Decomposition 3.1 Introduction

Transcription

1 Chapter 3 ECG analysis using Empirical Mode Decomposition 3.1 Introduction Feature extraction is the basic operation in almost all classification and analysis module as indicated in the earlier chapters. Considering the non-predictive nature of ECG morphology, it can be said that no predefined basis function based analysis can perform well in all kinds of ECG signals. This leads to the demand of a typical method which does not require any pre-choice of decomposing function and the transformation will be done as per the morphology of test signal, or in other words, a data-driven approach can serve better in almost all kinds of ECG signals. Empirical Mode Decomposition (EMD) is a general nonlinear, non-stationary signal processing method which was initially proposed for the study of ocean waves [104], and found immediate applications in biomedical engineering [105]-[106]. The major advantage of EMD is that the basis functions are derived directly from the signal itself. Hence, the analysis is adaptive, in contrast to Fourier analysis, where the basis functions are linear combinations of fixed sinusoids. A non-stationary signal like ECG is better analyzed by a time-frequency based approach like EMD. In this chapter the application of EMD is described for ECG enhancement and feature extraction. 3.2 Introduction to Empirical Mode Decomposition Empirical Mode Decomposition is a relatively new data analysis method which decomposes a multi frequency complex signal into a set of functions (IMF) with gradually decreasing frequencies. The 51

2 decomposition is based on the extraction of the energies associated with various intrinsic time scales. Thus it is basically a technique for breaking down a signal without leaving the time domain information. The decomposition is based on the following assumptions: (i) The signal has at least two extrema- of which one is maximum and other is minimum; (ii) The characteristic time scale is defined by the time difference between the extremas; (iii) If the data does not contain extrema but has inflexion points, then it can be differentiated once or more times to enhance the extrema. Final results can be estimated by integrating the output Development of Empirical Mode Decomposition Technique According to the principle of EMD, it decomposes a signal into a sum of oscillatory functions called intrinsic mode functions (IMF). An IMF should satisfy the following two conditions: (i) In the total data set, the number of extrema and the number of zero crossings must be equal or may differ at most by one. (ii) At any point, the average of upper and lower envelop defined by the local maxima and local minima respectively must be zero. The steps of Empirical Mode Decomposition of any signal x(t) are as follows: 1. At first all the local maxima and minima of the given signal are identified. 2. Cubic spline interpolation is used to connect all the local maxima and thus upper envelope of the mother signal is constructed. 3. The procedure is repeated for the local minima to produce the lower envelope. 4. The mean wt, of upper and lower envelope is calculated and the difference cl] between the signal x(t) and flj, is computed as, i.e. x(t)-ml=dl(t) (3]) 5. If t/, (f) satisfies the conditions of IMF, then d] is the first frequency and amplitude modulated oscillatory mode of x(t). 52

3 6. If dx is not an IMF, then the shifting process described in steps (1), (2), (3) are repeated on dx. Thus dn is calculated as, dl-mll = du(t) (3.2) in which tnn is the mean of upper and low envelope value oidx. Figure 3.1 shows formation of upper and lov/er envelope along with their mean. "Test Signal Upper Envelop Mean (ml) ofenvelops Lower Envelop Figure 3.1: Formation of upper and lower envelop and the mean for a typical test signal 7. Let after k cycles of operation, dlk becomes an IMF, that is, dhk-i)-»hk =dlk((t) (3.3) 8. Then, it is designated as cx = dxk, the first IMF component from the original data. 9. Subtracting c, from x(t), rx is calculated as, ri - x(t) cx (3.4) which is treated as the original data for next cycle. 53

4 Figure 3.2 : Empirical Mode Decomposition of a composite signal 10. Repeating the above process for n times n no. of IMFs are obtained along w.th the final residue rn. The decomposition process can be stopped when r, becomes a monotonic function, from which no more IMF can be extracted. A popular stopping criteria is to have the value of normalized standard difference (NSD) within a predefined threshold [107] where 1 IU,. k= I By summing up, we finally obtain f2 * - (3.5) dim 54

