Isolation of multiple electrocardiogram artifacts using independent vector analysis

Introduction

An electrocardiogram (ECG) is an important tool to measure the electrical activity generated by the SA (sinoatrial) node that causes the upper heart chambers (atria) to contract. ECG is an effective tool for investigating the heart related problems like arrhythmia diagnosis and widely adopted in a number of practical applications. ECG signals are utilized for automatic detection of myocardial infarction in Acharya et al. (2017). Kumar, Pachori & Acharya (2017) investigated the ECG signals for detection and characterization of coronary artery disease. Similarly in Acharya et al. (2017), the authors presented the heart failure detection technique based on ECG signals and the extraction of fetal ECG from maternal ECG is achieved in Su & Wu (2017). Qingxue & Zhou (2018) developed person identification technique based on ECG signal processing. Moreover, ECG based silent myocardial infarction as well as long term risk of heart failure is diagnosed in Qureshi et al. (2018). Meanwhile, modern efficient ECG data recording and analysis systems are also been designed even in wireless scenario (Tao et al., 2018; Elgendi et al., 2018; Han et al., 2018; Tanguay et al., 2018; Orphanidou, 2018). However, the recorded ECG signals are normally affected by different types of electro-physiological and non electro-physiological artifacts. The artifacts affected ECG can not be adopted in the sensitive applications. Hence, efficient removal of artifacts is necessary for ECG signals analysis for various applications. Removal of these artifacts before further processing make the design of ECG instrument simpler and produce accurate results.

In literature it is well known that among ECG artifacts, baseline wandering (BW), electrode movement (EM), and muscle artifacts (MAs) are more challenging to separate from the recorded ECG signals (Hesar & Mohebbi, 2017; Varanini et al., 2016; Zarzoso & Nandi, 2001). BW is normally generated through body movements, breathing, and lose sensors contacts. EM is the result of variations of electrodes positions over the human body surface, MA is caused by contraction of the muscles near the electrode (Limaye & Deshmukh, 2016). The main challenges associated with the removal of these artifacts are their unpredictable amplitudes and variable frequency range (Hegde, Deekshit & Satyanarayana, 2012).

Ecg data and artifacts

Realistic simulated and real ECG data are considered for simulations. Real data is taken from the MIT-BIH database (Moody, Muldrow & Mark, 1984). The acquired signals in the MIT-BIH Noise Stress Test Database are digitized using uni-polar ADCs with 11-bit resolution. This database is open source for further research. The MIT-BIH database contains the ECG signals and their artifacts. The artifacts considered in this work are as follows:

• Muscle artifact: Muscle artifacts are the results of muscle contraction having low amplitudes and a large frequency range from 0–10 kHz.

• Baseline wandering: Baseline wandering originates due to body movements, breathing, and loose sensor contact. Body movements cause unpredictable large amplitude and low-frequency artifacts. Breathing also causes low frequency drifting between 0.15 and 0.3 Hz.

• Electrode movement: Electrode movement is generated due to electrode position away from the skin contact, changing the electrode and skin impedance causing potential variations in the recorded ECG signal.

• Other artifacts: Other ECG artifacts include power line interference, device noise, Electro-surgical noise, quantization noise, aliasing, etc.

The time-domain real ECG, BW, EM, and MA signals are demonstrated in Fig. 1 with 2,000 data samples of each signal as a first data set.

