# Fetal ECG Extraction Based on Overcomplete ICA and Empirical Wavelet Transform

Theodoros Lampros, Nikolaos Giannakeas, Konstantinos Kalafatakis, Markos Tsipouras, Alexandros Tzallas

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Theodoros Lampros, Nikolaos Giannakeas, Konstantinos Kalafatakis, Markos Tsipouras, Alexandros Tzallas. Fetal ECG Extraction Based on Overcomplete ICA and Empirical Wavelet Transform. 19th IFIP International Conference on Artificial Intelligence Applications and Innovations (AIAI), Jun 2023, León, Spain. pp.45-54, 10.1007/978-3-031-34171-7_3. hal-05411770

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# Fetal ECG Extraction Based on Overcomplete ICA and Empirical Wavelet Transform

Theodoros Lampros<fnref n="1" />(✉), Nikolaos Giannakeas<fnref n="1" />, Konstantinos Kalafatakis<fnref n="1" />, Markos Tsipouras<fnref n="2" />, and Alexandros Tzallas<fnref n="1" />

**Abstract.** Continuous fetal heart monitoring during pregnancy can be crucial in detecting and preventing many pathological conditions related to fetal heart development. In particular, because of its potential to provide prenatal diagnostic information, the noninvasive fetal electrocardiogram (NI-fECG) has become the focus of several recent studies. Due to its higher temporal frequency and spatial resolution, NI-fECG makes possible the “beat-to-beat” monitoring of the Fetal Heart Rate (FHR) and allows for a deeper characterization of the electrophysiological activity (i.e. electrical conduction of the heart) through morphological analysis of the fetal waveform. However, acquisition of the fetal ECG from maternal abdominal recordings remains an open problem, mainly due to the interference of the much stronger maternal ECG. This paper proposes a novel hybrid method for accurate fetal ECG extraction based on Reconstruction Independent Component Analysis (R-ICA) and Empirical Wavelet Transform (EWT) enhancement. The RICA-EWT method was tested on real signals acquired from pregnant women in different stages of labour. The results indicate its robustness and efficiency in different SNR levels.

**Keywords:** Fetal ECG extraction · Reconstruction ICA · Empirical Wavelet Transform · Fast Fourier Transform · Wavelet Thresholding

## 1 Introduction

Non-invasive fetal electrocardiography (NI-FECG) uses electrodes placed on the mother's abdomen to detect and record the electrical activity of the fetal heart. This technique can provide information about the fetal heart rate, rhythm, and overall cardiac health without requiring invasive procedures. NI-FECG is a relatively safe and non-invasive technique that poses no significant risk to the mother or fetus. It can be performed at any stage of pregnancy and is often used to monitor the fetal heart rate during labour and delivery and assess fetal well-being in high-risk pregnancies.

<footnote n="1">¹ Department of Informatics and Telecommunication, University of Ioannina, Arta, Greece
{grgiannakeas,k.kalafatakis,tzallas}@uoi.gr</footnote>

<footnote n="2">² Department of Electrical and Computer Engineering, University of Western Macedonia, Kozani, Greece
mtsipouras@uowm.gr</footnote>
The extraction of a non-invasive fetal electrocardiogram (NI-FECG) involves the processing and analysis of the electrical signals recorded by the electrodes placed on the mother's abdomen. There are various algorithms used for NI-FECG extraction. Template Subtraction [1], Blind Source separation (BSS) [2], Adaptive Filtering [3], and Artificial Neural Networks [4] have been proposed in the literature. To denoise and enhance the extracted fetal ECG, some of the most common approaches are Empirical Mode Decomposition (EMD) [5], Wavelet-Based denoising (WD) [6], and Extended Kalman Smoothing (EKS) [7]. Hybrid algorithms [8, 9] combine multiple methods to improve the accuracy and reliability of the extracted features.

One of the most popular algorithms for fetal ECG extraction is Independent Component Analysis (ICA). However, ICA enforces a hard orthonormality constraint on the data, which makes it difficult to learn overcomplete features. In addition, ICA is sensitive to whitening. In the case of multichannel, nonstationary, and nonlinear signals such as abdominal ECG recordings, these properties make it challenging to scale ICA to high-dimensional data. Overcomplete ICA refers to using more basis functions than inputs to represent a signal. This approach can be useful in cases where the signal is complex or has a high degree of variability. By using more basis functions than inputs, an overcomplete representation can capture more detailed features and variations in the signal, which can be beneficial for fetal ECG extraction.