5 N (3.6) Residue rn is the mean trend of x(t). The IMFs c,, c2,..cn represent the finally obtained amplitude and frequency modulated output set. Their frequency gradually decreases as the order of the IMFs increases. So it can be said that if a complex signal is formed by a number of component waves of different oscillation modes with variation in frequency, it is possible to identify the component waves by EMD based decomposition. Figure 3.2 represents a typical test signal x(t) and the corresponding IMFs along with the residue. The mother signal x(t) is the combination of a high frequency triangular waveform with increasing amplitude, a sine wave of linearly decreasing amplitude and a low frequency triangular wave of constant frequency. It is seen that all the mode of oscillations are visible after decomposition Properties of Empirical Mode Decomposition The discussion on theoretical development of the method of Empirical mode Decomposition remains incomplete unless its basic features are not known. In this section some of the important properties of EMD are discussed in brief. (a) Linearity: It is seen from the equation 3.6 that the representation of any signal x{t) based on IMF is linear. (b) Time-shift Property: As per equation 3.6, N (3.7) (c) Completeness: EMD generates the IMFs as an identity given in equation 3.6 which itself is a proof of completeness. Analytically it can be tested in the following way: It is seen that EMD decomposes the test signal into a set of IMFs of gradually decreasing frequency and time period. As a check of the completeness, the test signal can be reconstructed by the IMF components including the mean trend or residue. The difference between the reconstructed data and the original signal 55

6 is extremely small as indicated by the stopping criteria given in equation 3.5. Hence the completeness of decomposition is validated. (d) Orthogonality: As the decomposition process says, the IMF elements are all locally orthogonal to each other since each IMF is generated from the difference between the signal and its local mean through its upper and lower envelops. Therefore, (x(t)- x(t)).x(t) = 0 (3.8) Theoretically the orthogonality of EMD method is established by the above equation. But as the mean is calculated from the envelopes, it is not the true mean. Moreover, each successive IMF component is only part of the signal constituting x(t). For all these reasons equation (3.8) is not exactly true and a deviation is expected to appear which is very small in magnitude. Orthogonality of IMFs can also be verified numerically with practical data also [104], (e) Automatic removal of trend component: As discussed in the procedure of EMD, it does not require a mean or zero reference, rather, it is self-generated by the shifting process. Thus it only requires the location of the extrema. Without the need of the zero reference, EMD automatically eliminates the large DC term in data with nonzero mean. This property of EMD method can easily handle variance-stationary random processes [108]. (f) Adaptive generalized basis [109]: Hilbert Transform can be applied to each IMF components and an analytic signal can be achieved as, XcXt) = Aq{t) + jbcxt) or, XCi (t) = acj (t)ejnq (l)' where, ac (/) = +(Bq(t))2 (3-9) (3.10) dcac (t) and 2C is the instantaneous frequency given by, Qc =------:---- (3.H) 56

7 ,, Bq (t) where, 0)r (t) = tan (3.12) IMF component Cj(t) can be expressed as, C, (0 = Re[ac (0 exp(jr ^c (t)dt)] (3.13) in which Re represents the real part. Hence, finally express a signal in the following form, x(t) = Re[]Tflc. 0)exp(7 jhcj (t)dt)] ;=i (3.14) In this expression, the residue r is left as it is a monotonic function or a constant. Although the Hilbert transform can treat the monotonic trend as part of a longer oscillation, the energy involved in the residual trend could be overpowering. In consideration of the uncertainty of the longer trend, and in the interest of information contained in the other low-energy and higher-frequency components, the final non-imf component should be left out. It, however, could be included, if physical considerations justify its inclusion. Equation 3.14 gives the amplitude and frequency of each component as a function of time unlike Fourier transform which has the restriction of constant amplitude and frequency. Thus the basis function in EMD solely depends on the signal itself leading to its adaptive nature. (g) Filtering property: EMD decomposes multi-oscillatory time varying signals locally into a set of IMFs. From the properties of IMFs mentioned earlier, the average period of an IMF can be calculated from the number of local maxima in the IMF as, average _ period data length =_ * (3.15) number _of _ local _ max ima Repeated experiments indicate that the number of extrema of any IMF component is almost exactly the half of the previous IMF component, and its average period is the double of the previous IMF component. This feature doesn t change with the change of the data length. This indicates that the decomposition is a filtering process and EMD is a second order filter [110]. Theory and application of EMD as a second order filter bank is analyzed in [ 111]. 57

8 (h) Time domain scale filter property: Each IMF characterizes oscillation and frequency variable range of the signal at one characteristic time scale. By the shifting process, EMD generates IMF arrays from small scale to large scale. Depending on this feature, a time domain scale filtering can be developed. It is known that decomposition of a signal x(t) generates a set of N IMFs and a residue as, N *(0 = Xc»W+r«W (3-16) n=\ The low pass filtering of the signal x(t) can be represen:ed as, N Xlmv (0 = X ) + rn (0 Wher 1 < P ^ N (3-1'7) The high pass filtering of the signal x(/) can be represented as, %,/,(0 = Xc (/) + rn(0 where 1 ^r<n (3.18) n=! Band pass filtering of the signal x(t) can be represented as, r xbmd (0 = Xc«W + rn where 1 <q<r<n (3.19) Though conventionally filtering is done in frequency domain, time domain scale filtering doesn t need any frequency transform, and can be carried out in time domain through EMD. Therefore, this method needs less calculation and is easy to carry out and very efficient. All these features are of great importance for compact study of Empirical Mode Decomposition and its application in various engineering and non-engineering fields Application of Empirical Mode Decomposition This relatively new tool of signal decomposition finds its application in a number of fields as discussed below. 58