Frequency domain representation is shown in Fig. 2. It shows that most of the frequencies of ECG and artifacts lie in the range of 50 Hz. From Fig. 2 it is observed that all the frequencies of ECG signal and artifacts overlap with each other. Hence, to cleanly extract these ECG signals, some efficient BSS techniques are required. As it is already discussed, IVA is the more efficient BSS technique as compared to ICA and CCA (Moody, Muldrow & Mark, 1984). Based on the discussions, it is recommended to utilize IVA for ECG signals de-noising. Moreover, the recorded mixed ECG data is shown in Fig. 3 for a single data set with L = 2,000 samples. The measurement is taken in the presence of additive white Gaussian noise (AWGN) with signal to noise ratio (SNR) of 20 dB. Figure 3 basically contains mixture signals of all the individual source signals. The source signals are ECG, BW, EM and MA. The mixing process is performed in MATLAB such that the source signals matrix $\mathit{S}$ of size $4\times 2000$ is multiplied with a randomly generated mixing matrix $\mathit{A}$ of size $4\times 4$. Mixed data is recorded in matrix $\mathit{X}$, where $\mathit{X}$ is of size $4\times 2000$. It must be noted that in case of ICA a single data set as shown above is utilized while in case of IVA multiple copies of the source signals are recorded and processed for un-mixing i.e., multiple mixing matrices are observed and un-mixing is performed at a time. This is the main advantage of the IVA algorithm to un-mix the recorded signals and its delayed versions at a time. The realistic simulated ECG signals are generated in MATLAB version R2016a (MathWorks, Inc., Natick, MA, USA).

System model

This section presents the ECG signals and artifacts in the IVA data model. K number of independent sources i.e., ECG and artifacts are considered and all sources contain L number of samples for D data sets. The acquired data using ECG electrodes is expressed as:

(1) $${\mathbf{\text{X}}}^d={\mathbf{\text{A}}}^d{\mathbf{\text{S}}}^{d}1\le d\le D,$$

The matrices ${\mathbf{\text{S}}}^d$ contains the source data vectors $\mathbf{\text{s}}{{}^d}_1,\mathbf{\text{s}}{{}^d}_2,...,\mathbf{\text{s}}{{}^d}_K$, where every vector having length L. All vectors are real valued random vectors having zero mean. The mixing matices ${\mathbf{\text{A}}}^d$ are also real with random values for D number of data sets. Hence, the the IVA algorithm responsible to estimate these unknown matrices while utilizing the mixed data. The source data is represented by $({\mathbf{\text{S}}}^1{)}^T,({\mathbf{\text{S}}}^2{)}^T,...,({\mathbf{\text{S}}}^D{)}^T$ in D data sets. After the estimation of ${\mathbf{\text{A}}}^d$ through the IVA algorithm, the resultant source signals as given in Qamar et al. (2022) are expressed as:

(2) $${\mathbf{\text{Y}}}^d={\mathbf{\text{W}}}^d{\mathbf{\text{X}}}^d$$

The ${\mathbf{\text{W}}}^d$ is inverse of ${\mathbf{\text{A}}}^d$ and is called the un-mixing matrix estimated for D data sets. The estimated source data vectors are ${\mathbf{\text{y}}}_1^d,{\mathbf{\text{y}}}_2^d,...,y_k^d.$

Proposed iva-based ecg artifacts separation

Multi-channel ECG signals are recorded in the presence of various artifacts i.e., BW, EM, and MA as well as noise. The number of ECG and artifact signals are denoted by K, each signal has data block length L with D number of data sets. The recorded mixed data contains D number of data sets $({\mathbf{\text{X}}}^1{)}^T,({\mathbf{\text{X}}}^2{)}^T,...,({\mathbf{\text{X}}}^D{)}^T$ as shown in Fig. 3 for SNR of 20 dB. Since, the artifact signals have overlapped frequencies with the original ECG signal as illustrated in Fig. 2, the role of the BSS algorithms is to estimate the source signals from the recorded mixed signals. The BSS algorithms know nothing except independence and non-Gaussianity of the source signals.

The estimated sources of each BSS algorithm have scaling and order ambiguities. The scaling issue can be easily resolved considering the source signals with unit variance and also scaling the un-mixing vector to extract the unit variance sources. The arbitrary order of the estimated signals in each data set can be corrected using the permutation matrix, which is common in each data set (Anderson, Adali & Li, 2012).

