Degenerate Unmixing Estimation Technique (DUET) for Fetal ECG Blind Source Separation

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Procedia Computer Science 00 (2019) 000–000

Procedia Computer Science 159 (2019) 610–619

23rd International Conference on Knowledge-Based and Intelligent Information & Engineering Systems 23rd International Conference on Knowledge-Based and Intelligent Information & Engineering Systems

Degenerate Unmixing Estimation Technique (DUET) for Fetal ECG SourceTechnique Separation(DUET) for Fetal ECG Degenerate UnmixingBlind Estimation Blind Source Separation Dzati Athiar Ramlia* , Fong Mei Linga, Norsalina Hassanb a a Nibong Tebal, 14300, Penang, b Malaysia School of Electrical & Electronic Engineering, Universiti Sains Malaysia, b Seberang Perai Polytechnic, Jalan Permatang Pauh, 13500, Permatang Pauh, Penang, Malaysia a School of Electrical & Electronic Engineering, Universiti Sains Malaysia, Nibong Tebal, 14300, Penang, Malaysia b Seberang Perai Polytechnic, Jalan Permatang Pauh, 13500, Permatang Pauh, Penang, Malaysia a

Abstract

Dzati Athiar Ramli * , Fong Mei Ling , Norsalina Hassan

Abstract Monitoring the health of fetus at early stage is very crucial. One of the non-invasive ways is by evaluating the pattern of electrocardiogram (ECG) signals of mother’s abdomen and thorax. As these raw signals are mixed signals that consist of mainly Monitoring the(MECG) health of early stage an is very crucial. One of the non-invasive ways is by signals evaluating the patternFast of maternal ECG andfetus fetal at ECG (FECG), effective extraction method of FECG from the mixed is imperative. electrocardiogram (ECG)Analysis signals of mother’sisabdomen thorax.signal As these raw signals are mixed signals that separation consist of mainly Independent Component (FastICA) one of theand common processing algorithms for blind source (BSS). maternal (MECG) ECG (FECG),case an effective method of FECG from mixedissignals However,ECG it works onlyand for fetal even-determined when theextraction number of sources (MECG andthe FECG) equalistoimperative. the numberFast of Independent Analysis (FastICA) is one abdomen of the common signal processing algorithms for blind source separation (BSS). mixtures (twoComponent mixed signals i.e. from the mother’s and the mother’s thorax). For the underdetermined case in which the However, works would only for case when the number ofcase sources (MECG and FECG) is equalFastICA to the number of number of itsources be even-determined more than the number of mixture (for the of twins or triplets’ pregnancy), algorithm mixtures (two mixed signals i.e.inverse from the mother’s abdomen the mother’simpossible. thorax). ForThus, the underdetermined case inEstimation which the fails as the computation of the mixing matrix of ICAand is theoritically Degenerate Unmixing number of (DUET) sources would be more the number mixture sparsity (for the algorithm case of twins or triplets’ in pregnancy), FastICA Technique algorithm whichthan is based on signalofrecovery is implemented this research so as toalgorithm discover fails as the computation of even-determined the inverse mixing of ICA is theoritically Thus, Degenerate Unmixing Estimation its feasibility to solve both andmatrix underdetermined cases. Fromimpossible. the experimental results, the DUET performance is Technique which is basedcase, on signal recovery sparsity is implemented in this researchtosobe as valuable to discover promising. (DUET) Althoughalgorithm for even-determined FastICA is better than algorithm DUET performance, DUET is proved in its feasibility to solve both even-determined underdetermined cases.toFrom experimental results, the DUET performance is solving the underdetermined case problem, and yet the low FECG signal noisethe ratio (SNR) value is observed reflecting the high promising. interference.Although for even-determined case, FastICA is better than DUET performance, DUET is proved to be valuable in solving the underdetermined case problem, yet the low FECG signal to noise ratio (SNR) value is observed reflecting the high interference. © 2019 The Author(s). Published by Elsevier B.V. © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2019 The Author(s). Published byKES Elsevier B.V. Peer-review Peer-review under under responsibility responsibility of of KES International. International. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility(FECG); of KES Blind International. Keywords: Fetus Electrocardiogram Sourse Separation (BSS); FastICA, DUET. Keywords: Fetus Electrocardiogram (FECG); Blind Sourse Separation (BSS); FastICA, DUET.