9 ECG analysis using Empirical Mode Decomposition chapter S Oceanography: EMD is a well proved tool for analysis of local properties of complicated ocean wave in detail as mentioned in [112]. The result is better than the other methods specially in the low frequency region. Geography: Signal decomposition and analysis based on EMD method is also used in case of seismic wave study. Seismic signals consist of several typically short energy bursts and thus it consists of several patterns having different dominant frequency, amplitude and polarization. Among all the waves, S wave or the secondary wave is one of the most significant waves as it arrives second in the earthquake seismogram. It allows seismologists to determine the nature of the inner core of earth through which the earthquake propagates. It is reported [113] that S wave detection is done better in EMD domain than other conventional techniques including wavelet. Medicine: Medical science is greatly influenced by the advancement of technology nowadays. It is of great importance to study and analyze different physiological signal trapped (invasive or noninvasive) from different organs for detection of diseases. Almost all biological signals are subjected to various types of noises. As almost all biological signals are non-stationary, it is expected that Empirical Mode decomposition based method can perform well for signal enhancement and feature extraction. For example, it is reported [114] that automatic techniques can be developed for the extraction of lower esophageal sphincter pressure using the statistical properties of IMFs from esophageal manometric data in Gastroesophageal Reflux Disease. It is also used to remove the wall components from the Doppler ultrasound signals [115] used for detection of vascular diseases providing better accuracy specially in low blood flow condition.. In this report EMD based ECG noise elimination and feature extraction method is detailed in the coming sections. Moreover, EMD can be applicable in neuroscience also [116]. Fault Diagnosis: emd is also applicable for machine learning in automatic mechanical fault detection for rotating or vibrating bodies in mechanical system like gearbox [117]. 59

10 Image Processing: Empirical Mode Decomposition based image segmentation, edge detection, face recognition etc. are relatively new fields of applications of this technique as reported in [118], [119]. In this application bi-dimensional EMD is required and it is reported that the first or a few high frequency IMF image is very significant for edge characterization. After handling these IMF images by a suitable threshold, the obtained edge of the image becomes clear. Moreover, EMD based image preprocessing leads to higher accuracy in hyperspectral image classification [ 120]. It is also used in face recognition for biometric authentication. Speech and Audio Signal Processing: The filtering property of hmd is applied in speech and audio signals for signal enhancement and audio source localization [121]. Finance: Financial time series analysis [122] is concerned with the theory and practice of asset valuation over time. It is a highly empirical discipline, but like other scientific fields, theory forms the foundation for making inference and forecasting over the condition of market. Some works on financial time series analysis using EMD is also reported [123]. Apart from all these application of EMD is also investigated in the field of information fusion, musical tempo estimation, speaker identification, study of ozone record etc. 60

11 3.3 Analysis of ECG using EMD In this section the technique of ECG analysis in EMD domain is discussed. All the methods including wavelet based approach are non adaptive and hence not globally applicable. Basically due to dynamic changes in the behavior of heart and related organs, the ECG signals may exhibit time-varying as well as non-stationary behavior. Moreover, the unpredictable nature of high and low frequency noises makes the task of noise elimination and feature extraction a difficult one for conventional filtering technique or other non adaptive approaches. Hence a fully adaptive approach like Empirical Mode Decomposition can perform better in almost all cardiac conditions. Moreover, most of the earlier works requires two fold operations for ECG feature extraction - first some conventional filtering method for ECG noise elimination and then some analytical approach for detection of QRS and other features. It requires more computational 61

