A new approach for denoising multichannel electrogastrographic signals

Biomedical Signal Processing and Control 45 (2018) 213–224

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Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc

A new approach for denoising multichannel electrogastrographic signals D. Komorowski ∗ , B. Mika Silesian University of Technology, Faculty of Biomedical Engineering, Department of Biosensors and Processing of Biomedical Signals, Roosevelt 40, 41-800 Zabrze, Poland

a r t i c l e

i n f o

Article history: Received 12 April 2017 Received in revised form 2 May 2018 Accepted 28 May 2018 Keywords: EGG Adaptive filtering NA-MEMD ICA

a b s t r a c t Electrogastrography (EGG) can be considered as a non-invasive method for the measurement of gastric myoelectrical activity. The multichannel signal is non-invasively captured by disposable electrodes placed on the surface of a stomach. The recorded signal can include not only EGG components, but also the interfering signals from other organs, for instance, the disturbances connected with respiratory movements and random noise. In order to correctly calculate the parameters of the EGG examination and improve the patient’s diagnosis, the EGG signal requires effective methods for removing disturbances. The aim of this work was to investigate a new approach for denosing the multichannel electrogastrographic signals, performed by means of the Noise-Assisted Empirical Mode Decomposition (NA-MEMD) and adaptive filtering. The proposed method uses NA-MEMD for extracting the reference signal for adaptive filtering in the cosine domain. The suggested technique was validated by comparing the obtained results with the outcomes acquired by the reference method based on the classical bandpass filtering, Independent Component Analysis (ICA) and adaptive filtering. The effectiveness of the proposed algorithm was established by examining the influence of adaptive filtering on the basic diagnostic parameters, calculated from the EGG signal, such as the dominant frequency (DF), the normogastric rhythm index (NI), the frequency instability coefficient (FIC), and the power instability coefficient (PIC). In addition, the effectiveness of the noise attenuation by the proposed method was verified. The paper presents the results of research carried out for the five healthy subjects. Validation of the proposed method was performed using real human EGG signals and real EGG signals with added synthetic noise. © 2018 Elsevier Ltd. All rights reserved.

1. Introduction Electrogastrography is the cutaneous measurement of the myoelectrical activity of the stomach performed by using disposable surface electrodes placed on the abdominal skin of the patient [1]. The one-channel EGG data was obtained for the first time in 1922 by Walter Alvarez [2]. The EGG is a non-invasive test, relatively inexpensive and easy to perform. Due to the fact that the EGG recording does not disturb the myoelectrical activity of the stomach, it can play significant role as an additional evaluation tool in the diagnosis of gastric motility disorders [3]. Electrogastrography is particularly appreciated and increasingly used by pediatricians and neonatologist because of its non-invasiveness and relatively small inconvenience [4–6].

∗ Corresponding author. E-mail addresses: [email protected] (D. Komorowski), [email protected] (B. Mika). https://doi.org/10.1016/j.bspc.2018.05.041 1746-8094/© 2018 Elsevier Ltd. All rights reserved.

From the pacemaker area of stomach, located on the greater curvature between the fundus and corpus, spontaneous electrical depolarization and repolarization generates the myoelectrical excitation. The main component of the gastric myoelectrical activity, the so-called the gastric slow wave, has a frequency ∼0.05 Hz (3 cycles per minute (cpm)). For appropriate spread of the gastric peristalsis in a form of a mechanical wave, the gastric slow waves must propagate from the pacemaker region circumferentially and distally toward the pylorus. The correct speed and direction of the propagation of the slow wave is the crucial mechanism that controls and integrates the stomach wall motility, which is responsible for the proper emptying of the stomach [7]. Gastric disorders, such as vomiting, dyspepsia and bloating are usually a consequence of the disturbances in the emptying of the stomach contents. Compared to the other electrophysiological signals, the clinical applications of the EGG are still limited, mainly because the amplitude of the EGG signal is relatively weak ∼40–500 ␮V and the frequency band is very low (in the range from 0.008 to 0.15 Hz (0.5–9.0 cpm)) [8]. For this reason, there are potential difficulties to extract the EGG components from the surrounding background

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Fig. 1. The fragment of 1-minute EGG data (left), its spectrum (right) with the dominant frequency (DF), and dominant power (DP) indicated.

noise related to the undesirable signals, such as respiratory, heart, duodenal, and colonic electrical activity. Since the EGG is the mixture of the other signals the direct visual analysis of the raw EGG data is difficult or nearly impossible. Usually, the EGG processing is based on spectral analysis and is performed by computer applications. The typical EGG examination generally takes about 2 h and is divided into three parts: preprandial (fast), meal, and postprandial. According to the conventional method of the EGG analysis [7,9], the recorded signal is usually divided into ∼30-minute fragments, one preprandial and two or more postprandial (the meal part is excluded from examination). Each of 30-minute fragments of the EGG examination is divided into 1- to 4-minute (long) segments, then the power spectrum density (PSD), the dominant power (DP), and the dominant frequency (DF) are calculated for each segment. The DF is defined as a value of frequency for the highest peak (dominant power) of the PSD in the range of 0.5–9.0 cpm [7]. A graphical illustration of DF is depicted in Fig. 1. Based on the DF, the normogastric rhythm index (NI) is defined as the ratio of the number of segments with DF in the range of 2.4–3.6 cpm to the total number of segments [3,5,9]. The normogastria range slightly differs, depending on the institution. The EGG recording can also posses some pathological rhythms: bradygastria (0.5–2.4 cpm), and tachygastria (3.6–9.0 cpm). According to the literature, the percentage of normogastria ryhthms for the healthy subject is about 70 [3,10]. The EGG signal recording procedure is described in detail by Kenneth Koch in [7], and Jieyun Yin et al. in [10]. The definitions and descriptions of other parameters that are commonly calculated for EGG signals can be found in the literature [3,7,9,10]. Various methods of filtering out the background noise and the automatic analysis of the signal have been developed and widely presented in the literature, for example, bandpass filtering [11], fast Fourier transform [7], running spectral analysis [12], autoregressive modeling [13], neural network [14], continuous wavelet transform (CWT) [15,16], independent component analysis (ICA), and adaptive filtering [13,17,18]. In a classical way of EGG signals processing, the conventional low-pass or bandpass filter are usually applied. Using these methods may result in the waveform distortion of gastric signal [13,18]. In cutaneous EGG recordings [10,13,19,20] the waveform distortion may be due to the fact that frequencies (or its harmonics) of other biological signals: the respiratory disturbance (12–25 cpm), small intestine, distal ileum (∼8 cpm), colonic signal or noise may be close to or overlap with gastric signals. Adaptive filtering allows improving the signal-to-noise ratio (SNR) of the EGG, simultaneously keeping the gastric signal component less affected [1,13,17]. Getting a reference signal for adaptive filtering in practical biomedical applications is not an easy task and is frequently mentioned in the literature as the inherent weakness of adaptive technique [21]. The aim of this paper was to present a novel approach to different types of artifact mitigation in the multichannel EGG signal by using the combination of two methods: the NA-MEMD algo-