The IVA algorithms separate the mixed recorded signals as a first data set and their delayed versions as other data sets. This separation is performed using the minimization of the mutual information among the estimated source component vectors (SCVs). The cost function of IVA is demonstrated in Anderson, Adali & Li (2012) and illustrated here as:

(3) $$I_{IVA}=\sum _{k=1}^K(\sum _{d=1}^{D}H[y_k^d]-I[y_k])-\sum _{d=1}^D\log \left|\begin{array}{c}{\mathbf{\text{W}}}^d\end{array}\right|-C$$

The $I[y_k]$ represents mutual information within $k_{th}$ SCVs. H is the entropy, ${\mathbf{\text{W}}}^d$ is the un-mixing matrix of $d_{th}$ data set and C is a constant factor which is equivalent to $H[{\mathbf{\text{X}}}^1,{\mathbf{\text{X}}}^2,...,{\mathbf{\text{X}}}^D]$ depending only on the recorded mixed data. The IVA algorithms minimize the cost function of Acharya et al. (2017) and maximizes the mutual information within each SCV.

ICA is a well-known blind source separation technique used for linearly mixed signals utilizing statistical independence of the source signals (Uddin et al., 2015). CCA considers the mixed recorded signals as well as its delayed versions by exploiting the SOS. The IVA combines the advantages of CCA and ICA by exploiting the SOS and HOS. Moreover, numerous variants of IVA algorithms, such as IVA-GGD (Anderson et al., 2014), IVA-L (Kim et al., 2007) and IVA-G (Anderson, Adali & Li, 2012) exist in literature and their dominance is already proven. Motivated by this, this research implemented various versions of IVA algorithms to verify their validity for ECG artifacts removal. All these algorithms utilize the IVA cost function given in Acharya et al. (2017) to estimate the un-mixing matrices. In the case of complex-valued data, the IVA-G algorithm includes the pseudo-co-variance matrix in the cost function. This algorithm also ignores the HOS and sample to sample dependency. The IVA-L utilizes the HOS for un-mixing while ignoring the sample to sample dependency and SOS. The matrix gradient approach is used in the implementation of the IVA-L algorithm. The IVA-GGD algorithm utilizes the HOS and SOS for source signal estimation considering multivariate Gaussian prior. This algorithm also avoids sample to sample dependency. Moreover, processing of the original as well as the delayed versions makes the IVA algorithms more practical compared to the ICA technique. Based on these advantages, various variants of IVA algorithms are implemented in this article and their performance is tested for the ECG artifacts removal.

Simulation results

In this section, simulation results of the proposed IVA based technique for ECG artifacts removal from the recorded mixed signals is presented. The IVA algorithms considered for simulations are IVA-GGD, IVA-L and IVA-G. Performance of these algorithms is evaluated for various SNRs ranging from 0 to 20 dB. Results are compiled using Monte Carlo simulation. The ECG artifacts considered for simulation are baseline wandering (BW), electrode movement (EM), and mascle artifacts (MA). Real and simulated ECG signals are utilized in the simulations. The real ECG signals are downloaded from MIT-BIH database and the simulated ECG signals are generated in MATLAB. The number of source signals considered are K = 4, the number of data sets D = 4, and length L of the processing data blocks in each data set ranges from 50 to 2,000 samples. Moreover, to evaluate the effectiveness of the proposed IVA technique for ECG artifacts removal different performance evaluation criterion are used that are given below:

• The corresponding root mean square error $(CRMSE)$ used in Chen et al. (2017) is expressed below:

(4) $$CRMSE={\displaystyle \frac{RMS({\mathbf{\text{s}}}_{ECG}^d-{\mathbf{\text{y}}}_{ECG}^d)}{RMS({\mathbf{\text{s}}}_{ECG}^d)}}$$

• The ${\mathbf{\text{s}}}_{ECG}^d$ and ${\mathbf{\text{y}}}_{ECG}^d$ represent the original simulated ECG and the reconstructed ECG signals simultaneously at data set $d$.

• Common inter-symbol-interference ( $IS{I}_{com}$) (Anderson, Adali & Li, 2012) is also utilized as a performance measure that is presented as:

(5) $$IS{I}_{com}={\displaystyle \frac{1}{2K(K-1)}}\left[{\psi }^{\mathrm{\prime }}+{\psi }^{\mathrm{\prime }\mathrm{\prime }}\right]$$

• The ${\psi }^{\mathrm{\prime }}=\sum _{n=1}^K(\sum _{m=1}^K{\displaystyle \frac{g_{m,n}^{\mathrm{\prime }}}{ma{x}_p{g}_{n,p}^{\mathrm{\prime }}}}-1)$