12 cost and time. Requirement of more time for detection of features leads to late diagnosis of the occurrence of pathological events in heart, which may be fatal for cardiac patients. In the following sub-sections an EMD based single run approach for noise elimination and QRS detection is explained. Here noises are estimated by statistical technique from the set of decomposed signals and then the QRS region is reconstructed from the relevant components of decomposed signals. A typical ECG signal and the resulting IMFs after EMD based decomposition is shown in figure 3.3. It is seen that the lower order IMFs represent the fast or high frequency oscillations and higher order IMFs correspond to slow or low frequency oscillations, as expected EMD based ECG Noise Elimination EMD is a very promising tool for ECG denoising. Generated IMFs represent a frequency and amplitude modulated set of signals which can be analyzed to retain the required ones and reject the others. Thus an adaptive filtering operation can be performed on the test signal. This section explains a new algorithm to produce clean ECG from its raw recorded version using EMD. This technique extends the adaptive nature of filtering by making it completely data driven. As different IMFs are produced from different ECG signals, this IMF based approach is unique since no pre-defined cut-off frequency is needed like conventional filtering. Sub-section elaborates the method of baseline wander removal technique whereas sub-section deals with the power frequency elimination procedure Baseline Wander Correction It is known from the previous section that Empirical Mode Decomposition decomposes a signal into IMFs of gradually decreasing frequency and baseline wander is expected to present in some higher order IMFs. The residue of EMD operation may contain some part of total baseline drift but it is not possible to have the entire baseline problem contained in the residue. This is because baseline wander may contain multiple extremas and zero crossings which the residue cannot have as per its property. So it is a difficult task to identify the no. of higher order IMFs which contributes to baseline shift. Moreover, they should not contain any useful information. 62

13 If the entire ECG signal is piecewise divided into small segments, baseline wander basically generates a slope change from segment to segment. The absolute sum of all the slopes approximately indicates the magnitude of baseline drift. The more the sum, the greater the baseline wander. As the baseline components are present in the low frequency IMFs, partial reconstruction of the last few IMFs including residue may represent baseline drift, but it is difficult to identify the order of IMFs responsible for baseline drift. So here a global slope minimization technique is used where last few IMFs are removed one by one as long as the 63

14 global slope becomes minimum. The flowchart for baseline wander correction method is represented in figure 3.4. The steps are as follows: FFT of the original signal (i.e. signal with baseline wander) is done to note the frequency contents in the signal. The dataset of N samples are divided into P segments each having n no. of samples. Each segment contains, say, M no. of ECG waves. At the two ends of each segment arbitrarily two points are identified in the same part (preferably in TP segment, though not mandatory) of two extreme ECG signals. TP segment is best suited for this segmentation purpose as this region does not have any appreciable potential value. Points in this segment are selected by calculating the change of slope on both side of the selected point upto a certain number of samples. If the slopes are almost equal, then the point is considered. Moreover, form the ideal of heart rate the further TP segments can be identified. Then consecutive points are connected to draw P straight lines (figure 3.5A). Slope of each straight line is calculated. Absolute values of all the slopes are added to achieve global slope of the wave under discussion. The global slope is minimized by eliminating higher order IMFs one by ons starting from the highest order one upto a certain IMF (fig. 3.5B, 3.5C, 3.5D, 3.5E). The FFT of the reconstructed wave is done tc check the presence of useful components in the baseline corrected ECG if any. It is a common practice to consider baseline wander frequency below 0.5Hz. During slow heart rate (Bradycardia) the lowest frequency content in ECG is 0.67Hz [124]. As the heart rate is not constant, it is wise to consider the frequency of useful components to be above 0.5Hz (high frequency noise is not considered). 64

15 Fig. 3.5 A-Original ECG wave showing segments and slopes; B,C,D- Stepwise representation of baseline correction method; E - Reconstructed baseline corrected signal; F-Extracted baseline If by comparing the FFT of reconstructed wave and that of the original wave it is seen that some useful frequency component is lost in the process, the last eliminated IMF is considered during reconstruction. Then the required feature (mainly P and/or T wave) of the wave is preserved and baseline wander is removed. Figure 3.5 E is the baseline corrected signal and figure 3.5 F represents the baseline error extracted by the proposed method Power Frequency Elimination The basic idea of power line removal using EMD is to perform selective reconstruction of the ECG from the IMFs. It is seen from the previous sections that lower order IMFs contain high frequency components and higher order IMFs contain low frequency components of ECG signal. The basic principle of denoising via EMD is to select a partial list of IMFs which are not representative of noises to reconstruct ECG. The flowchart of the proposed algorithm is shown in figure 3.6. The method is elaborated below. 65

16 Figure 3.6: Flowchart for ECG powerline noise correction algorithm From figure 3.3 it is clear that the first IMF contains mostly high frequency noise and some QRS information. The next few IMFs contain useful information regarding ECG and high frequency noises. Hence, if these IMFs are removed some important information regarding ECG may be lost, if they are retained, some high frequency noise may present with the ECG information. This is illus rated in figure

17 It shows that if only first IMF is removed and all others are retained, the resulting output contains considerable level of noise and may lack some of useful high frequency part. If some more IMFs are straight away removed, the resulting wave will be distorted at the sharp edges specially the R peak. This is because R peak has a sharp and high frequency oscillation mode which is mostly represented in the higher order IMFs. This problem should be dealt in right perspective i.e., the possible method should be simple, reliable and diagnostically feasible. A QRS preservative window may retain QRS region with all its noises, if any. Moreover, in some leads S wave has a sharp and long depression below the baseline. Again some coronary artery diseases like Myocardial Infarction are diagnosed by the presence of a long and sharp Q wave in ECG along with other indicative features. In these cases S peak and Q peak may also be distorted along with R. So there is a possibility of distortion of entire QRS complex if first few IMFs are simply removed for denoising as shown in figure 3.8. As a result QRS complex detection will be erroneous. 67

