2016 10th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP)
Adaptive Signal Processing Techniques for Extracting Abdominal Fetal Electrocardiogram Radek Martinek (IEEE Member), Radana Kahankova, Hana Skutova, Petr Koudelka (IEEE Member), Jan Zidek, and Jiri Koziorek VSB – Technical University of Ostrava Faculty of Electrical Engineering and Computer Science 17. listopadu 15/2172, Ostrava-Poruba, Czech Republic
[email protected],
[email protected] Abstract—The extraction of the Fetal Electrocardiogram (fECG) from the composite Electrocardiogram (ECG) signal obtained from the abdominal lead is discussed. The main point of this paper is to introduce some of the most used Least Mean Squares (LMS) based Finite Impulse Response (FIR) Adaptive Filters and to determine which of them are the most effective under varying circumstances. Experimental results suggest the ideal combination of the chosen settings for these functions. Results of fECG extraction are assessed by Percentage Root-Mean-Square Difference (PRD), input and output Signal to Noise Ratios (SNRs), and Root Mean Square Error (RMSE). Based on simulations conclusions, optimal convergence constant value and filter order were empirically determined. Setting the optimal value of the convergence constant and filter order of adaptive algorithm can be considered a contribution to original results. These results can be used on real records fECG, where it is difficult to determine because of the missing reference.
The strong Maternal Electrocardiogram (mECG) along with the weak fECG is overlapping in time and in frequency as well. Reducing the maternal component from a composite abdominal signal is therefore a very challenging task. Many different approaches have been proposed for detection and extraction of the fECG with various degrees of success. These techniques include several methods that are shown in the Figs. 1, [3], [5]. II. METHODS FOR FECG ELICITATION The interference elimination can be implemented using a single channel or a multichannel of the source signal. These signals are then processed by various methods. These methods can be divided into two groups – adaptive and non-adaptive. The difference is in the existing or non-existing ability of the system to adapt to the unexpected circumstances.
Keywords—fECG, mECG, adaptive filtering, Matlab, LMS, NLMS, BLMS, DLMS
I. INTRODUCTION The Fetal Electrocardiogram (fECG) describes the electrical activity of the fetal heart and provides clinically significant information about the physiological state of a fetus during the pregnancy or the labor. Early diagnosis of the hypoxic states (hypoxemia, hypoxia, and asphyxia) achieved by monitoring fECG can increase the effectiveness of the treatment, [1], [2], and [18]. There are two different techniques to record fECG – invasive and noninvasive. The first one is the direct method of the measurement that is provided transvaginally by an Invasive Scalp Electrode (ISE). This method is considered to be accurate because the signal is recorded directly from the fetal scalp, however it brings many problems and risks such as infections for the mother and the child as well. Noninvasive techniques measure electrical signals by multichannel skin electrodes placed on mother’s abdomen. This kind of measuring is more convenient, non-invasive and can be used not only during the labor but before it, too. On the other hand, signal measured by this method is characterized by a significant amount of overlapped undesired signals such as bioelectric potentials (maternal muscle activity, fetal movement activity, generated potentials by respiration and stomach etc.), power line interference and mainly the component of the maternal heart activity [3], [4].
978-1-5090-2526-8/16/$31.00 ©2016 IEEE
Fig. 2. Methods for fECG elicitation
A. Non-adaptive methodologies Non-adaptive methodologies include Wavelet Transform based techniques, Correlation methods, Subtraction methodologies, Single Value Decomposition (SVD), Blind Subspace Separation (BSS), Averaging techniques, Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) filtering, Wiener filtering and Fixed filtering methods such as Low Pass Filtering (LPF) and High Pass Filtering (HPF), [3], [19]. The drawback of the non-adaptive techniques is that they are time-invariant in nature, which has been overcome by the adaptive methods, which are more effective in reducing the
2016 10th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP)
noise that is overlapping in time and frequency. Non-adaptive methods are useful for data pre-processing or for noise elimination in case of the classic ECG.
systems (more in [1], [6], [7], and [8]), genetic algorithms and Bayesian adaptive filtering frame works which comprise Kalman filters.
B. Adaptive methodologies As mentioned before, an adaptive filter is a filter characterised by an ability to self-adjust the filter coefficients according to an optimized training algorithm which is driven by a back propagated error signal. Adaptive filters are used in noise cancelation to remove the noise adaptively from a signal and to improve the Signal to Noise Ratio (SNR).
This paper focuses primarily on the Least Mean Squares (LMS) based FIR Adaptive Filters methods. In the chapter below there are mathematical descriptions of the most important methods such as LMS, normative LMS (NLMS), BLMS and DLMS.