* Corresponding author. Tel.: +6045996028; fax: +6045996909. E-mail address: [email protected] * Corresponding author. Tel.: +6045996028; fax: +6045996909. E-mail address: [email protected] 1877-0509 © 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review ofPublished KES International. 1877-0509 ©under 2019 responsibility The Author(s). by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. 1877-0509 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of KES International. 10.1016/j.procs.2019.09.216



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1. Introduction Electrocardiogram (ECG) which is an electrical signal, is a useful and non-invasive early diagnosis tool to be used in monitoring and detecting any abnormalities of fetus heart activity. It can be employed by placing electrodes on a pregnant woman’s abdomen in order to obtain the electrical signals [1] [2]. However, the raw ECG signal obtained from this activity is a mixture of maternal ECG (MECG) and other unwanted signals such as electrical activity from the uterus muscles [2], [3]. Due to these problems, FECG has a significant lower signal-to-noise ratio compared to the MECG. Therefore, an effective algorithm to separate MECG and FECG from the raw ECG signal is imperative. Recently, many algorithms have been developed so as to extract individual signal from its mixed signal such as adaptive filtering, blind source separation, singular value decomposition and others. Among these algorithms, fast independent component analysis (FastICA) algorithm, which is based on blind source separation (BSS) is widely used by scientists and researchers in extracting individual source signal [4], [5], [6], [7]. Although the use of FastICA is encouraging, it has a limitation in extracting MECG and FECG from the raw mixed ECG data because it cannot be able to cover cases of twins or triplets’ pregnancy. There are two cases in BSS fetus monitoring which are even-determined and underdetermined. When the number of sources (FECG and MECG) equals to the number of mixed signals (raw ECG data from mother’s abdomen and raw ECG data from mother’s thorax), it is known as even-determined case while for underdetermined case, it has a greater number of sources than the number of mixed signals. This case happens for twins or triplets’ pregnancy. FastICA has been proven to work well for the even-determined case to extract FECG from mixed signals as reported in many researches [5],[6],[7],[8]. FastICA extracts the output estimated signals with the assumption that the number of input mixed signals, M is equal to the number of sources, N, that is 𝑀𝑀 = 𝑁𝑁. When it comes to the underdetermined case in which the number of sources, N is more than the number of input mixed signals, M, that is 𝑁𝑁 > 𝑀𝑀, FastICA algorithm is no longer valid to compute the inverse mixing matrix. In this study, the capability of DUET algorithm to be implemented for even-determined case and also for the underdetermined case is evaluated in this study. The objective of this study is to evaluate the performance of DUET and to compare its performance with FastICA for even-determined and underdetermined cases. The methodology of BSS, FastICA and DUET is described in Section 2. Following, the results and discussions are presented in Section 3 and finally, the conclusion is given in Section 4. 2. Methodology 2.1. Blind Source Separation (BSS) BBS theory originates from the cocktail party effect scenario where human’s auditory sense is capable to emphasize on the single source of signal from the environment that has multiple sources of signals happening simultaneously, as described in Plauth et al.[9]. BSS aims to recover the original source signals from their mixture without knowing the prior knowledge of the mixing system. Biomedical engineering, speech recognition, remote sensing, communication system and speech recognition are some of the potential application of BSS [10]. BSS can be categorized into four algorithms depending on the nature of the sources: the higher-order statistics (HOS), the secondorder statistics (SOS), the nonstationary and the sparsity[11]. HOS algorithm works based on mutual independence between the sources while SOS and nonstationary algorithm manipulates the temporal structure of the sources. On the other hand, sparsity algorithm is suitable for the underdetermined case as it works on sparse approach by discovering new subspaces from the set of time-frequency representation of the observed mixture signals. Here, regardless the number of sources, they can be inferred by the sparse algorithm instead of using the inverse mixing matrix as in the case where the sources must be equal to the mixtures [10]. 2.2. Fast Independent Component Analysis (FastICA) In FastICA method, instantaneous mixing is considered to estimate the independent source signals as represented in Equation 1.  (1) 𝑥𝑥𝑛𝑛 (𝑡𝑡) = 𝐴𝐴𝑠𝑠𝑛𝑛 (𝑡𝑡)