18 To overcome all these difficulties, a simple algorithm to choose required IMFs is proposed. The steps are elaborated below: 1) First the cumulative mean of the IMFs are calculated. In this step first the mean of Is' IMF is calculated. Then the other IMFs starting from the 2nd one are added to it one by one and signal mean is calculated in each reconstruction as, K Ak Mean[Y'jc(i)\, (3.20) 1=1 where k varies from ] to N. As high frequency noise is approximately of zero mean, it is expected that a zero or very low value of signal mean should correspond to noise. Almost all cases the 1a IMF represents noise and some useful high frequency component also. Hence a threshold signal mean level is determined upto which the cumulative mean should be considered as noise signal mean. The set of IMFs having a cumulative mean above that threshold value are considered to have useful information of ECG. Mean values corresponding to IMF no. are shown in figure 3.9. This method fails to identify the noisy IMFs in some cases especially when the signal has a nearly zero mean. It occurs if the ECG has sharp large R peak and large S wave in opposite direction. Inverse T wave also contributes in this difficulty. Thus an IMF power based test better performs to identify noisy IMFs as described below. 68

19 Figure 3.9: Plot of signal Mean vs. IMF no. 2) A confirmative test is made by calculating signal power of each IMF. It is a common observation that the presence of power frequency noise in ECG results in small amplitude and high frequency oscillation around the actual ECG trace. Because of small amplitude, the signal power corresponding to noise must be small. Here the power of each IMF is calculated as, PK =10xlogJO]Tlq(/)l2 (3.21) where k is IMF number. The corresponding plot of IMF energy vs. IMF no. is shown in figure A IMF Power It is seen that there is a moderate band of power in all IMFs except some lower order (i.e. high frequency) IMFs in which the power is drastically small. It is seen that the set of IMFs with sufficiently lower power 69

20 and that of extremely smaller value of signal mean are same. Hence there is a possibility to have mostly noise in those IMFs and they can be disregarded during reconstruction. In case if number of noisy IMFs calculated from signal mean and signal energy are different, the lower of the two is selected for removal to minimize the distortion of the reconstructed wave. So the denoised signal Xd is obtained as, (3.22) where P is the noise order of IMF. Because of this lower order IMFs removal, some important high frequency contents may be lost. They are retrieved back by a peak correction method as explained below Correction of High Frequency Peaks This partial reconstruction leads to deformation in the sharp peaks of the signal as discussed earlier and shown in the figure 3.7. Here a signal coirection technique is used to remove this error. It is seen from figure 3.11 (A) and (B) that, although direct removal of IMFs generates a denorsed output signal Xd [figure 3.11 (B)], amplitude of sharp peaks are reduced. Hence a signal peak correction technique is employed. It is noticed that removed peak magnitude is contained in the eliminated noise as sharp spikes with amplitude higher than the rest part of the noise. So the actual noise is approximated as some fraction of the spike magnitude and the required peak information is extracted from the noise as, t L M x = ^Tic(i) Kx [Max{^ c(i)}] (3.23) i=i /=] where M xis magnitude information; L is the order of IMF upto which it contains noise level, c(t) is ilh IMF and K is a constant multiplying factor whose value is chosen to be 0.5 by trial and error method. This 70

21 (A) Signal with power line noise ^TOfFttV y^ci '+' **../ I \ i > i i i \ Time in second (B) Powerline noise removal with peak reduction Arpitucte ) ' l I i i Time in second (C) Peak Information Mx 1 ' J in o cv Time in second /I»\ (D) Final output A rp itu te ATpItLCte Time in second Figure 3. II: (A)~ Original Signal with power line noise; (B)- Peak reduction due to direct elimination of noisy IMFs; (C)- Peak information as stored in M ; (D)-Final denoised output 71