  ${\psi }^{\mathrm{\prime }\mathrm{\prime }}=\sum _{m=1}^K(\sum _{n=1}^K{\displaystyle \frac{g_{m,n}^{\mathrm{\prime }}}{ma{x}_p{g}_{p,m}^{\mathrm{\prime }}}}-1)$

  and ${\mathbf{\text{G}}}^d={\mathbf{\text{W}}}^d{\mathbf{\text{A}}}^d$ with $g_{m,n}=\sum _{d=1}^D|g_{m,n}^d|$. The $IS{I}_{com}$ is normalized so that its maximum value is one and minimum vale is zero, where zero value corresponds to ideal separation performance.

• The $U_{W^d{A}^d}$ is utilized as another evaluation criteria and is expressed as:

(6) $$U_{W^d{A}^d}=\sum _{n=1}^K(\sum _{m=1}^K{g}_{m,n}^{\mathrm{\prime }}-1)$$

The ideal separation corresponds to zero value of $U_{W^d{A}^d}$.

First, the effectiveness of the IVA-based technique in comparison with ICA and CCA techniques is demonstrated. The results of the three techniques are demonstrated while utilizing the Fast-ICA algorithm (Uddin, Ahmad & Iqbal, 2017) of the ICA, the GMCA algorithm (Li et al., 2009) of CCA and the IVA-G algorithm of the IVA. Simulations are performed at an SNR of 20 dB. The performance evaluation criteria used is CRMSE. In the case of the ICA algorithm, the value of the data set is one. Performance evaluation is carried out for different values of L ranging between 100 to 2,000 samples in a single data set. The results of ICA, CCA and IVA algorithms are demonstrated in Fig. 4. The simulation results clearly show that the IVA outperforms ICA and CCA algorithms. These results also verify that the IVA algorithm is less sensitive to the processing data block lengths. The performance improvement at a block length of $L=100$ is around 85 $\mathrm{\%}$ for the IVA technique and 15 $\mathrm{\%}$ for the CCA technique as compared with the ICA technique. Similarly, we demonstrate the $IS{I}_{com}$ performance of all these algorithms for the same conditions as given in the above simulations. The results are demonstrated in Fig. 5. This figure also shows the effective performance of the IVA algorithm. The extracted ECG signals for these three algorithms are also demonstrated in Fig. 6. It shows that the IVA algorithm outperforms other algorithms and is also less sensitive to AWGN noise.

Second, the quality of the separated ECG signals from various artifacts using the IVA algorithms using ( $IS{I}_{com}$) is evaluated. Here, the simulated ECG signal corrupted by various artifacts i.e., BW, MA, and EM is considered. Linearly mixed instantaneous signals are generated using randomly generated mixing matrices in MATLAB. The mixed recorded signals are shown in Fig. 7 for a single data set. The mixing process of Figs. 3 and 7 is same, the difference in signals is such that Fig. 3 contains the simulated ECG signals and Fig. 6 shows the realistic ECG signal. Three IVA algorithms are applied to the simulated ECG signals for artifacts removal. The reliability of the ECG signals for all three algorithms is evaluated for different values of SNRs. The simulations are performed over four recorded data sets independently. In each run, the pure ECG signal is extracted and artifacts are separated from the recorded mixed signals.

The $IS{I}_{com}$ performance of the IVA algorithms for different number of iterations is performed. Results are shown in Fig. 8 for 20 dB SNR and a block length of 1,000 samples. It shows similar performance of all the algorithms at steady state condition. Furthermore, performance of the IVA algorithms is also evaluated for different values of the input data block lengths in different data sets. Simulation results are shown in Fig. 9 at 20 dB SNR. These results show that the IVA-L algorithm is more sensitive to length of the processing data blocks. At a block length of 100 samples in each data set the performance improvements of the IVA-G and IVA-GGD are $18\mathrm{\%}$ and $19\mathrm{\%}$ as compared to the IVA-L.

