS; (c)(c) FECG Figure 9.9.9. FECG estimation: (b) FECG extracted EKS; FECG extracted by EKF; (d) FECG extracted by ANFIS-EKS; (e) FECG extracted by ANFIS-EKF. extracted EKF; FECGextracted extractedby byANFIS-EKS; ANFIS-EKS; (e) extracted byby EKF; (d)(d)FECG (e) FECG FECGextracted extractedby byANFIS-EKF. ANFIS-EKF.
The FECG signalsobtained obtainedusing using the par-MPF from abdominal signals are shown in inin The FECG signals three other abdominal signals are shown The FECG signals obtained usingthe thepar-MPF par-MPFfrom fromthree threeother other abdominal signals are shown Figure 10. To further illustrate the advantages of our algorithm, another experiment was conducted Figure Figure10. 10.To Tofurther furtherillustrate illustratethe theadvantages advantagesofofour ouralgorithm, algorithm,another anotherexperiment experimentwas wasconducted conducted using another AECGwithout withoutlead_4. lead_4.The The SNR and SNRcor are calculated ininTable 2. 2. SNReig and using another AECG and are calculated Table using another AECG without lead_4. The SNR SNR are calculated in Table 2. SNR cor eig eig cor 20 20 0 0 -20 -20 0 0
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cor Lead 1 Lead 2 cor Lead 3 cor Lead 1 Lead 2 Lead 3 par-MPF 2.0864 1.6820 2.0849 1.7120 2.4119 2.1926 Methods SNReig SNReig SNReig Methods SNRcor SNRcor SNRcor SNR SNR SNR SNR SNR SNRcor cor eig EKS [10] 1.7497 1.5677 1.8250eig 1.3714cor 1.3903eig 0.7797 par-MPF 2.0864 1.6820 2.0849 1.7120 2.4119 2.1926 EKF [11] 1.2245 1.1506 1.2367 0.8392 1.3590 0.7465 par-MPF 2.0864 1.6820 2.0849 1.7120 2.4119 2.1926 EKS [10] [12] 1.7497 1.7497 1.5677 1.8250 1.3714 1.3903 0.7797 ANFIS-EKS 1.8334 1.6152 1.8709 1.4889 1.4452 1.4917 EKS [10] 1.5677 1.8250 1.3714 1.3903 0.7797 EKF [11] [12] 1.2245 1.2245 1.1506 1.2367 0.8392 1.3590 0.7465 ANFIS-EKF 1.5097 1.3160 1.5491 1.2557 1.3767 0.9247 EKF [11] 1.1506 1.2367 0.8392 1.3590 0.7465 ANFIS-EKS [12] 1.8334 1.6152 1.8709 1.4889 1.4452 1.4917 ANFIS-EKS [12] 1.8334 1.6152 1.8709 1.4889 1.4452 1.4917 ANFIS-EKF [12] 1.5097 1.3160 1.5491 1.2557 1.3767 0.9247 From the results, we1.5491 can see that the signal-to-noise ratio ANFIS-EKF [12] experimental 1.5097 1.3160 1.2557 1.3767 0.9247
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higher than that of the other four algorithms; furthermore, the difference between the signal-to-noise
From the experimental results, we can see that the signal-to-noise ratio of our algorithm is higher than that of the other four algorithms; furthermore, the difference between the signal-to-noise
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From the experimental results, we can see that the signal-to-noise ratio of our algorithm is higher ratio of the small. It can be furthermore, concluded that performance of the is better than than that ofpar-MPF the otherisfour algorithms; thethe difference between thealgorithm signal-to-noise ratio of that of the other Bayesian algorithms. the par-MPF is small. It can be concluded that the performance of the algorithm is better than that of the other Bayesian algorithms. 5.2.2. Abdominal and Direct Fetal ECG Database 5.2.2. Abdominal and Direct Fetal ECG Database The clinical data used in this section are from the Abdominal and Direct Fetal ECG Database. The five-minute multichannel fetalsection ECG are recordings, cardiologist-verified annotations of all The clinical data used in this from thewith Abdominal and Direct Fetal ECG Database. fetalfive-minute heartbeats, multichannel were from five women in labor at with the Medical University ofannotations Silesia, Poland. The fetal ECG recordings, cardiologist-verified of allEach fetal record includes four signals from the maternal abdomen and a simultaneously recorded reference heartbeats, were from five women in labor at the Medical University of Silesia, Poland. Each record direct fetal ECG fromfrom the fetal scalp; allabdomen of the signals sampled atrecorded 1 KHz [22,23]. Thedirect first 5000 includes four signals the maternal and awere simultaneously reference fetal points werethe used plot the ECG as shown inat Figure whereThe (a) is the5000 fetalpoints scalp were ECG ECG from fetaltoscalp; all of thewaveform signals were sampled 1 KHz11, [22,23]. first signal, (e) are the abdominal signals. used toand plot(b) thetoECG waveform as shown in Figure 11, where (a) is the fetal scalp ECG signal, and (b) of the filtering algorithms using the signal Abdomen_1 are shown in Figure 12. These to (e)The are result the abdominal signals. fives The algorithms to the differentusing shapes the AECG, whichare included theFigure interference of result ofadapted the filtering algorithms theofsignal Abdomen_1 shown in 12. These noise. However,adapted the performance of theshapes EKF was theAECG, worst among these algorithms, and theofFECG fives algorithms to the different of the which included the interference noise. was mixedthe with more noise. TheEKF results FECG extraction using EKS,and ANFIS-EKS, and However, performance of the was of thethe worst among these algorithms, the FECG was ANFIS-EKF had relatively low noise. In contrast, the FECG extraction using the par-MPF had the mixed with more noise. The results of the FECG extraction using EKS, ANFIS-EKS, and ANFIS-EKF best quality. low noise. In contrast, the FECG extraction using the par-MPF had the best quality. had relatively 2000 1000 0 -1000 -2000