Fig. 2. The block diagram of the adaptive filtering with the reference signal obtained by using the NA-MEMD algorithm (proposed method).

Fig. 3. The block diagram of the adaptive filtering with the reference signal obtained by using the ICA algorithm (reference method).

rithm (for obtaining the reference signal) and adaptive filtering in the cosine domain. The proposed method based on NA-MEMD algorithm can be successfully applied to obtain the reference signal.

2. Methods In this section, the adaptive filtering algorithm for the multichannel EGG signal is presented. The process of adaptive filtering requires a reference signal, which was obtained by the NA-MEMD and ICA methods. This section is organized as follows: first, the process of the acquisition of EGG signals is described, then NAMEMD, ICA, and the adaptive filter are introduced. Fig. 2 shows the block diagram of the proposed method. The method was validated by using both the traditional bandpass filtering (in the range of 0.5–9.0 cpm) and adaptive filtering with the reference signal obtained by means of the ICA algorithm. Fig. 3 presents the scheme of the second reference (validation) method.

2.1. Procedure of EGG recording The EGG signals (time series) used in the presented work were recorded using a wireless four-channel biological amplifier [22]. The resolution of the analog-to-digital converter used in the amplifier was 24 bits. The signals were sampled with frequency 250 Hz per channel, and next filtered by anti-aliasing low-pass digital FIR filter with the cut-off frequency set to 2.0 Hz, and next re-sampled to 4 Hz. During the signal recording process, the standard electrode configuration was applied [9]. Fig. 4 presents the position of the electrodes on the abdomen surface during recording process. The recordings were collected from five healthy subjects (young women), who volunteered to participate in the study. Their average age was equal to 25.75 years (range: 24–31) and average BMI was 19.83 (range: 18.6–21.1). Every volunteer gave a written consent to participate in the study. The research project was approved by the Bioethics Committee of the Silesian Medical University. The time of the examination was from 120 to 180 min. Before the test, all participants fasted for about 12 h. During the EGG recording, the stomach was stimulated by 400 ml of cold water.

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8. Calculate the mean of the V multidimensional space of envelopes. 1 ev (t). V V

m(t) =

(1)

v=1

Fig. 4. The position of the standard electrodes (A1, A2, A3, A4) for the 4-channel EGG recording [23].

2.2. Empirical mode decomposition Empirical mode decomposition (EMD) was introduced by Dr. Norden Huang in the mid 90s as an effective tool for the adaptive local time-frequency decomposition of the time series signal into the intrinsic mode functions (IMFs) [24,25]. The IMFs capture some physical attributes of non-linear and non-stationary signals, and therefore, EMD has been successfully used for processing, and analyzing biomedical signals [25–28]. However, the standard EMD has certain drawbacks, for example, sensitivity to noise, mode-mixing [29], and aliasing problems when the cubic splines are fitted at the extreme points [30,31]. To avoid these and other limitations, many improvements of the classical EMD have been proposed and the new algorithms have appeared, for instance, the Ensemble Empirical Mode Decomposition (EEMD). The EEMD method involves adding white Gaussian noise (WGN) to the original signal [29]. Some changes were also suggested in the operation of EMD for analyzing multichannel signals [32]. These ideas have resulted in a novel algorithm called Multivariate Empirical Mode Decomposition (MEMD), which is widely described in the literature [32–34]. In this study, the latest version of the MEMD algorithm (i.e., NA-MEMD) was used to obtain the reference signal from the multichannel EGG. This method involves creating additional channels (one or more) containing different amounts of white Gaussian noise, adding them as the independent signals to the existing signal (one or multichannel) and then performing the MEMD algorithm [31,35,36]. NA-MEDM can be used in the processing of both univariate or multivariate signals [36]. Quoting [31,36], the short description of the NA-MEMD algorithm is presented below:

9. Extract the detail d(t) = x(t) − m(t). 10. Check the stopping criterion for multivariate IMF. If d(t) satisfies the criteria to stop it, use this procedure for the x(t) − d(t), else use the d(t). 11. Remove components corresponding to noise from the obtained results; leave only IMFs corresponding to the original ndimensional input signal. As a result of processing the EGG by means of NA-MEMD, the multichannel EGG is transformed into a set of IMFs. In general, the interpretation of a individual IMF component is a quite serious problem. Since the aim was to extract the component related to the slow wave, the physical properties of this wave are known (i.e., the typical range of frequencies); thus, in order to choose an “appropriate” IMF, a frequency criterion is proposed in this paper. This criterion is based on the calculation the instantaneous normogastria index (INI) for each obtained IMF [23]. The INI parameter denotes the ratio of the number of instantaneous frequency components with the frequency between 2.4 and 3.6 cpm (0.04–0.06 Hz) to the all number of the instantaneous frequencies of the processed IMF. The values of instantaneous frequencies were calculated by means of the Hilbert–Huang transform (HHT) [25]. The “appropriate” IMF is that of the highest value of INI, and it is used as the reference signal for the further adaptive filtering. In our study, NAMEMD was used with the one extra channel with the uncorrelated white Gaussian noise. 2.3. Independent component analysis According to the literature [14,37–39], Independent Component Analysis (ICA) presents good performance in solving the problems concerning so-called the blind source separation. In this study, the ICA algorithm has been performed to extract the reference signal from the four channels of the EGG data for adaptive filtering. From a biological point of view, the EGG is a mixture of electrical activity of the stomach, signals originating in the neighbouring organs (e.g., duodenum, lung, and small intestine), and random noise. Because the components of EGG signals are generated by the different sources, they can be acknowledged to be statistically independent. In addition, the ICA method assumes that the source signals considered as the random variables are nongaussian distributed. Assume that the n EGG signals:

 

1. Verify if the input signal satisfies the criteria of an IMF if it does not, go to the next step, else finish the algorithm. 2. Add an extra k-channel (k ≥ 1) with uncorrelated white Gaussian noise. 3. Add it to the n-dimensional input signal (n ≥ 1) in order to obtain the new (n + k) dimensional input signal. 4. Create V-point Hammersley sequence that will be used for uniformly sampling a (n − 1) dimensional sphere. 5. Calculate the projections qv (t) of the signal x(t) along all directions of the vector dv for v = 1, . . ., V, this will allow to obtain a set of projections {qv (t)}Vv=1 . V

6. Find the time instants {ti v }v=1 corresponding to the maxima of

V the set of projected signals  {qv (t)}v=1 . 7. Perform interpolation ti v , x(ti v ) to obtain the multivariate

signal envelope {ev (t)}Vv=1 .

X1 (t), X2 (t), X3 (t), . . ., Xn (t) ∧ n ∈ N+ \ 1

obtained by the multichannel electrogastrography, are linear combination of the n unknown mutually, statistically, independent source components: S1 (t), S2 (t), S3 (t), . . ., Sn (t), that is, the signal of electrical activity of the stomach (S1 (t)), the signals of the other adjacent organs and the random noise (S2 (t), . . ., Sn (t)). The multichannel EGG data can be expressed by the vector X:



X = [X1 (t), . . ., Xn (t)]T S = [S1 (t), . . ., Sn (t)]T

⇒ X = A · S,

where A is the unknown non-singular mixing matrix. Owing to the fact that there is no information about matrix A, the task of

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. . ., T − N + 1, T is the length of EGGk and N denotes the order of the adaptive filter. Let the vector Zj = [zj (1), zj (2), . . ., zj (N)] be the discrete cosine transform of the vector Fj (i.e., DCT(Fj ) = Zj ). If the vector Wj = [wj (1), wj (2), . . ., wj (N)] is the vector of the filter weights then, the output of the adaptive filter yj takes the form: yj = Zj · WjT .

(2)

The filter weights fulfill the following formula: wj+1 (n) = wj (n) +

Fig. 5. The block diagram of the noising process of EGG source signal.

the ICA method is to find the estimator E of the matrix A−1 that gives it good approximation. As a consequence, the independent components, that is, the source signals Si for i = 1, 2, . . ., n, can be calculated according to the formula S = E · X. The key for finding a good approximation of the A−1 matrix by using the ICA algorithm is to assume that each source signal Si has a nongaussian distribution. The main idea of the ICA method could be written ICA = contrast function + optimization algorithm. The contrast function is a quantitative measure of the nongaussianity of the random variables Si (i.e., source signals). For instance, kurtosis (the fourth-order cumulant) could be the contrast function as the classical measure of the nongaussianity. However, kurtosis has some drawbacks; thus, the negentropy was applied in the ICA used in this paper [38,39]. According to the Central Limit Theorem, under certain conditions the distribution of a sum of independent random variables tends towards to the Gaussian distribution [39]. If we take into consideration the arbitrary row vector e¯ of the matrix E, which is good approximation of the relative row vector of the unknown matrix A−1 , then the vector e¯ is that particular one which maximizes the nongaussianity distribution of the sum y = bT X. Vector b is the unknown row of the matrix A−1 that should be determined. If b = e¯ then y = Si , that is, the ith source signal (i.e., the independent component). The details of the ICA algorithm are widely presented in the literature [37–41]. In this study, the Matlab implementation of the FastICA algorithm with the negentropy as the contrast function, ¨ proposed by Hyvarinen and Oja [39], has been successfully applied to analyze the EGG data. 2.4. Adaptive filtering in the cosine transform The adaptive attenuation of noise in the each of the four channels of the EGG recording was performed in the discrete cosine transform (DCT) domain by using the filter proposed by Liang [17]. The reference signal for the adaptive filter was derived by means of the ICA algorithm applied to the 4-channel EGG data. Assume that the coordinates of the vector D = EGGk = [d1 , d2 , . . ., dT ] denotes the values of T samples of the recorded EGG signal from the channel number k, of the multichannel EGG. The filter weights are updated consistent with the least mean square (LMS) algorithm [13,42]. If T −N 2 1 the mean square error T −N e , (ej = dj − yj ) between the filter j=1 j output (yj ) and the primary input (dj ) reaches the minimum, then the output signal Y = [y1 , y2 , . . ., yT−N ] is the best, in the terms of the least square error, estimate of the primary input signal D = EGGk . N is the number of filter weights, that is, the order of the adaptive filter. Let the vector Fj = [fj , fj+1 , . . ., fj+N−1 ] be the reference signal obtained by the ICA or the NA-MEMD algorithms where j = 1, 2,