Simply it is a technique for adaptive elimination of undesired signals (such as the maternal component) from the abdominal signal to obtain the fECG signal. The system can adjust and alter to the existing circumstances, and optimize its results. A theoretical multichannel adaptive noise cancelation system shown in Fig. 2 illustrates an example of an adaptive elicitation technique. It consists of two kinds of the input signals recorded from multiple leads – the abdominal ECG signals (AB1-ABn) and the thoracic ECG signals (TH1-THn). Each abdominal signal consists of both maternal and fetal signals and it is the primary input. The thoracic signal is considered to be completely maternal and is used as the reference input. Finite Impulse Response Filter weights of the adaptive systems are updated by the training algorithms based on the back propagated error signal, which is the desired fECG signal (fECG1-fECGn). The maternal component is considered to be an undesired signal for elimination. Each of the adaptive systems produces a signal which is approximately the noise. This signal is subtracted with the ECG signal so that the error signal that is back propagated to the training algorithm is the fetal heart signal with some noise. There are many different methodologies to obtain fECG using adaptive filters by using one or several maternal reference channels (as shown in Fig. 1). These methodologies include least mean square (LMS) algorithms, recursive least square (RLS) algorithms, artificial intelligence techniques, fuzzy inference
Fig. 2. A theoretical multichannel adaptive noise cancelation system
III. THEORETICAL BACKGROUND Least mean squares (LMS) algorithms are classified as adaptive filters that can change the filter coefficients to become a system that produces the least mean squares of the error signal (the difference between the desired and the actual signal). It is a stochastic gradient descent method in that the filter is only adapted based on the error at the current time [9]. A. Standard LMS The standard LMS algorithm performs the following operations to update the coefficients of an adaptive filter: x Calculates the output signal y(n) from the adaptive filter. x Calculates the error signal e(n) by using the following equation:
( )=
( ) −
( ).
x Updates the filter coefficients by using the following equation:
( + 1) =
( ) + 2
( ) ( ),
where μ is the step size of the adaptive filter, w(n) is the filter coefficients vector, and x(n) is the filter input vector. Step size is a crucial parameter that can improve the convergence speed of the adaptive filter. It determines both how quickly and how closely the adaptive filter converges to the filter solution, > @>@
2016 10th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP)
B. Normalized LMS (NLMS) The normalized LMS (NLMS) algorithm is a modified form of the standard LMS algorithm. The NLMS algorithm updates the coefficients of an adaptive filter by using the following equation:
( + 1) =
( )+
( )
( ) ‖ ( )‖
.
It is obvious that the NLMS algorithm is almost identical to standard LMS algorithm except that the NLMS algorithm has a time-varying step size μ(n), > @ C. Block LMS (BLMS) The Block LMS Filter block implements an adaptive leastmean-square (LMS) filter, where the adaptation of filter weights occurs once for every block of samples. This algorithm provides significant improvements in decreasing mean-squared error (MSE) and consequently minimizing signal distortion. Instead of updating the filter vector for every sample as for the standard LMS in Eq. (1), the filter vector is updated once every Lth sample The weight update relation for BLMS algorithm is as follows,
( + 1) =
∑
( ) +
(
+ ) (
+ ),
=
+
.
This gives the filter output of BLMS algorithm in its final form as follows:
( )=
( ) ( ).
D. Delay LMS (DLMS) The DLMS algorithm is extensively used in different applications of adaptive filtering due to low computational complexity and stability. The DLMS algorithm is introduced to minimize the error between a given preferred signal and output of the linear filter by adjusting recursively the parameters of a linear filter. The weight update relation for DLMS algorithm is as follows:
( )
( ) (
( + 1)
( −
−
) (
) −
( ) +
− (
−
), ),
( ) ( − ),
A. Percent Root-Mean-Square Difference (PRD) The PRD is one of the measure indexes commonly used in ECG compression literature ([8]) and it is determined by:
where D is the total delay inserted into the error feedback path of the LMS algorithm. If D = 0, then Eq. (7), Eq. (8) and Eq. (9) represent the usual LMS adaptive algorithm. With the advantage of a higher throughput rate, the DLMS algorithm has the drawback of a slower convergence rate compared to the LMS algorithm due to the inserted delay D. [11] IV. DEFINITION OF THE PARAMETERS The measurement of the quality of the fECG extraction procedures is based on the estimation of the similarity of the recovered signals and the ideal fECG signals and the absence of the noise. There are two main parameters that can be helpful
=
( )−
∑ =1
∑ =1 2
()
2
()
∙ 100
where xorg denotes the original signal (ideal fECG) and xrec the signal recovered by the algorithm. The closer this value is to zero the similar are both signals. The problem is the lack of an upper limit which makes it difficult to compare figures from different pairs of signals, as it depends on the amplitude of the signals. That is why the paper also focuses on the other parameters to reach the optimal quality of the extraction >@ B. Signal to noise ratio (SNR) The relation between the signal and the noise is described by SNR, whose expression is following:
where the sample index n and block index k are related as:
to control the effectiveness of the fECG extraction - Percent Root-Mean-Square Difference (PRD) and SNR.