22 step is very important for QRS detection using EMD method as it retains the QRS texture as it is. Finally this magnitude information Mv is added to the earlier reconstructed signal to get ECG signal free from power frequency noise as, xd=xd+mx (3.24) The peak information MT and finally obtained denoised signal xa are shown in figure 3.11 (C) and 3.11 (D) respectively EMD based QRS detection It is mention in chapter I and 2 that automatic computerized classification for cardiac diseases mostly depends upon the extracted features form the ECG signal. As QRS complex detection is the entry point of almost all feature extraction algorithm, a number of research has been made on this subject. Some of the previous works on this subject are mentioned in chapter 1. The complexity of detecting QRS region is that it is completely non stationary. Hence a data driven approach can perform better in QRS complex detection. In this regard EMD based approach may be very promising to capture various types of QRS region. QRS complex is the high frequency component in the ECG wave. In this EMD based method the raw ECG signal is passed through an EMD based decomposition process and baseline wander and power frequency noises are eliminated as described in earlier sections. Thus a set of IMFs is achieved, which contains only the useful information including the QRS complex. The steps to identify QRS complex from these set of IMFs are described below: * It can be expected that the first few IMFs will have the QRS information as QRS region is a high frequency component than the rest part of ECG. The selection of first two IMFs from the denoised set of IMFs has an advantage that it contains only the high frequency parts and most low frequency waves like P and T waves are filtered out from consideration. But as these IMFs are in the mid-band IMFs of the entire set, they must be lacking some high frequency information as shown in the figures 3.6 and 3.7. Hence the peak correction factor is added to it as earlier. So the QRS complex is expected to present in the signal given by, 72

23 L+2 Yans='LC^ + Mx {325) i+i where Mx is given by equation (10). Figure 3.12: (A) - Denoised ECG (B) - Plot of YQKS (C) Plot of YQRS ahanml This improves the QRS identification accuracy as most of the interfering waves are eliminated as shown in the figure 3.12(B). Next the signal is squared as, ^QRS,enhanced ^QRS (3.26) It enhances the QRS region as shown in figure 3.12(C). This squared signal may have different shape for different waves as QRS complex has different morphology. If it comprises of sharp, long upright R 73

24 with small Q and S waves of opposite polarity [figure 3.12(A)], then the squared signal results in a signal having three consecutive peaks as shown in figure 3.12(C). The central peak is the R wave with Q and S peaks on either of it. Hence the Q onset and S offset are given by the minimum amplitude points of YQRS enha ced before the Q peak and after the S peak point respectively as shown in figure 3.12(C). In some cases Q or S or both may be very small in magnitude or absent. In that case the YQRS morphology will vary accordingly and QRS complexes are denoted by the onset and offset of central large peak of YQRS enhancej. 3.4 Experimental results and analysis In this section the testing results of the proposed method is presented. A noisy database of samples is taken for validation. In most of the reported works a clean signal is taken and some artificially generated noises are added with it to get a noisy signal and then the proposed algorithm is used. This method has a problem that it is difficult to get a clean signal and the actual noise may be of different kinds than the artificial one. So here denoised signals are considered as clean signals and the extracted baseline wander and power frequency interference are considered as imposed noise. Linear combination of noises extracted from one or more database is used as a test noise for a clean ECG generated from some other database. Different combinations of baseline wanders and power line interferences are used as input noise that gives the reference of noises in actual sense. For quantitative evaluation of proposed algorithm, the power P of clean signal and filtered signal are measured by, L P = 10xlogIO Jbt(«)l2 (3.27) «=i where Ln is the length of database. Then Percentage Noise Retention (PNR) is calculated as, PNR = P,h ~ P" X100% P CS (3.28) 74

25 where PJs is power of denoised signal and Pcs is power of clean signal. PNR indicates the change in power of clean signal due to addition and elimination of noise in percentage of initial clean signal power. It can be taken as a measure of noise present with the clean signal after EMD based denoising. Moreover, the correlation between the clean and noisy signal and the same for clean and denoised signal is calculated as, L Px, 2 = _ R 0 («)f2 (3.29) n-0 n=0 where px is the cross-correlation coefficient between the clean signal xcs («) and noisy signal Xvl (n) and p2 is the same between clean signal xa (ri) and denoised signal Xv2 (n). The proposed method for ECG enhancement is tested with baseline wanders only, with power line interference only and for both baseline and power line noise combined case. The results are demonstrated in following three sub-sections. Moreover, a comparison of the performance parameters in case of present method and conventional Butterworth filtering is presented in sub-section Sub-section deals with the results for QRS complex detection using the proposed method. A performance based comparison of this method with some of other reported methods is also given in this sub-section Clean signal with baseline wander (BW) As mentioned earlier, the baseline shifted signal is obtained as, xi.(0 = xjo+k,y,cjbw) (3,30) m where (t) is the signal with baseline error, (BW) stands for each baseline drift, Cm is tn' linear coefficient, m is number of individual baselines added and is a multiplying factor to modulate the baseline. Thus different forms of baseline are made and the test results are shown below in table 3.1.A typical baseline wander and corresponding filtered signal is shown in figure