In order to further investigate the IVA algorithms, we evaluate the $U_{W^d{A}^d}$ performance of the IVA algorithms at SNR of 20 dB for different number of iterations. Results are given in Fig. 10. It shows that the IVA-L converges faster as compared to IVA-G and IVA-GGD algorithms. The IVA-L converges at approximately 10 iterations, the other two converges at 25 iterations approximately. Although the IVA-L converges fast with same steady state results as achieved by other algorithms.

In the third part of simulations, we demonstrate the practical performance of the IVA algorithms for real ECG artifacts removal. The ECG artifacts considered in this part are BW, EM and MA. Removal of these artifacts is a challenging task due to their variable amplitudes and frequencies. The IVA algorithms considered in this section are IVA-L, IVA-G and IVA-GGD. The separated signals of the IVA algorithms are shown in Fig. 11 for 20 dB SNR. The results shows that three algorithms perform well for ECG artifacts removal. Moreover, the error signals are also demonstrated in Fig. 12, where error signal is the difference of the real and separated ECG signals. The resultant very low amplitudes of the error signals shows the effectiveness of the IVA algorithms.

The algorithms performance is also investigated for different values of the input data block lengths in each data sets. The $IS{I}_{com}$ performance is evaluated and the results are shown in Table 1. The data block lengths considered in each data set ranges from 50 to 2,000 samples with SNR of 20 dB. These results show that the IVA-GGD and IVA-G are less sensitive to lengths of the processing data blocks as compared to IVA-L. Furthermore, the algorithms performance is also evaluated for various SNR values with input data block length of 2,000 samples in each data set. The results are demonstrated in Table 2 for SNR ranges from 0 to 20 dB. Performance of the algorithms degrade for lower values of SNR. The IVA-GGD and IVA-G provide a little better results as compared to IVA-L for lower SNR values.

Finally, larger data blocks with more ECG signals are considered. ECG and interfering source signals utilized in this part of simulations have data block lengths ranging from 100 to 10,000 samples. Five ECG signals i.e., ECG₁, ECG₂, ECG₃, ECG₄ and ECG₅ are considered from the MIT-BIH database for further analysis. The source signals are shown in Fig. 13. This figure contains the BW, EM, MA and ECG signals. Larger samples are considered to further investigate the behavior of the ICA, CCA, and IVA algorithms. The mixing and un-mixing procedures are performed as discussed above. The ISI_com performance of all three algorithms is evaluated while considering the 20 dB SNR. Results of all the five ECG signals i.e., ECG₁, ECG₂, ECG₃, ECG₄ and ECG₅ are demonstrated in Table 3. This table shows approximately the same performance of a single algorithm for all five ECG signals. The ISI_com performance of the ECG2 is also demonstrated in Fig. 14 to observe the performance improvement for increased lengths of the processing data blocks. Although, in addition to Table 3 the results of all the other ECG signals can also be included as figures but restricted to ECG2 only to avoid the unnecessary length of the article. Furthermore, the reconstructed ECG signal i.e., ECG2 in Fig. 15 is also demonstrated for all three algorithms.

Discussion and conclusion

The ECG artifacts removal problem is investigated in this article. Both realistic simulated and real ECG signals are utilized for simulation. The artifacts considered are baseline wandering, electrode movement and muscle artifacts. Removal of these artifacts is difficult due to their variable amplitudes and frequencies. The IVA technique is compared in this article shows that it outperforms the CCA and ICA techniques. We further investigated the IVA technique for ECG artifacts removal. For comparison purpose, we consider three IVA algorithms to get more clear ECG signals in the presence of various artifacts. In addition, we utilized different evaluation criterion to confirm performance of the proposed technique. The $IS{I}_{com}$ performance of the IVA algorithms for different values of the input data block lengths in different data sets. Simulation results are shown in Fig. 9 at 20 dB SNR. These results show that the IVA-L algorithm is more sensitive to length of the processing data blocks. At a block length of 100 samples in each data set the performance improvements of the IVA-G and IVA-GGD are $18\mathrm{\%}$ and $19\mathrm{\%}$ as compared to the IVA-L. As a concluding remarks, we can say that the IVA algorithms are less sensitive to input data block lengths and input SNRs as compared to the ICA technique. Thus, IVA is proved to be an efficient and more practical technique for ECG de-noising.

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