SNRIN = 10∙ log
∑ ∑
() ()
()
where xorg denotes the original signal (ideal fECG) and xnoise the signal that is producing the undesired signal (mECG).
SNROUT = 10∙ log
∑ ∑
() ()
()
where xorg denotes the original signal (ideal fECG) and xrec the signal recovered by the algorithm. The SNR quantifies the relation between the fetal signal and the rest of the unwanted components (mECG). In the general fECG inverse problem, this is not an operative definition of the SNR, since it requires knowing the contribution of the fetal signal and the noise. Since our signals are synthetic, this information is available [13]. C. Root mean square error (RMSE) The last parameter used in this paper is RMSE defined by the following equation:
=
∑
−
,
where sigorg denotes the original signal (ideal fECG) and sigrec the signal recovered by the algorithm. RMSE is a measure of the differences between values predicted by a model or an estimator and the values observed. The closer this value is to zero the more accurate is the system, [14], [15].
2016 10th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP)
V. RESULTS AND DISCUSSION The authors’ goal is to provide results based on simulations with LMS based FIR Adaptive Filters contained in MATLAB® function ‘adaptfilt’. They suggest the ideal combination of the chosen settings for these functions based on the results of Percentage Root-Mean-Square Difference (PRD), input and output Signal to Noise Ratios (SNRs), and Root Mean Square Error (RMSE). Fig. 3 shows synthetic signals used for the experiments. The signals included synthetic distorted abdominal signal, which was used as an input to the adaptive system and was created out of the synthetic thoracic (mECG) and ideal abdominal (fECG) signal using FIR filter.
Each adaptive filter is used to extract fECG. Results of fECG extraction are assessed by the parameters introduced in the previous section. The attention is focused mainly on the value of the parameter PRD, which should be reduced as much as possible while maintaining the value of the SNR positive. That ensures that the output signal’s appearance is approaching the ideal fECG and the amount of the noise remains smaller than the signal. The parameter RMSE should be as close to zero as possible. Using MATLAB® the value of the step size (μ) was set to 0.1 and Adaptive filter length value (l), which is the number of coefficients or taps, defaults to 10. That is, however, inadequate in the case of fECG extraction. For the first stage of the experiments, much more suitable value of the filter length was chosen and remained constant while the value of the step size altered. In the area where the value of the PRD was the lowest, and the SNR was positive (the filter is the most effective) the chosen values of the step size altered minimally so reaching the ideal value would be possible. Table I summarizes the results for each filter. DLMS and BLMS filters optimal step sizes appear to be 0.0007 and for the LMS filter 0.0006. The values of the μ achieved in the previous step were constant in the following step to find the ideal value of the filter length. All the results are summarized in the Table II.
Fig. 3. Synthetic signals used for the experiments.
The synthetic ideal fetal signal was then used as the reference for the calculation of the performance parameters such as SNR, PRD and RMSE. The value of the SNR before application of any used adaptive filter was -11.559 dB, TABLE I.
μ (-)
In Table III suggested setting for each filter based on the results of the performance parameters can be seen. In the Fig. 4 – 7 there are the examples of the synthetic signal before and after the application of each filter with the setting that was evaluated as the most suitable. There are also the ideal fetal signal and the distorted abdominal signal plotted for the visual inspection of the quality of the results.