1 N

ej (n)zj (n), N zj (n) 2

(3)

n=1

where wj (n) is the nth filter weight for the j-moment (j = 1, . . ., N − 1), and  is the coefficient controlling the convergence rate [17,18]. In this study the value of the order of the adaptive filter (N) and the value of the coefficient controlling convergence rate () were experimentally set to N = 45 and  = 0.00375. The slow convergence is a drawback of the adaptive filtering performed in the time domain by using the LMS algorithm. The rate of convergence of  this method depends on the ratio  min , where min and max are the max smallest and the largest eigenvalue of the autocorrelation matrix of the input signal. Because the orthogonal transformation of the input signal decreases the range of the eigenvalues of the autocorrelation matrix, it simultaneously speeds up the convergence of the method [43]. For this reason, in this study the discrete cosine transform (DCT) was applied as the orthogonal transformation of the input signal [17,18,43]. 2.5. Validation method In order to validate the novel noise reduction technique dedicated to the multichannel EGG, the following two steps were performed. First, the influence of the adaptive filter on the basic diagnostic parameters calculated from the EGG signal, such as the dominant frequency [3,5,9], the normogastric rhythm index, the frequency instability coefficient (FIC), and the power instability coefficient (PIC) [5,9] were examined. Secondly, the effectiveness of the attenuation of the disturbance noise by the proposed method was verified. 2.5.1. Diagnostic parameters Below, the method of the basic diagnostic parameter calculations (connected with EGG examination), used in the validation process, is briefly presented. According to the conventional method of EGG processing, the analysis was carried out for the 30-minute fragments of the human EGG for both the preprandial and the postprandial parts. The each 30-minute fragment of the EGG examination was divided into to 3minute (long) segments and next, the power spectrum density, the dominant power, and the dominant frequency were calculated for each segment. On the bases of these parameters, the specific coefficients for the EGG signal, that is, the normogastric rhythm index (NI), frequency instability coefficient (FIC), and power instability coefficient (PIC) were calculated. The frequency instability coefficient (FIC) is defined by the formula (4) [9]:

 N 1

FIC =

N

k=1

(DF(k) − DF Avg )

DF AvgNormo

2

,

(4)

where N is the number of segments (in our case 3 min long) in the analyzed fragment (30-minute), DF(k) is the dominant fre-

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Fig. 6. In the first column, there is an example of source, 4-channel EGG signal (red), and 4-channel EGG with added noise (EGGn) (SNR = 0 dB) (blue). In the next two columns, there are spectra for the source EGG (second column) and for EGGn (third column). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

quency for the kth segment, and DFAvgNormo is the average dominant frequency for all segments classified as the normal rhythm. PIC coefficient is defined in an analogous manner (i.e., DF is change to DP in the Eq. (4)). 2.5.2. Signals used in the study For validation process, suitable test signals based on the real, human EGGs, were prepared in the following way. First, the real EGG signals were filtered by the 4th order bandpass Butterworth filter in the frequency range of 0.5–30 cpm (0.008–0.5 Hz). Next, the EGG signal from each channel was standardized by dividing each sample by the standard deviations (Std) of that channel. Assuming that the source EGG is pure, without inferences, the synthetic noise was added to each channel of the 4-channel source EGG in such a way that the signal to noise ratio (SNR) for the signal from each channel  was the sameand equal to one of the following values of SNR ∈ 0, 3, 6, 10, 20 dB. Consequently, for one source 4-channel EGG data we obtain five, 4-channel EGG signals with added noise, each of which are denoted EGGn (EGGn = EGG + noise) in further analysis. Following the literature [44,45], the SNR parameter can be defined as the ratio of the power of the desired signal (e.g., EGG) to that of the noise, and can be expressed by the formula (5):

 SNR = 10log10

L 2 (EGGs (k)) k=1 L 2 (Ns (k)) k=1



,

(5)

where L is the number of samples of the analyzed signal, EGGs (k) and Ns (k) are the kth sample of EGG signal and noise respectively. The synthetic noise added to the source EGG is the sum of three noisy sinusoidal signals and three WGN signals. The frequencies f1 , f2 , and f3 of the sinusoidal signals were randomly chosen from the ranges of the potential interferences for example, signal from distal ileum and jejunum (8–10 cpm), colon and duodenum (11–13 cpm) [19], and respiration (15–25 cpm) [10]. The amplitudes A1 , A2 , and A3 of sinusoidal signals, are random values but compatible with the mean amplitude of the real EGG data. The block diagram of test EGGn signals construction is shown in Fig. 5 An example of source, 4-channel EGG signal and 4-channel EGG with added noise and their spectra are shown in Fig. 6. 2.5.3. Attenuation assessment The following procedure was applied to validate the noise attenuation: both recorded EGG signals and those with the added noise, were divided into fragments of 720 samples (3 min), and the power spectrum for each fragment of the signal was calculated by using the periodogram method with Tukey’s window (˛ = 0.25). On the basis of received spectra, the averaged spectrum was determined (approximately that method corresponds to the calculation of the overall spectrum for the standard EGG analysis) [9]. The process was repeated for signals that have undergone adaptive filtering. Next, the surfaces below the spectra were calculated in normogastric 2.4–3.6 cpm, bradygastric (0.5–2.4) cpm, and tachygastric (3.6–9.0 cpm frequency ranges. The calculations were performed