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The FECG signals obtained using the par-MPF by the three other abdominal signals of r01 are The FECG signals obtained using the par-MPF by the three other abdominal signals of r01 are shown in Figure Figure13; 13;the the algorithm performance evaluated by calculating the SNR and shown in algorithm performance waswas evaluated by calculating the SNR andeig SNR cor eig
usingcorthese three signals of signals r01, andofthe results are results shown in 3. All of the 3. algorithms the using these three r01, and the areTable shown in Table All of theextracted algorithms SNR FECG with different qualities;signal however, the proposed algorithm not onlyalgorithm extracted the extracted the FECG signal with different qualities; however, the proposed not FECG only without noise, but the quality of the signal was finer, and thus, it is helpful for the follow-up extraction extracted the FECG without noise, but the quality of the signal was finer, and thus, it is helpful for of the R waveextraction and FHRVofanalysis. the follow-up the R wave and FHRV analysis. Finally, the signals r04, r04, r07, r07, r08 r08 and and r10 r10 in in the the Abdominal Abdominal and and Direct Direct Fetal Fetal ECG ECG Database Database were were Finally, the signals processed using using the the above above filtering filtering algorithm algorithm [24–26]. [24–26]. Because Becausethe thesignals signalsof ofAbdomen_2 Abdomen_2of ofr07, r07, processed Abdomen_1 of r08 and Abdomen_2 of r10 were poor, they were excluded from the experiments. Abdomen_1 of r08 and Abdomen_2 of r10 were poor, they were excluded from the experiments. The The comparison the SNR eig and SNRcor among the five algorithms is shown in Figures 14 comparison of theofSNR eig and SNRcor among the five algorithms is shown in Figures 14 and 15, and 15, respectively. respectively. In Figures 14 and 15, the X-axis and Y-axis indicate the number of the signal used in these In Figures and 15, respectively. the X-axis and Y-axis indicate of the see signal these experiments and14the SNR, From Figures 14 andthe 15,number we can clearly thatused for allinsignals experiments andofthe respectively. Figures 14 for andKS, 15,EKF, we ANFIS-EKS can clearly and see ANFIS-EKF. that for all tested, the SNR the SNR, proposed method isFrom higher than that signals tested, the SNR of the proposed method is higher than that for KS, EKF, ANFIS-EKS and ANFIS-EKF. The higher SNR here means a better extraction performance. Figures 14 and 15 show
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means a better extraction performance. Figures 14 and 15 show that16the of 19 performance indices ofindices the proposed method are obviously higher than those than of thethose otherofalgorithms, that the performance of the proposed method are obviously higher the other thatnothe performance indices of the proposed are obviously higher than those of the other and matter how abdominal ECG changes,method the algorithm maintains a good performance. The algorithms, and no the matter how the abdominal ECG changes, the algorithm maintains a good algorithms, and no matter abdominal changes, the The algorithm a good EKF achievedThe the EKF lowest SNRhow and showed the poorest performance. results maintains indicate the performance. achieved thethe lowest SNR andECG showed the poorest performance. Thethat results performance. The EKF achieved the lowest SNR and showed the poorest performance. The results algorithm in this paper effectively extracted a high-quality FECG from different pregnant women. indicate that the algorithm in this paper effectively extracted a high-quality FECG from different indicatewomen. that theTherefore, algorithm in this paper has effectively extracted a clinical high-quality FECG from different Therefore, this algorithm has this great prospects forgreat clinical application. pregnant algorithm prospects for application. pregnant women. Therefore, this algorithm has great prospects for clinical application. 400 400 200 200 0 -200