THE PARAMETERS OF THE QUALITY FOR EACH FILTER FOR THE DIFFERENT STEP SIZES
LMS
DLMS
BLMS
SNR (dB)
PRD (%)
RMSE (-)
SNR (dB)
PRD (%)
RMSE (-)
SNR (dB)
PRD (%)
RMSE (-)
0.0001
-0.528
13.376
0.012
-0.53
13.393
0.012
-0.536
13.45
0.012
0.0004
-0.081
5.710
0.008
-0.085
5.737
0.008
-0.103
5.835
0.008
0.0005
-0.034
5.533
0.008
-0.039
5.566
0.008
-0.06
5.684
0.008
0.0006
0.003
5.533
0.008
-0.003
5.572
0.008
-0.026
5.713
0.008
0.0007
0.034
5.624
0.008
0.027
5.670
0.008
0.002
5.835
0.008
0.0008
0.061
5.765
0.008
0.053
5.817
0.008
0.026
6.008
0.008
0.0009
0.084
5.934
0.008
0.076
5.992
0.008
0.047
6.209
0.008
0.001
0.105
6.117
0.009
0.097
6.182
0.008
0.066
6.424
0.009
0.0011
0.124
6.308
0.009
0.116
6.378
0.009
0.083
6.645
0.009
0.01
0.673
15.725
0.013
0.65
15.935
0.014
0.292
22.366
0.016
2016 10th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP)
TABLE II.
THE PARAMETERS OF THE QUALITY FOR EACH FILTER FOR DIFFERENT FILTER LENGTH LMS
NLMS
DLMS
BLMS
SNR (dB)
μ=0.0006 PRD (%)
Time (s)
offset=10, step=0.1 SNR PRD Time (dB) (%) (s)
SNR (dB)
μ=0.0007 PRD (%)
Time (s)
SNR (dB)
μ=0.0007 PRD (%)
Time (s)
1
-6.178
305.856
7.422
-5.995
291.558
13.123
-6.149
303.332
6.954
-6.153
303.674
0.934
5
-5.262
230.978
8.245
-4.185
163.086
9.211
-5.215
227.617
8.810
-5.234
228.879
1.082
10
-3.234
108.863
8.224
-1.374
42.68
9.176
-3.051
100.552
8.747
-3.076
101.452
1.133
15
-1.415
38.98
8.140
-0.491
20.756
9.192
-1.292
35.546
8.815
-1.321
36.1
1.168
20
-0.58
16.592
8.302
-0.051
12.805
9.341
-0.522
15.594
8.822
-0.551
15.975
1.297
25
-0.184
8.362
8.325
0.193
9.696
9.461
-0.15
8.149
8.839
-0.176
8.381
I.36
30
0.003
5.533
8.292
0.302
9.316
9.321
0.027
5.670
9.340
0.002
5.835
1.375
35
0.077
5.199
8.414
0.348
9.984
9.417
0.096
5.511
8.871
0.069
5.695
1.337
40
0.103
5.703
8.325
0.379
10.753
9.342
0.121
6.075
8.888
0.09
6.306
1.334
50
0.133
6.562
8.511
0.441
12.099
9.379
0.152
6.969
9.098
0.116
7.264
1.442
75
0.206
8.140
8.568
0.58
15.198
9.479
0.229
8.714
9.179
0.182
9.120
1.679
100
0.282
9.748
8.661
0.696
18.138
9.659
0.308
10.458
9.610
0.252
10.957
1.869
150
0.433
13.063
8.759
0.924
22.966
9.858
0.468
14.043
9.442
0.396
14.785
2.345
200
0.557
15.459
9.725
1.103
27.077
10.727
0.593
16.581
10.803
0.505
17.466
2.859
Filter length (-)
The results had shown successful reduction of the undesired signals. All of the performance parameters had been improved after the application of the adaptive filters. All of the filters’ best results (according to the values of the parameters PRD, SNR and RMSE) appeared with the value of filter length in interval 30-35 and the filter step size 0.0006-0.0007. TABLE III. Filter
OPTIMAL VALUES OF THE PARAMETERS Parameters Step
Length
LMS
0.0006
30
NLMS
-
35
DLMS
0.0007
30
BLMS
0.0007
30
Fig. 4. Adaptive filter BLMS
The worst results belong to the NLMS filter. It also has the negative of a very low filtering speed. The BLMS filter outperforms the other filters. The filtering speed is incomparably faster with the same quality of the output signal.
Fig. 5. Adaptive filter DLMS
2016 10th International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP)
REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
[7]
Fig. 6. Adaptive filter LMS
[8]
[9] [10]
[11]
[12]
[13]
Fig. 7. Adaptive filter NLMS
VI. CONCLUSION The authors’ suggest further research in this field. There is a need to test other algorithms and more suitable synthetic data should be used. On the other hand, there is also need for the tests with real data. The problem is the lack of real data available for the public use. There is an existing cooperation between the authors and a hospital on creating a database of the real data that can be used for experiments in the future. The Generators introduced by authors in [16] and [17] is also a solution for this problem.
[14]
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[18]
ACKNOWLEDGMENT This paper has been elaborated in the framework of the project SP2016/146 and SP2016/162 of Student Grant System, VSB-TU Ostrava.
[19]
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