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where n represents the number of signals, 𝑥𝑥(𝑡𝑡) is the mixed signals in time domain, A is the mixing matrix and 𝑠𝑠(𝑡𝑡) is the original source signals in time domain. By computing the demixing matrix, 𝑊𝑊 = 𝐴𝐴−1 which is also known as the inverse mixing matrix, the output from the demixed matrix is the estimated source signals and is given as in Equation 2. (2)

𝑦𝑦𝑛𝑛 (𝑡𝑡) = 𝑊𝑊𝑥𝑥𝑛𝑛 (𝑡𝑡)

Here, n represents the number of signals, 𝑦𝑦(𝑡𝑡) is the output estimated signals in time domain, W is the inverse mixing matrix and 𝑥𝑥(𝑡𝑡) is the mixed signals in time domain. The mixed MECG and FECG are obtained from thoracic region and abdominal region of the mother, respectively by placing electrodes as shown in Fig. 1. On the other hand, Fig. 2 explains the mixing of original sources and demixing the mixed signals into estimated signals. The original source signals in time domain are represented by 𝑠𝑠1 (𝑡𝑡) and 𝑠𝑠2 (𝑡𝑡). The input mixed signals are represented by 𝑥𝑥1 (𝑡𝑡) and 𝑥𝑥2 (𝑡𝑡). FastICA can be differentiated using different measures of non-Gaussianity such as negentropy and kurtosis[1],[6],[12].

Fig.1 ECG signals from mother's thorax and abdomen [1]

Fig.2 Mixing and demixing process [1]

2.3. Degenerate Unmixing Estimation Technique (DUET) DUET works by estimating the independent components using relative attenuation and delay pairs which are obtained from ratios of time-frequency representations of the mixtures. An important theory of DUET is that it is possible to separate unpredicted number of sources with only two anechoic mixtures that do not overlap much in terms of time-frequency representations[13]. The anechoic mixing which is frequently described when using the DUET algorithm can be explained in Equations 3 and 4. 𝑥𝑥1 (𝑡𝑡) = ∑𝑁𝑁 𝑗𝑗=1 𝑠𝑠𝑗𝑗 (𝑡𝑡)

(3)

𝑥𝑥2 (𝑡𝑡) = ∑𝑁𝑁 𝑗𝑗=1 𝑎𝑎𝑗𝑗 𝑠𝑠

𝑗𝑗

(𝑡𝑡 − 𝛿𝛿𝑗𝑗 )

(4)

where 𝑁𝑁 is the number of sources while 𝑎𝑎𝑗𝑗 is the relative attenuation and 𝛿𝛿𝑗𝑗 is the relative delay which occurs between the sources and sensors. In DUET, a two-dimensional weighted histogram is plotted based on the local attenuation estimation and local delay estimation of the time-frequency representations of the mixed signals. The number of peaks showed in the two-dimensional weighted histogram corresponds to the number of sources. The location of each peak is the exact attenuation and delay of each source, which form the mixing parameter pairs[13]. Fig. 3 shows an example of a two-dimensional weighted histogram with six source mixture. By locating the mixing parameter pairs, the mixtures can be separated by assigning each time-frequency bin to the source. The mixtures are demixed through masking and maximum-likelihood combining. Then, the estimated signals are reconstructed from the time-frequency



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representation by converting it back into the time domain. However, if the sources have too many overlapping timefrequency bins in between, there will be trouble in resolving the histogram peaks[14]. Therefore, estimated signals cannot be resolved using DUET if there are too many overlapping.