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Fig. 7. The graphical illustration of the calculation of the PDR. PBrady (green), PNormo (blue), PTachy (gray) correspond to the power in the bradygastric, normogastric and tachygastric range, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 8. The graphical illustration of SNR calculation for real, human EGG signal by the standard snr(x,fs) Matlab function. Fundamental (blue), noise (green), excluded harmonics (black). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

for the following 4-channel signals: the source EGG, EGGn, EGGn after bandpass filtering (0.5–9.0 cpm), and EGGn after adaptive filtering. Lastly, the power distribution ratio (PDR) was calculated for the signal from each channel separately by formula (6):

PDR = 10log10

PNormo PBrady + PTachy



,

(6)

where PNormo , PBrady and PTachy correspond to the power in the normogastric, bradygastric and the tachygastric ranges, respectively. The PNormo , PBrady and PTachy can be expressed by formulas (7)–(9): PBrady =

LB 

P(k),

(7)

k=FB

PNormo =

LN 

P(k),

(8)

k=FN

PTachy =

LT 

P(k),

(9)

k=FT

where P(k) is the kth sample of power spectrum, the FB and LB are the numbers of the first and the last samples in the bradygastry range, the FN and LN are the numbers of the first and the last samples in the normogastry range, the FT and LT are the numbers of the first and the last samples in the tachygastry range. Fig. 7 shows the graphical interpretation of PBrady , PNormo , and PTachy . In addition, for the all analyzed signals the SNR was computed by the standard snr(x,fs) Matlab function. In that case, the standard snr(x, fs) function returns the SNR value in dBc (decibels relative to the carrier) of a real sinusoidal input signal x, sampled at a rate fs. This SNR calculation excludes the power contained in the lowest six harmonics, including the fundamental [46]. The illustration of snr() calculation is presented in Fig. 8. 3. Results This section presents the results of the noise reduction in the EGG signal obtained by the proposed method. In order to assess the performance of adaptive filtering with the reference signal obtained by the NA-MEMD algorithm, the results were compared to the outcomes of two other methods: the bandpass filter (commonly used method), and the adaptive filter with the reference signal received by ICA. As the combination of adaptive filtering and ICA algorithm has already been depicted in the literature [17,39], so it was chosen as the good reference method to that suggested in this study.

Fig. 9. An example of EGG signals’ spectra: spectrum of source EGG (Sig. 5) (blue), EGGn (SNR = 3 dB) (cyan), after bandpass filtering (EGGnBF – black), after adaptive filtering with reference signal obtained by NA-MEDM (EGGnAF(IMF) – red) and after adaptive filtering with reference signal obtained by ICA (EGGnAF(ICA) – green). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The 4-channel EGG data (Sig.1,...,Sig.5) from five healthy subjects (all women) were taken into consideration. Spectra of the processed EGG signals: source EGG, EGG with added noise (EGGn), EGGn after bandpass filtering EGGnBF , EGGn after adaptive filtering with reference signal obtained by NA-MEDM EGGnAF(IMF) and EGGn after adaptive filtering with reference signal obtained by ICA EGGnAF(ICA) are shown in Fig. 9. 3.1. Reference signals Fig. 10 illustrate an example of NA-MEMD decomposition (on IMFs functions) of arbitrarily chosen channels of the 4-channel EGG. Fig. 11 presents an example of four reference signals for adaptive filtering of the 4-channel EGG chosen from the NA-MEMD decomposition for each channel part. Their power spectra are shown in Fig. 12. 3.2. The influence of the adaptive filtering on the diagnostic parameters of EGG To verify the impact of the investigated method on the basic diagnostic parameters of EGG, the values of the NI, FIC and PIC coefficients were determined. The calculations were performed for

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Fig. 10. NA-MEDM decomposition on IMF functions of EGGn (SNR = 3 dB), from arbitrarily chosen channels, in this case A1. INI – instantaneous normogastry index, IBI – instantaneous bradygastry index, ITI – instantaneous tachygastry index.

Fig. 11. An example of IMFs function obtained by NA-MEMD, used as the reference signals for the adaptive filtering of the 4-channel EGG.

Fig. 12. The power spectra of the reference signals (IMFs) from Fig. 11 for the each channel (A1, A2, A3, A4) of EGG data.

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Fig. 14. The box plot with: the mean (Mean) (red), minimum (Min), maximum (Max), and standard deviation (Std) of normogastria index (NI) calculated for (five, 4channel, i.e., 20 time series): source EGG signals, and these with added noise (EGGn) (SNR = 6 dB), EGGn after bandpass filtering (EGGnBF ), EGGn after adaptive filtering with reference signal obtained by NA-MEDM (EGGnAF(IMF) ) and adaptive filtering with reference signal obtained by ICA (EGGAF(ICA) ).

Fig. 13. Example of the values of NI coefficients for source EGG signal (Sig.5 (SNR = –dB),  channel: A1,  A2, A3, A4), and these with added synthetic noise (EGGn) (SNR ∈

0, 3, 6, 10, 20

dB). The blue bars denote results for the EGGn, cyan for

EGGnBF , yellow and brown bars represent the values for EGGAF(IMF) and EGGAF(ICA) signals, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