The Empirical Wavelet Transform (EWT) [10] is a signal processing technique that decomposes a signal into a set of localized oscillatory components. It is a data-driven approach that does not rely on predefined basis functions but instead adapts to the local features of the signal. The EWT is based on the Hilbert transform, a mathematical operation that allows for the extraction of the amplitude and phase components of a signal. The EWT works by iteratively filtering the signal into a set of bands, using the Hilbert transform to extract the amplitude and phase components, and applying a local frequency estimation to obtain a set of oscillatory components.

This work focuses on providing a robust system for extracting the NI-FECG from abdominal recordings and estimating the Fetal Heart Rate (FHR). For this reason, we employ a modified version of ICA called Reconstruction ICA (R-ICA) [11] to extract overcomplete representations of multichannel abdominal recordings, signal Quality Indices to verify the quality of the extracted fetal component and denoising and enhancement using the Empirical Wavelet Transform (EWT).

## 2 Materials and Methods

The proposed methodology consists of two distinct processing pipelines. For the fetal ECG extraction stage, the abdominal signal, which consists of four channels, is separated in overcomplete modes, i.e., five, six, and seven Independent Components using R-ICA. Fetal-specific signal Quality Indices evaluate the fetal components in each mode, and the best raw fetal ECG is selected for further processing. In the denoising stage, the short-time Fourier transform (STFT) represents the frequency content of the extracted fECG; then the EWT decomposes the signal into Intrinsic Mode Functions (IMF) and undesired artifacts, such as baseline wander, and high-frequency noise is removed. Figure 1 (a) and (b) illustrate the proposed method.
<figure><img src="image_4.png" /><figcaption>Fig. 1. (a) Fetal ECG extraction, (b) Fetal ECG denoising</figcaption></figure>

## 2.1 Dataset

To evaluate the performance of our algorithms, we used set A of Physionet Challenge 2013 (Fig. 2) [12]. The data consist of a collection of 74 one-minute, four-channel non-invasive FECGs sampled at 1 kHz, obtained from multiple sources using a variety of instrumentation with differing frequency response, resolution, and configuration. The length of the individual signals is 1 min with a sampling frequency of 1 kHz and a resolution of 12 bits. Set A consists of reference annotations validated by experts and indicates the positions of the individual R-peaks. A total of 38 recordings from the dataset were used for this study.

<figure><img src="image_5.png" /><figcaption>Fig. 2. Example of records in the Challenge Dataset (record a014).</figcaption></figure>
## 2.2 FECG Extraction

The standard ICA optimization problem can be formulated as

$$ \min \sum_{i=1}^{M} \sum_{j=1}^{K} g(W_j x^i) \qquad (1) $$

$$ \text{Subject to } WWT = I, \qquad (2) $$

where W is the weight matrix and g is a nonlinear convex function. The orthonormality constraint in Eq. 2 makes ICA difficult to learn overcomplete representations of data. Reconstruction ICA replaces the hard orthonormality criterion with a soft reconstruction cost, as shown in Eq. 3

$$ \min \frac{1}{m} \sum_{i=1}^{M} W^T W x^i + \lambda \sum_{i=1}^{M} \sum_{j=1}^{K} g(W_j x^i) \qquad (3) $$

where λ is a scaling constant, which can determine the relative importance of two terms above. This reconstruction penalty, allows the algorithm to learn sparse representations on the data without whitening, when W is overcomplete. In this work we used the R-ICA algorithm to separate the 4-channel abdominal mixture into 5, 6 and 7 Independent Components. We did not extract a larger number of components as we observed that increasing the number of components to more than seven caused redundancy in our extracted data. Figure 3 shows an example of our extraction approach.

### 2.2.1 Signal Quality Indices

To select the best IC corresponding to the fetal ECG and assess the separation algorithm's accuracy, we used specific signal Quality Indices presented below.

* Approximate entropy (AppEn): AppEn is a common-use feature for quantifying irregularity in time series data with no knowledge about the system. Larger values correspond to more complexity and irregularity in the data.

* Spectral entropy: Spectral entropy, based on Shannon entropy, can quantify the regularity or uncertainty of the power spectrum during a specific period. Higher irregularity in Spectral entropy indicates a more uniform power spectrum distribution (Fig. 4).

* bSQi [12]: The bSQi index uses the detection of QRS complexes by 2 detection algorithms and detects the percentage of common strokes in algorithms. The QRS detection algorithms used on this work are the Pan-Tompkins algorithm, modified for fetal QRS detection [14], and the maxsearch algorithm available in Open-Source Electrophysiological Toolbox (OSET) [15].