26 Figure 3.13: (A) - Clean ECG (B) - Added baseline drift (C) - Resulting noisy signal (D) - Extracted baseline (E) - Denoised signal TABLE 3.1: PERFORMANCE OF EMD BASED FILTER FOR ECG BASELINE CORRECTION Database Input clean signal power (db) Added BW noise power (db) Output filtered signal power (db) PNR (%) P\ Pi P247s PI74s300' P219s44I* P150s

27 P107sl99' " 7T ;... r-- ) Stands for Physionet PTB diagnostic database; 2 Stands for MIT - BIH Arrhythmia database Clean signal with power line (PL) noise Figure 3.14: (A) - Clean ECG (B) - Added power line interference (C) - Resulting noisy signal (D) - Extracted power line (E) - Denoised signal Similar to the earlier one, a signal with power frequency noise is obtained as xr,«) = xjf)+k2vcf(pl)t (331) P where Xpl (?) is signal with power line noise and (PL) represents each power line noise, Cp is the p'1' linear coefficient, p is number of individual baselines added and K2 is modulating factor of baseline. The test results are tabulated in table 3.2 and the figure 3.14 shows the performance of the filtering process. 77

28 TABLE 3.2: PERFORMANCE OF EMD BASED FILTER FOR ECG POWERLINE NOISE CORRECTION Database Input clean signal Added PL noise Output filtered PNR power (db) power (db) signal power (db) (%) P247s P174s P219s PI50s P107sl P Pi Clean signal with baseline wander and power line noise In the same way a noisy signal with baseline wander and power line noise is prepared as ^W=',(0+r,Ec.(JF), +K Cf(PL)f (3.32) m p where xlm. pl(t) is the signal having both baseline wander and power line noise. In figure 3.15, the clean signal, baseline noise, power line noise, noisy signal, extracted total noise and finally the filtered signals are shown. table 3.3 contains the experimental results for this case. TABLE 3.3 EMD BASED FILTERING FOR ECG BASELINE WANDER AND POWERLINE NOISE Database Input clean signal Added noise Output PNR P Pi power (db) power (db) filtered signal power (db) (%) P247s P174s P219s P150s PI07s

29 Figure 3,15: (A) - Clean ECG (B) - Added baseline drift (C) - Added power line noise (D) - Resulting noisy signal (E) - Extracted total noise (F) - Denoised signal In all three cases, sufficiently low value of PNR indicates the suitability of the proposed method for denoising. Moreover, a variety of noises are used to make a clean signal noisy with different types and different magnitudes of noise to check the versatility of the method. Again wide difference of crosscorrelation coefficients /?, and p2 indicates the structural difference of noisy and filtered signals due to elimination of noise. Value of p2 very close to unity proves the morphological similarity of clean and denoised signals. 79

30 3.4.4 Performance comparison of proposed ECG enhancement technique with Butterworth filtering method Present method of EMD based ECG enhancement is compared with the performance of standard Butterworth filter. Some noisy ECG signals as used earlier are taken as test signal. A Butterworth bandpass filter is designed with lower cutoff frequency 0.5 Hz and upper cutoff frequency 30 Hz. The cutoff frequencies are experimentally determined and also supported by [124] and [125]. The ECG signals and noise levels are similar to that of table 3. PNR and cross correlation coefficient p2 are calculated for the filtered signals as tabulated in table 3.4 below. TABLE 3.4: COMPARISON OF BUTTERWORTH FILTER AND PROPOSED METHOD Butterworth filter Proposed method Database PNR% Pi PNR(%) Pi P247s P174s3D P2I9s P150s P107sl It is clear from the comparison of table 3 and 4 that proposed EMD based method performs better for ECG enhancement. Figure 3.16 also supports the same result. 80

31 Figure 3.16: Comparison of Butterworth filtering and proposed method for ECG enhancement, (A) - Noisy signal (B) - Output of Butterworth bandpass filter (C) - Output of EMD based filter (proposed method) QRS detection Once the filtered signal is finally obtained, the method described in section 3.2. is used to detect the QRS region. As different diseases generate different texture of waveform, some commonly faced ECG patterns are considered for verification of the algorithm. The proposed method is quantitatively analysed by two statistical parameters - measurement sensitivity (Se) and specificity (Sp) which are defined as, TP Sensitivity (Se %) = X100 % and TP + FN TN Specificity (Sp %) = Xl00% TN + FP 81