20 human EGG recordings (five, 4-channel examinations) and 100 recordings with added synthetic noise (EGGn) (five, 4-channel EGG with five levels of noise determined by the SNR coefficient). The diagnostic parameters were computed for all analyzed signals (EGG, EGGn, EGGnBF , EGGnAF(IMF) , EGGnAF(ICA) ). The minimum, maximum, mean, and standard deviation values of the normogastria index (NI) for the pure EGG signals, noisy EGG, and these after processing by the proposed method (Fig. 2), the reference method (Fig. 3), and traditional bandpass filtering are summarized in Table 1. Fig. 13 shows the bar graphs of calculated NI values for the analyzed 4-channel, source EGG recording (Sig.5, (denoted in the figure by SNR  =−)), and those with the added noise SNR ∈  0, 3, 6, 10, 20 dB. The blue bars (for each value of SNR) denote the results obtained for the source EGG signal (Sig.5) with added noise (EGGn), the cyan for EGGnBF , while yellow and brown bars represent the values of EGGn after the adaptive filtering with the reference signal obtained by NA-MEMD (EGGnAF(IMF) ) and ICA (EGGnAF(ICA) ) respectively. Figs. 14–16, present the examples of mean (Mean), minimum (Min), maximum (Max), and standard deviation (Std) of NI, FIC, and PIC parameters for all types of investigated signals, that is: EGG, EGGn, EGGnBF , EGGnAF(IMF) , EGGnAF(ICA) in the form of box plot graph. In these charts the mean value is marked in red. The influence of the proposed method on the value of basic diagnostic parameters in reference to the parameters obtained by the validation methods, that is, bandpass filtering and adaptive filtering with ICA, are contained in the Tables 2 and 3, respectively. The outcomes were classified into three groups: improved, unchanged, and weakened. SNR, PDR and NI were improved if the results were a higher value than those obtained by the reference method (the higher the better), whereas for FIC and PIC parameters lower values than the reference were recognized as improved results (the lower

Fig. 15. The box plot with marked Mean (red), Min, Max, Std of FIC calculated for (five, 4-channel, i.e., 20 time series): source EGG, EGGn (SNR = 10 dB), EGGnBF , EGGnAF(IMF) , EGGAF(ICA) .

Fig. 16. The box plot with marked Mean (red), Min, Max, Std of PIC calculated for (five, 4-channel, i.e., 20 time series): source EGG, EGGn (SNR = 10 dB), EGGnBF , EGGnAF(IMF) , EGGAF(ICA) .

the better). The graphical illustrations of these relations are shown in the Figs. 17 and 18. 3.3. The efficiency of the proposed denoising process To evaluate the efficiency of the presented filtering method in attenuating the noise in the 4-channel EGG, the PDR defined in Section 2.5 Method Validation and SNR were used. For all tested signals processed by each of examined method, the Mean, Min, Max, and Std values of PDR and SNR coefficients were calculated (the larger mean value, the better). The resulting PDR and SNR are summarized in Tables 4 and 5.

D. Komorowski, B. Mika / Biomedical Signal Processing and Control 45 (2018) 213–224 Table 1 Normogastric rhythm index (NI) values of all analyzed 4-channel EGG signals, and those with added noise (EGGn) (SNR ∈



221



0, 3, 6, 10, 20

dB), processed by each examined

method: without filtering (EGGn), bandpass filtering (EGGnBF ), adaptive filtering with the reference signal obtained by both NA-MEMD (EGGnAF(IMF) ) and ICA (EGGnAF(ICA) ) algorithm. Normogastric rhythm index (NI) (%) Added noise SNR (dB)

EGGn Mean ± Std (%) [Min Max] (%)

EGGnBF Mean ± Std (%) [Min Max] (%)

EGGnAF(IMF) Mean ± Std (%) [Min Max] (%)

EGGnAF(ICA) Mean ± Std (%) [Min Max] (%)

0

45.56 ± 6.28 [11.11 77.78] 52.78 ± 4.80 [22.22 77.78] 52.22 ± 7.16 [22.22 88.89] 53.89 ± 7.55 [11.11 88.89] 56.67 ± 6.77 [22.22 88.89] 55.56 ± 7.98 [22.22 88.89]

52.22 ± 5.35 [22.22 77.78] 53.33 ± 6.92 [22.22 88.89] 55.00 ± 5.25 [22.22 88.89] 56.67 ± 9.79 [22.22 88.89] 57.22 ± 11.67 [22.22 88.89] 57.22 ± 11.67 [22.22 88.89]

56.67 ± 7.64 [22.22 77.78] 65.00 ± 3.44 [33.33 88.89] 67.22 ± 5.78 [44.44 88.89] 63.89 ± 8.25 [33.33 88.89] 71.67 ± 8.71 [33.33 88.89] 68.33 ± 5.86 [44.44 88.89]

60.00 ± 4.92 [33.33 77.78] 62.78 ± 6.60 [22.22 88.89] 59.44 ± 3.26 [11.11 88.89] 62.22 ± 6.77 [33.33 88.89] 62.22 ± 7.04 [11.11 88.89] 63.33 ± 8.01 [33.33 88.89]

3 6 10 20 –

Legend: Mean–mean value; Min–minimum value; Max– maximum value; Std–standard deviation. SNR = – the source (original) EGG signal without added synthetic noise.

Table 2 The influence of proposed method on examined parameters: SNR, PDR, NI, FIC, PIC (for all, i.e., 120 time series) in the relation to EGGnBF . Percentage of Add. SNR (dB)

0 3 6 10 20 –

Improved results

Unchanged results

Weakened results

SNR

PDR

NI

FIC

PIC

SNR

PDR

NI

FIC

PIC

SNR

PDR

NI

FIC

PIC

40 40 25 40 45 45

85 85 75 80 60 70

40 50 70 55 75 50

65 40 35 55 65 45

40 40 30 25 60 50

40 35 35 30 30 40

15 15 25 20 40 30

40 45 30 40 25 40

20 40 35 40 25 30

0 0 0 0 0 0

20 25 40 30 25 15

0 0 0 0 0 0

20 5 0 5 0 10

10 0 10 5 15 5

40 20 35 35 15 20

Add. SNR – means the EGG signals with added synthetic noise (SNR ∈





0, 3, 6, 10, 20

dB).

SNR (signal-to-noise ratio) = – the source EGG signal without added synthetic noise. PDR – power distribution ratio. FIC – frequency instability coefficient. PIC – power instability coefficient. NI – normogastry index. Improved results – SNR, PDR, NI (the higher the better); FIC, PIC (the lower the better).