* kSQi: fourth moment (kurtosis) of signal.

## 2.3 FECG Denoising

The fECG component obtained by the R-ICA method is not completely noise-free. It still contains several types of noise, such as electrode artifacts, baseline wander, and other
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Results of the R-ICA algorithm. The 4-channel abdominal signal is separated into A = 5, B = 6, and C = 7 extracted components. This is shown to better represent the fetal component of interest. However, increasing the number of extracted features can result in producing redundant signals.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Spectral Entropy (SE) from an extracted fetal ECG can be interpreted as a measurement of the time uncertainty in frequency domain. In the power spectrum of EEG signals, when the spectrum peak is narrow, its entropy value is small. It indicates that the signal has an obvious consecutive rhythm. A more uniform distribution of spectral entropy in the frequency domain indicates a higher quality fetal signal.</figcaption></figure>
high frequency noise that can be attributed to maternal ECG interference. To remove such artifacts that can affect FHR estimation, we used the Empirical Wavelet Transform (EWT) combined with a soft thresholding function. The steps of our proposed demising algorithm are described below.

1 Compute the Fast Fourier Transform (FFT) of the input signal to obtain its frequency spectrum

2 Segment the FFT spectrum by finding all the local maxima and obtaining the segmentation boundaries according to their distance

3 Construct adaptive wavelet filter banks according to the detected boundaries

4 Threshold the empirical wavelets according to the soft thresholding function [16]

$$ \hat{C}_i(t) = \begin{cases} \text{sign}((c_i(t))[c_i(t)] - \lambda), & |c_i(t)| \ge \lambda \\ 0, & |c_i(t)| < \lambda \end{cases} \quad (4) $$

where i and t are positive integers, $c_i(t)$, is the component obtained after decomposition, $\hat{C}_i(t)$ is the denoised version of $c_i(t)$, $\lambda$ is the threshold corresponding to $c_i(t)$, and sign() is the sign function. The threshold $\lambda$ is calculated as [17]:

$$ \lambda = b\sigma_i\sqrt{2\ln N} \quad (5) $$

5 Perform the Inverse EWT to compute the Intrinsic Mode Functions (IMF'S).

6 Select the IMF's that contain the useful signal information.

7 Reconstruct the input signal.

In this work, we decomposed the input fetal ECG into 10 IMF's. An example of the denoising process is presented in Fig. 5.

## 3 Results

R-peak detection was performed using the JQRS detector [14], with the following parameters: 0.5 detector threshold, 1.5-s window size, 150-ms refractory period. We evaluated our proposed methodology using the Sensitivity (SE), Positive Predictive Value (PPV), Accuracy (ACC), and F1 score (F1) metrics:

$$ SE = TP/(TP + FN). \quad (6) $$

$$ PPV = TP/(TP + FP). \quad (7) $$

$$ ACC = TP/(TP + FP + FN). \quad (8) $$

$$ F1 = (2*SE*PPV)/(SE + PPV). \quad (9) $$

Where TP stands for True Positive, FP for False Positive and FN for False Negative. The results are shown in Table 1.

We also compared our results with our previous work [19] and recent works published in the same Dataset. To test our previously presented algorithm, we used the same metrics and QRS detector parameters as in this work for consistency. We can see from Table 2 that our proposed system offers an improvement from our previous work and other recent works that were tested on the Challenge Dataset.
<figure><img src="image_8.png" /><figcaption>Fig. 5. Empirical Wavelets produced from EWT. The first IMF represents the signal baseline wander, while IMF's 2 to 9 are wave harmonics related to Power Line Interferences. Finally, most of the signal information is contained in IMF 10.</figcaption></figure>