32 where TP stands for true positive that indicates the accurate detection of QRS complex, 77V is true negative which represents accurate detection of non-qrs region, FP stands for false positive indicating a detection of QRS where it is not present and FN or false negative indicates failure of algorithm to detect a real QRS region. Results are separately shown for PTB diagnostic database (table 3.5a) and MIT-BIH Arrhythmia database (table 3.5b) taken from Physionet data bank. TABLE 3.5a: RESULT FOR QRS DETECTION WITH PTB DIAGNOSTIC DATABASE Type of data No. of beats FP FN Se (%) Sp(%) Normal MI Hypertrophy Dysrhythmia TABLE 3.5b: RESULT FOR QRS DETECTION WITH MIT-BIH ARRHYTHMIA DATABASE Total no. of beats Normal Others FP FN Se (%) Sp (%) It is seen from table 5a that the algorithm runs well for the PTB diagnostic database especially for normal and infracted beats but performance deviates a little for hypertropic and dysrhythmic beats. It is seen that most of the reported works are validated with MIT-BIH Arrhythmia database. Hence the proposed method is also tested with 21 arbitrarily chosen files from the same database which mostly contains normal, BBB, paced, PVC and some fused beats. It is seen that the results are comparable to some of the earlier reported works as indicated in table 3.6. Further investigations can be made to extract other temporal features and also in some different cardiac irregularity conditions. 82

33 TABLE 3.6: COMPARISON OF EMD BASED QRS DETECTION PERFORMANCE WITH STANDARD METHODS SI. No. Method Database used Se (%) Sp (%) 1 Z.E.H.Slimane et. al. [126] MIT-BIH Ghaffari et al. [127] MIT-BIH Christov (Algo. 2) [128] MIT-BIH C.Li et. al. [129] MIT-BIH Proposed method PTB Diagnostic database 98.75* 99.20* 6 Proposed metho MIT-BIH * averaged 3.5 Conclusion The objective of this chapter is to introduce a fully adaptive technique for ECG denoising and QRS detection in a single-run procedure. Empirical mode decomposition (EMD) method is a powerful technique for nonlinear and non-stationary time series data analysis. It is basically a shifting process that produces IMFs which is nothing but a set of amplitude and frequency modulated signals. Thus a complicated signal can be decomposed into a collection of IMFs so that the instantaneous frequencies can be defined. These IMFs form the basis of the decomposition and are complete and practically orthogonal. The expansion in terms of the IMF basis has the appearance of a generalized Fourier analysis with variable amplitudes and frequencies. It is the first local and adaptive method in frequency- time analysis. In this section time domain scale filter property is discussed for ECG enhancement. The generated IMFs appear in gradually decreasing frequency with last one being the residue or mean trend of the signal. Hence the selection a higher, lower or middle order IMFs can generate low, mid or high frequency bands of the test signal respectively. As ECG is a non-stationary signal, its frequency components may vary from person to person or even for the same person in long duration recording. So an automatic technique must be applicable to all kinds of ECG signals. Unlike Fourier or Wavelet transform, EMD extracts its basis function from the signal itself and thus generates IMFs by a signal dependent shifting process as described earlier. This method is advantageous than wavelet transform based analysis because the later one requires a predefined basis function like Daubechies, Morlet Haar etc. and different wavelet function can result in different output. So wavelet selection and analysis based on it is a difficult task. On the other hand, EMD 83

34 based approach generates unique output for a given test signal as the basis function is derived from test signal only. For baseline wander correction, the entire database the fragmented and the slope of each section is minimized by adaptively removing the higher order IMFs including residue. Thus the entire database under test becomes baseline corrected by global minimization of absolute slope. Power of each IMF is calculated and high frequency noise components are estimated by considering a lower threshold level of power as the high frequency ncise power is smaller than that of the IMFs responsible for actual components of the ECG. As direct elimination of those IMFs causes a distortion in QRS complex at their peaks, a statistical approach for peak correction is used to retain the QRS morphology. Thus this EMD based filtering removes only the noisy parts of signal retaining all required information as it is. Once the ECG enhancement is done, partial reconstruction is performed by a set of IMFs taking from the retained list to identify the QRS region and it is enhanced for better visualization of QRS complex. This minimizes the interference of large T or other waves with QRS complex during detection making the identification accurate. Main advantage of this method is that a single decomposition operation is required followed by a statistical approach for noise elimination and a QRS enhancement operation for QRS detection unlike other methods which needs two fold operation of the signal for signal enhancement and QRS detection. Thus lesser computation time and cost is required in this technique. The method is tested with ECGs of different cardiac conditions with a good detection sensitivity and specificity as shown in the results in section 3.4 but more variety of data can be considered for further validation. Moreover, further investigation can be made for detection of other waves like P, T etc. which may be required for different cardiac state identification. This method for ECG enhancement and QRS feature extraction is a part of an automatic computerized cardiac disease identification technique. Different types of classification methodologies are tested for the purpose and for different diseases as well, which are discussed in the next chapter. 84