Table 3 The influence of proposed method on examined parameters: SNR, PDR, NI, FIC, PIC (for all, i.e., 120 time series) in the relation to EGGnAF(ICA) . Percentage of Add. SNR (dB)

0 3 6 10 20 –

Improved Results

Unchanged Results

Weakened Results

SNR

PDR

NI

FIC

PIC

SNR

PDR

NI

FIC

PIC

SNR

PDR

NI

FIC

PIC

85 75 70 75 60 75

35 40 55 60 65 65

20 45 55 50 55 45

65 40 55 55 65 55

40 50 45 45 65 60

15 15 15 5 30 15

65 50 35 40 35 35

40 20 25 30 30 40

15 20 10 20 15 15

0 0 0 0 0 0

0 10 15 20 10 10

0 10 10 0 0 0

40 35 20 20 15 15

15 15 15 5 15 20

45 30 45 35 20 25

Add. SNR – For the EGG signals with added synthetic noise (SNR ∈





0, 3, 6, 10, 20

dB).

SNR (signal-to-noise ratio) = – the source EGG signal without added synthetic noise. PDR – power distribution ratio. FIC – frequency instability coefficient. PIC – power instability coefficient. NI – normogastry index. Improved results – SNR, PDR, NI (the higher the better); FIC, PIC (the lower the better).

Figs. 19 and 20 show an examples of the box plot graphs of the calculated PDR and SNR values (the larger mean value, the better) respectively, for the twenty EGG time series (5 signals × 4 channels) with added synthetic noise (SNR = 6 dB) processed by all considered methods. Tables 4 and 5 contain the Mean, Min, Max and Std values of the computed DPR and SNR (the larger mean value, the better)

for all analyzed, 4-channel EGG signals (EGGn, EGGnBF , EGGnAF(IMF) , EGGnAF(ICA) ). 3.4. Discussion The percentage changes in value for tested parameters, that is, SNR, DPR, NI, FIC, and PIC (for five, 4-channel EGG, and those with

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Fig. 17. The influence of the proposed method on examined parameters: SNR, PDR, NI, FIC, PIC (for all, i.e., 120 time series), yellow-SNR, brown-PDR, blue-NI, cyan-FIC, green-PIC in the relation to EGGnBF . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 18. The influence of the proposed method on examined parameters: SNR, PDR, NI, FIC, PIC (for all, i.e., 120 time series), yellow-SNR, brown-PDR, blue-NI, cyan-FIC, green-PIC in the relation to EGGnAF(ICA) . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 4 PDR values of all analyzed 4-channel EGG signals, and those with added noise (EGGn) (SNR ∈





0, 3, 6, 10, 20

dB), processed by each examined method: without filtering

(EGGn), bandpass filtering (EGGnBF ), adaptive filtering with the reference signal obtained by NA-MEMD (EGGnAF(IMF) ) and ICA (EGGnAF(ICA) ). PDR(dB) Added noise SNR (dB)

EGGn Mean ± Std (dB) [Min Max] (dB)

EGGnBF Mean ± Std (dB) [Min Max] (dB)

EGGnAF(IMFF) Mean ± Std (dB) [Min Max] (dB)

EGGnAF(ICA) Mean ± Std (dB) [Min Max] (dB)

0

−5.05 ± 0.20 [−6.05 −4.01]

−4.69 ± 0.24 [−5.68 −3.55]

−4.13 ± 0.25 [−4.93 −2.84]

−4.48 ± 0.10 [−5.19 −3.58]

3

−4.64 ± 0.24 [−5.81 −3.67]

−4.27 ± 0.26 [−5.61 −3.30]

−3.72 ± 0.25 [−5.11 −2.73]

−3.94 ± 0.22 [−5.29 −2.74]

6

−4.36 ± 0.23 [−5.54 −3.39]

−4.02 ± 0.27 [−5.26 −2.89]

−3.48 ± 0.29 [−4.50 −2.37]

−3.96 ± 0.18 [−5.99 −2.47]

10

−4.09 ± 0.34 [−5.36 −2.91]

−3.75 ± 0.40 [−5.09 −2.61]

−3.26 ± 0.34 [−4.55 −2.18]

−3.78 ± 0.43 [−5.44 −2.35]

20

−3.91 ± 0.36 [−5.34 −2.68]

−3.58 ± 0.40 [−5.08 −2.42]

−3.08 ± 0.34 [−4.37 −1.91]

−3.60 ± 0.30 [−5.31 −2.33]

–

−3.84 ± 0.35 [−5.22 −2.65]

−3.52 ± 0.39 [−4.78 −2.40]

−2.98 ± 0.24 [−4.32 −1.78]

−3.57 ± 0.36 [−5.40 −2.34]

Legend: Mean – mean value; Min – minimum value; Max – maximum value; Std – standard deviation. SNR = – the source (original) EGG signal without added synthetic noise.





added synthetic noise SNR ∈ 0, 3, 6, 10, 20 dB, i.e., 120 time series), processed by the proposed method, are summarized in the Tables 2 and 3. The percentage change in value was calculated with the respect to the SNR, PDR, NI, FIC, and PIC parameters computed for the EGG signals processed by the validation methods. The possible relationship between the computed parameters, that is, improvement of said parameters, the lack of change, and the weakness of these parameters (Tables 2 and 3) were taken into consideration. In most cases, for all the considered signals, an increase in SNR and PDR values are observed (Figs. 17 and 18-improved). For EGGn signals processed by the classical method (bandpass filtering), the mean value of NI decreases while the dispersion increases and dif-

fers from the results obtained for source EGG signals. After using the proposed method, the mean value of NI increases and the dispersion decreases. Furthermore, NI becomes closer and even exceeds the NI value of the source EGG. The increase of NI parameter can be caused by the noise attenuation from the proposed method. The graphical illustration of this phenomenon can be easily noticed in Fig. 14. The values of NI established in the validation process are consistence with the typical human physiological value, that is, about 70% for healthy subjects [3,10]. Because the signals were recorded for healthy volunteers, it can be accepted that the improvement and lack of change of the NI coefficient was achieved in almost 85–90% of cases for source EGG (Table 2) compared to validation methods.