Fig.3 Example of two-dimensional weighted histogram with six source mixtures [9] The DUET algorithm can be implemented using the following steps[13]. 1. Create the time-frequency representations of the input mixed signals, 𝑥𝑥1 (𝑡𝑡) and 𝑥𝑥2 (𝑡𝑡). 2. Compute the mixing parameters, namely the local attenuation estimation and local delay estimation, associated to the time-frequency representation. 3. Construct a two-dimensional smoothed weighted histogram. 4. Manually locate the peaks and peak centres in the histogram and determine the actual mixing parameters of the peaks. 5. Create the time-frequency binary masks for each peak centres located from step 4. 6. Apply the masks to the aligned mixtures. 7. Apply R peak detection for fudicial point counting. 8. Convert the estimated source from time-frequency representation back to time-domain representation. In this study, the R-peak counting algorithm is integrated to the existing DUET algorithm for fudicial point counting. 2.4. Experimental Data In this research, two different types of dataset are used as input mixed signals. First dataset is the raw ECG signal obtained from the online database, PhysioNet [15] and these data are used for the even-determined case experiments. Five sets of different raw ECG data are selected from the database i.e. ecgca102.edf, ecgca127.edf, ecgca192.edf, ecgca244.edf and ecgca252.edf which are named as dataset a, b, c, d and e, respectively in this study. The files are downloaded in MAT extension in order to be readable by MATLAB. Each dataset is 60 seconds duration and consists of five different ECG signals recorded from mother’s abdomen and mother’s thorax. For experimental data, one ECG signal from abdomen and one ECG signal from thorax in the dataset are used as the input mixed signals. For the underdetermined case experiment, the mixed speech signal data are used to simulate the mixture of one MECG and four FECG signal. Two different datasets are used and both datasets are obtained from [16] and [17] which are named as dataset 1 and 2, respectively. Both datasets have two different mixture of speech signals composed of five different speech sources. Dataset 1 is of 4 seconds duration while dataset 2 is of 5 minutes duration. 2.5. Performance Evaluation Subjective evaluation is done by plotting the output estimated signals to show the characteristic of the estimated signals. For ECG signals, MECG is expected to have higher magnitude compared to FECG. By plotting the output estimated signals, the magnitude of the signals can be observed. For the objective evaluation, signal-to-interference

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ratio (SIR) [1] is used to evaluate the performance of the output estimated signals as given in equation 5. Higher positive value of SIR measurement shows the better performance. 𝑆𝑆𝑆𝑆𝑆𝑆 = 10𝑙𝑙𝑙𝑙𝑙𝑙10 ∑𝑇𝑇

2 ∑𝑇𝑇 𝑘𝑘=0 𝐸𝐸𝑘𝑘

2 𝑘𝑘=0(𝑀𝑀𝑘𝑘 −𝐸𝐸𝑘𝑘 )

𝑑𝑑𝑑𝑑

(5)

𝐸𝐸𝑘𝑘 is the output estimated signals, 𝑀𝑀𝑘𝑘 is the input mixed signals and T is duration of the signals. 3. Results and Discussions 3.1. Even-determined case

For the even-determined case, only estimated signals from dataset a is shown for subjective evaluation as shown in Error! Reference source not found. and Fig. 5 below. It proves that both FastICA and DUET can be used to separate fetal and maternal ECG from mixed raw ECG signals. However, the characteristics of the estimated ECG signals extracted from FastICA algorithm and DUET algorithm deviated. Estimated FECG and MECG plotted in the graphs are identified based on the R-peak detection count which was executed before the subjective evaluation. The signal with higher R-peak count is identified to be the estimated FECG, while the signal with lower R-peak count is identified to be the estimated MECG. The results from FastICA algorithm are scaled and normalized in unit variance. Therefore, the magnitudes of the estimated fetal and maternal ECG are observed to be approximately 104 times smaller compared to the original mixed ECG signals obtained from online database. In contrary, DUET algorithm does not require the input mixed signals to be normalized. Thus, the estimated fetal and maternal ECG signals are showing real magnitude as in the original mixed ECG signals. From the above results extracted using DUET algorithm, it is obvious that the magnitude of the estimated FECG is smaller than that of the estimated MECG, which is true.

Fig. 4 Estimated FECG and MECG signals by using FastICA algorithm for ECG dataset a.