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6. Conclusions Conclusions 6. A Bayesian Bayesian filtering filtering framework framework for for extracting extracting the the FECG FECG from from aa single-channel single-channel mixture mixture of of the the A abdominalsignal signalMECG MECG FECG, including is proposed in this paper. Aabdominal modified abdominal andand FECG, including noise,noise, is proposed in this paper. A modified abdominal signal model dynamical model istoproposed to improve filteringThe accuracy. The MECG FECG and signal dynamical is proposed improve the filtering the accuracy. FECG and are MECG are the same time, substantially reducing running of the algorithm. In obtained at obtained the sameat time, substantially reducing the runningthe time of thetime algorithm. In addition, addition, simulated and clinical data were used to verify the performance of the filter. All the results simulated and clinical data were used to verify the performance of the filter. All the results show that show that the proposed methodextracted successfully extracted thescenarios, FECG inand many scenarios, andhad the the proposed method successfully the FECG in many the extracted FECG FECG had a high quality. aextracted high quality. Finally,the theproposed proposedmethod methodwas wascompared compared with some other Bayesian filter algorithms, such Finally, with some other Bayesian filter algorithms, such as as the andBayesian the Bayesian adaptive neuroinference fuzzy inference system. The proposed method the EKS,EKS, EKF EKF and the adaptive neuro fuzzy system. The proposed method provided a superiorofestimation the FECGs with the and other methods, andand when the aprovided superior estimation the FECGsof compared withcompared the other methods, when the MECG FECG MECG andoverlapped, FECG completely overlapped, was little effectand on ANFIS-EKF. the ANFIS-EKS and ANFIS-EKF. completely there was little effectthere on the ANFIS-EKS However, the FECGs However, the FECGs suffered a severe lossEKS when extracted by the Moreover, EKS and EKF methods. Moreover, suffered a severe loss when extracted by the and EKF methods. the performance indices the performance indices of the proposed method were obviously higher than those of the other of the proposed method were obviously higher than those of the other algorithms. Taken together, algorithms. Taken reveal together, experiments reveal that the strength of the method is the these experiments thatthese the strength of the proposed method is the bestproposed with respect to signal best with respect to signalpar-MPF extraction. The proposed par-MPF been verified to obtain extraction. The proposed algorithm has been verifiedalgorithm to obtainhas a high signal-to-noise ratioa high signal-to-noise ratio FECG signal from a signal. single-channel abdominal signal. However, whether FECG signal from a single-channel abdominal However, whether the algorithm is suited for theextraction algorithmof is twin suited for theisextraction of further twin FECGs the FECGs an issue for study.is an issue for further study. Acknowledgments: Acknowledgments:This Thisresearch researchwas wassupported supportedby byNational National Natural Natural Science Science Foundation Foundation of of China China (Grant (Grant No. No. 61571173); supported by by Zhejiang Provincial Natural Science Foundation of China under Grant 61571173);the theresearch researchwas was supported Zhejiang Provincial Natural Science Foundation of China under No. LY14F010021. The research was also supported by the Welfare Project of the Science Technology Department Grant No. LY14F010021. The research was also supportedand by Smart the Welfare Project of theInnovation Science Technology of Zhejiang Province (Grant No. 2015C31085, 2016C33079) City Collaborative Center of Department of Zhejiang Province (Grant No. 2015C31085, 2016C33079) and Smart City Collaborative Zhejiang Province. Innovation Center of Zhejiang Province. Author Contributions: Zhidong Zhao and Wen Xu conceived and performed the theoretical derivation; Huiling and YanjunZhidong Deng designed the experiments; Wen Xu, Yefei Zhang and derivation; Haihui Ye Author Tong Contributions: Zhao and performed Wen Xu conceived and performed the theoretical designed and performed the analogue simulations; Wen Xu wrote the paper. Huiling Tong and Yanjun Deng designed and performed the experiments; Wen Xu, Yefei Zhang and Haihui Ye designed and performed the analogue simulations; Wen Xu wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
Conflicts of Interest: The authors declare no conflict of interest.
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