D. Komorowski, B. Mika / Biomedical Signal Processing and Control 45 (2018) 213–224 Table 5 SNR values of all analyzed 4-channel EGG signals, and those with added noise (EGGn) (SNR ∈





0, 3, 6, 10, 20

223

dB), processed by each examined method: without filtering

(EGGn), bandpass filtering (EGGnBF ), adaptive filtering with the reference signal obtained by NA-MEMD (EGGnAF(IMF) ) and ICA (EGGnAF(ICA) ). SNR(dBc) Added noise SNR (dB)

EGGn Mean ± Std (dBc) [Min Max] (dBc)

EGGnBF Mean ± Std (dBc) [Min Max] (dBc)

EGGnAF(IMFF) Mean ± Std (dBc) [Min Max] (dBc)

EGGnAF(ICA) Mean ± Std (dBc) [Min Max] (dBc)

0

−9.99 ± 0.35 [−12.84 −6.81]

−6.38 ± 0.45 [−10.21 −2.32]

−6.31 ± 0.54 [−9.72 −2.07]

−9.53 ± 0.90 [−13.41 −4.23]

3

−8.70 ± 1.03 [−14.85 −4.67]

−5.69 ± 0.58 [−9.07 −1.21]

−5.82 ± 1.14 [−9.18 −0.81]

−7.70 ± 0.89 [−12.99 −3.57]

6

−7.69 ± 0.66 [−11.19 −3.33]

−5.43 ± 0.95 [−9.72 −0.68]

−5.79 ± 1.22 [−11.09 −0.31]

−6.84 ± 0.84 [−12.17 −0.95]

10

−6.61 ± 1.05 [−10.07 −1.87]

−4.90 ± 1.46 [−9.41 1.64]

−4.79 ± 1.02 [−9.37 2.13]

−6.24 ± 1.37 [−10.96 −1.80]

20

−5.77 ± 0.96 [−9.87 0.11]

−4.68 ± 1.49 [−9.49 2.51]

−4.55 ± 1.66 [−9.74 3.97]

−5.30 ± 1.20 [−10.96 0.29]

–

−5.63 ± 1.02 [−9.79 0.70]

−4.60 ± 1.50 [−9.44 2.91]

−4.02 ± 0.91 [−8.90 2.99]

−5.52 ± 1.46 [−12.01 0.57]

Legend: Mean – mean value; Min – minimum value; Max – maximum value; Std – standard deviation. SNR = – The source (original) EGG signal without added synthetic noise.

Fig. 9 shows an example spectra of the 4-channel EGG signal processed by proposed and validation methods. The cyan curve is the power spectrum of EGGn (SNR = 3 dB) and the red curve is that of the proposed adaptive noise cancellation output (EGGnAF(IMF) ). Comparing those two spectra (for each channel), it can be clearly noticed, that the respiratory components (around 0.27 Hz) and the unknown artifacts (near 0.009 Hz) are significantly attenuated, whereas the gastric component (around 0.05 Hz (3 cpm)) left not affected. It is especially clearly visible in the channel A4.

4. Conclusions Fig. 19. The box plot with marked Mean (red), Min, Max, Std of PDR calculated for (five, 4-channel, i.e., 20 time series): source EGG, EGGn (SNR = 6 dB), EGGnBF , EGGnAF(IMF) , EGGAF(ICA) . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 20. The box plot with marked Mean (red), Min, Max, Std of SNR calculated for (five, 4-channel, i.e., 20 time series): source EGG, EGGn (SNR = 6 dB), EGGnBF , EGGnAF(IMF) , EGGAF(ICA) . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

FIC coefficient values are also decreased (decreased FIC means more stable dominant frequency) in the relation to the values computed for signals processed by validation methods. In Fig. 15, it is clearly stated that the mean value of FIC increased for EGG signals with added noise, but decreases for the signals processed by the proposed method. After our method application, the mean FIC value almost returned to the value of source EGG signals. The PIC coefficient behaves in the similar manner (Fig. 16).

The presented results confirm the relatively high potential of the proposed method for denoising non-stationary and non-linear 4channel EGG data. After the series of experiments (for both human EGG signals and those with added noise), by using the suggested method, it was found that the proposed algorithm is suitable for EGG signals processing. The obtained results are promising for both purposes, that is, removing the noise and improving the values of the standard EGG parameters. Since the proposed algorithm successfully reduces the noise in the recovered signals, it could be a useful tool for extracting more accurate information from the propagation of the slow wave. It seems to be important for the diagnosis of stomach diseases [7]. However, the obtained outcomes need to be compared with the other results of healthy patients and those who suffer from stomach disorders. In the future, it would be advisable to compare the results of the analysis of EGG by means of the combination of adaptive filtering and the NA-MEMD method with the results of the digestive diseases clinical research.

Acknowledgements The authors would like to thank Andre Woloshuk for his English language corrections. ´ The authors wish to acknowledge Dr. B. Krusiec-Swidergoł and Prof. K. Jonderko from Department of Basic Biomedical Science, School of Pharmacy, Medical University of Silesia, Sosnowiec, who helped us with the EGG data acquisition in their laboratory. Also, the authors wish to acknowledge Dr. S. Pietraszek who helped us with the design the EGG amplifier.

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