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Fig.5 Estimated FECG and MECG signals by using DUET algorithm for ECG dataset a. Table 1 shows the SIR measurements for dataset a, b, c, d and e experimented using FastICA and DUET algorithms. Both FastICA and DUET algorithms are successfully able to extract the estimated MECG and FECG signals. Based on the average SIR values shown in the table, the MECG SIR values for FastICA and DUET are observed as positive, while the FECG SIR values are observed as negative. This observation is as expected as the MECG is supposed to have stronger signal than FECG. Therefore, the extracted MECG signals have less interference compared to the extracted FECG signals. However, comparing the SIR measurements between FastICA and DUET, FastICA has better performance in extracting the source signals as its capability to filter out the interferences is better than DUET hence providing stronger output estimated signals. Table1 SIR measurement for even-determined case Dataset FastICA Maternal

DUET Fetal

Maternal

Fetal

Dataset a

5.182

0.263

-1.148

-0.843

Dataset b

14.263

-2.081

2.048

-0.225

Dataset c

25.027

-2.760

-0.657

-0.994

Dataset d

15.260

-2.191

-0.247

-0.797

Dataset e

11.382

-1.660

0.054

-1.983

Average SIR (dB)

14.223

-1.686

0.010

-0.770

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3.2. Underdetermined case For the underdetermined cases, subjective evaluation is done by observing the output estimated signals as shown from Fig. 6 to Fig. 9. The expectation is to have a number of different output estimated signals based on the expected number of sources. Two different sets of data i.e. dataset 1 and dataset 2 are input into the FastICA and DUET algorithms. The results from the two sets of data are plotted into non-overlapping graphs where they show the individual output estimated signals extracted. The graphical results for both datasets show that FastICA algorithm fails to extract the output estimated signals from the mixed data as shown in Fig. 6 and 7. For both datasets, it is expected to have five output estimated signals. However, FastICA algorithm is only able to extract two different output estimated signals. The other three output estimated signals are plotted but duplicating the two different estimated signals.

Fig.6 Estimated source signals in non-overlapping graph using FastICA algorithm for dataset 1



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Fig. 7 Estimated source signals in non-overlapping graph using Fast ICA algorithm for dataset 2 However, for DUET algorithm, five different output estimated signals can be observed clearly from the graphs. The results show that the DUET algorithm is capable to extract the five output estimated signals as shown in Fig. 8 and 9 below.

Fig. 8 Estimated source signals in non-overlapping graph using DUET algorithm for dataset 1

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Fig. 9 Estimated source signals in non-overlapping graph using DUET algorithm for dataset 2 For the underdetermined case, the SIR measurements (objective evaluation) for dataset 1 and 2 are shown in Table 2. It is expected that five output estimated signals are extracted. From the table, it clearly shows that the FastICA algorithm fails to extract out five output estimated signals. Using FastICA algorithm, only two different output estimated signals are extracted, and the other three output estimated signals duplicates the two different output estimated signals. On the other hand, DUET algorithm is successful to extract the five different output estimated signals. However, the SIR measurement for both datasets are less than 0dB, which means that high interferences exist in the output estimated signals. Table 2 SIR measurement for underdetermined case Dataset Fast ICA

DUET

Dataset 1

Dataset 2

Dataset 1

Estimated Source 1

-1.1263

-2.9836

1.744

Dataset 2 3.085

Estimated Source 2

-1.1263

-2.9836

-0.981

-2.926

Estimated Source 3

8.9288

44.25

-0.425

-2.987

Estimated Source 4

8.9288

-2.9836

0.249

-0.642

Estimated Source 5

8.9288

44.25

-1.263

-2.970

Average SIR (dB)

(not valid)

(not valid)

-0.135

-1.288

4. Conclusion FastICA has much better performance than DUET because the MECG signal extracted using Fast ICA has less interference. However, FastICA algorithm fails to extract the output estimated signals accurately for underdetermined case. Although DUET algorithm can be used for underdetermined case, the extracted output estimated signals have high interference and further noise filtering is needed to improve the performances.



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Acknowledgements This work was supported by Universiti Sains Malaysia 1001/PELECT/9014057.

under

Research University Grant (RU)-

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