<table><caption>**Table 1.** Results of our method in the Challenge Dataset. 38 one minute recordings from the dataset were included in this study. The variable Q stands for the number of extracted components from the abdominal mixture in which the fetal ECG was more accurately represented. SNR levels range from -2 to -18 dB, indicating various noise levels in the input signals.</caption><thead><tr><td>RECORD</td><td>Q</td><td>ACC(%)</td><td>F1(%)</td><td>PPV(%)</td><td>SE(%)</td><td>SNR</td></tr></thead><tbody><tr><td>a01</td><td>5</td><td>98.62</td><td>99.31</td><td>100.00</td><td>98.62</td><td>-11.28</td></tr><tr><td>a02</td><td>6</td><td>78.75</td><td>88.11</td><td>100</td><td>78.75</td><td>-17.94</td></tr><tr><td>a03</td><td>6</td><td>78.91</td><td>88.21</td><td>100</td><td>78.91</td><td>-12.28</td></tr><tr><td>a04</td><td>5</td><td>93.08</td><td>96.41</td><td>99.18</td><td>93.80</td><td>-9.57</td></tr><tr><td>a05</td><td>6</td><td>84.38</td><td>91.53</td><td>100.00</td><td>84.38</td><td>-10.66</td></tr><tr><td>a06</td><td>6</td><td>98.45</td><td>99.22</td><td>100.00</td><td>98.45</td><td>-9.76</td></tr><tr><td>a07</td><td>5</td><td>85.23</td><td>92.03</td><td>86.99</td><td>97.69</td><td>-12.28</td></tr><tr><td>a08</td><td>6</td><td>92.75</td><td>96.24</td><td>92.75</td><td>100.00</td><td>-14.39</td></tr><tr><td>a09</td><td>6</td><td>77.40</td><td>87.26</td><td>87.60</td><td>86.92</td><td>-18.12</td></tr><tr><td>a010</td><td>6</td><td>96.05</td><td>97.98</td><td>98.84</td><td>97.14</td><td>-10.41</td></tr><tr><td>a011</td><td>7</td><td>73.79</td><td>84.92</td><td>95.54</td><td>76.43</td><td>-17.35</td></tr><tr><td>a012</td><td>5</td><td>80.28</td><td>89.06</td><td>96.61</td><td>82.61</td><td>-11.61</td></tr><tr><td>a013</td><td>6</td><td>78.18</td><td>87.76</td><td>82.69</td><td>93.48</td><td>-10.63</td></tr><tr><td>a014</td><td>6</td><td>81.68</td><td>89.92</td><td>95.54</td><td>84.92</td><td>-0.15</td></tr><tr><td>a015</td><td>7</td><td>82.11</td><td>90.18</td><td>100</td><td>82.11</td><td>-9.82</td></tr><tr><td>a016</td><td>6</td><td>97.01</td><td>98.48</td><td>100</td><td>97.01</td><td>-11.74</td></tr><tr><td>a017</td><td>7</td><td>71.92</td><td>83.67</td><td>86.78</td><td>80.77</td><td>-13.19</td></tr><tr><td>a018</td><td>6</td><td>86.57</td><td>92.80</td><td>98.31</td><td>87.88</td><td>-2.69</td></tr></tbody></table>

(continued)
<table><caption>**Table 1.** (continued)</caption><thead><tr><th>RECORD</th><th>Q</th><th>ACC(%)</th><th>F1(%)</th><th>PPV(%)</th><th>SE(%)</th><th>SNR</th></tr></thead><tbody><tr><td>a019</td><td>5</td><td>72.73</td><td>84.21</td><td>96.55</td><td>74.67</td><td>-18.66</td></tr><tr><td>a020</td><td>7</td><td>81.38</td><td>89.73</td><td>86.76</td><td>92.91</td><td>-7.61</td></tr><tr><td>a021</td><td>5</td><td>78.99</td><td>88.26</td><td>93.97</td><td>83.21</td><td>-2.90</td></tr><tr><td>a022</td><td>6</td><td>94.56</td><td>97.20</td><td>98.58</td><td>95.86</td><td>-12.79</td></tr><tr><td>a023</td><td>6</td><td>79.10</td><td>88.33</td><td>92.98</td><td>84.13</td><td>-3.06</td></tr><tr><td>a024</td><td>6</td><td>80.30</td><td>89.08</td><td>92.17</td><td>86.18</td><td>-8.11</td></tr><tr><td>a025</td><td>5</td><td>80.00</td><td>88.89</td><td>91.53</td><td>86.40</td><td>-2.31</td></tr><tr><td>a026</td><td>5</td><td>81.08</td><td>89.55</td><td>92.31</td><td>86.96</td><td>-5.12</td></tr><tr><td>a029</td><td>4</td><td>72.18</td><td>83.84</td><td>94.12</td><td>75.59</td><td>5.65</td></tr><tr><td>a032</td><td>6</td><td>83.54</td><td>91.03</td><td>91.95</td><td>90.13</td><td>-11.47</td></tr><tr><td>a037</td><td>5</td><td>97.01</td><td>98.48</td><td>100</td><td>97.01</td><td>-13.74</td></tr><tr><td>a043</td><td>6</td><td>84.30</td><td>91.48</td><td>91.19</td><td>91.77</td><td>-11.32</td></tr><tr><td>a046</td><td>6</td><td>75.69</td><td>86.17</td><td>89.34</td><td>83.21</td><td>-9.88</td></tr><tr><td>a055</td><td>6</td><td>77.42</td><td>87.27</td><td>90.91</td><td>83.92</td><td>-2.81</td></tr><tr><td>a059</td><td>5</td><td>93.21</td><td>96.49</td><td>94.38</td><td>98.69</td><td>-9.39</td></tr><tr><td>a062</td><td>6</td><td>78.34</td><td>87.86</td><td>90.44</td><td>85.42</td><td>-13.28</td></tr><tr><td>a064</td><td>5</td><td>86.93</td><td>93.01</td><td>88.67</td><td>97.79</td><td>-7.60</td></tr><tr><td>a070</td><td>6</td><td>76.33</td><td>86.58</td><td>82.17</td><td>91.49</td><td>-5.93</td></tr><tr><td>a071</td><td>7</td><td>75.00</td><td>85.71</td><td>85.71</td><td>85.71</td><td>-3.81</td></tr><tr><td>AVERAGE</td><td></td><td>83.33</td><td>90.71</td><td>93.64</td><td>88.40</td><td>-7.45</td></tr></tbody></table>

<table><caption>**Table 2.** Comparative Results from other studies tested on the same Dataset. ACC, SE, PPV, and F1 values shown are average values reported for all recordings tested.</caption><thead><tr><th>Author(s)</th><th>ACC (%)</th><th>F1(%)</th><th>PPV(%)</th><th>SE(%)</th></tr></thead><tbody><tr><td>Panigrahy et al. [20]</td><td>84.89</td><td>91.82</td><td>92.18</td><td>91.47</td></tr><tr><td>DaPoian et al. [21]</td><td>Not reported</td><td>77.50</td><td>77.00</td><td>78.00</td></tr><tr><td>Jaros et al. [22]</td><td>68.25</td><td>75.68</td><td>81.31</td><td>72.60</td></tr><tr><td>Barnova et al. [23]</td><td>78.47</td><td>84.62</td><td>87.90</td><td>82.06</td></tr><tr><td>Previous work [19]</td><td>74.35</td><td>84.95</td><td>93.16</td><td>79.19</td></tr><tr><td>This work</td><td>83.33</td><td>90.71</td><td>94.64</td><td>88.40</td></tr></tbody></table>

# 4 Discussion

In this work, we presented a robust automated methodology for accurately extracting the Non-Invasive fetal ECG from multichannel abdominal recordings. We evaluated our system in many signals from different sources with different acquisition protocols and varying Signal to Noise Ratios (SNR). Results show that our method offers several advantages in the fECG extraction and the denoising stage.
As is evident from our presented results, an overcomplete representation of a noisy, nonlinear, and nonstationary signal, such as the abdominal ECG mixture, can lead to a more robust and more precise extraction of the fetal component of interest, even when presented with input data that vary in acquisition protocols and SNR levels. The R-ICA algorithm performed consistently both in low and high SNR scenarios. Furthermore, the EWT algorithm combined with a soft threshold function can represent the extracted fECG component subbands more helpfully than other signal decomposition algorithms, such as the Empirical Mode Decomposition (EMD) or Wavelet De-composition.

While our approach is effective in accurate fetal ECG extraction and FHR estimation, three limitations should be considered in real-world applications. First, in the extraction stage, the optimal number of the overcomplete basis of the input signal needs to be automatically determined to prevent the R-ICA model from overfitting and to produce redundant features. Also, while the EWT algorithm provides an improved signal decomposition, each mode's number of modes and frequency boundaries need to be pre-set. This is always difficult due to a lack of prior knowledge about the analyzed signal. Future work will focus on using machine learning methods to address these issues. Specifically, we plan to implement an Artificial Neural Network (ANN) using our signal Quality indices as predictive features, which will be able to classify the fetal ECG quality in several overcomplete modes of the input mixture and select the optimal level of separation.

**Acknowledgements.** We acknowledge the support of this work by the project "Immersive Virtual, Augmented and Mixed Reality Center Of Epirus" (MIS 5047221) which is implemented under the Action "Reinforcement of the Research and Innovation Infrastructure", funded by the Operational Programme "Competitiveness, Entrepreneurship and Innovation" (NSRF 2014–2020) and co-financed by Greece and the European Union (European Regional Development Fund).

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