Tremor suppression in ECG
 Ivan A Dotsinsky^{1}Email author and
 Georgy S Mihov^{2}
DOI: 10.1186/1475925X729
© Dotsinsky and Mihov; licensee BioMed Central Ltd. 2008
Received: 07 May 2008
Accepted: 19 November 2008
Published: 19 November 2008
Abstract
Background
Electrocardiogram recordings are very often contaminated by highfrequency noise usually powerline interference and EMG disturbances (tremor). Specific method for interference cancellation without affecting the proper ECG components, called subtraction procedure, was developed some two decades ago. Filtering out the tremor remains a priori partially successful since it has a relatively wide spectrum, which overlaps the useful ECG frequency band.
Method
The proposed method for tremor suppression implements the following three procedures. Contaminated ECG signals are subjected to moving averaging (comb filter with linear phase characteristic) with first zero set at 50 Hz to suppress tremor and PL interference simultaneously. The reduced peaks of QRS complexes and other relatively high and steep ECG waves are then restored by an introduced by us procedure called linearlyangular, so that the useful high frequency components are preserved in the range specified by the embedded in the ECG instrument filter, usually up to 125 Hz. Finally, a SavitzkyGolay smoothing filter is applied for supplementary tremor suppression outside the QRS complexes.
Results
The results obtained show a low level of the residual EMG disturbances together with negligible distortion of the wave shapes regardless of rhythm and morphology changes.
Background
Electrocardiogram (ECG) recordings are very often contaminated by residual powerline (PL) interference [1–4], baseline drift [5–7], artefacts and EMG disturbances due to involuntary muscle contractions (tremor) of the patient [8–12]. The baseline drift resulting from electrochemical processes at the electrodetoskin barrier [7] is a typical lowfrequency noise that distorts the susceptible ST segment [6, 13]. Interference and tremor have overlapping frequency bands. Therefore, many algorithms are aimed at their common suppression [14–17] in order to provide an accurate automatic delineation of the ECG wave boundaries [18].
Specific digital filter for PL interference cancellation, called subtraction procedure, has been developed some two decades ago and permanently improved later on [19]. It does not affect the signal frequency components around the rated PL frequency. Moving averaging is applied on linear segments of the signal (usually found in the PQ and TP intervals, but also in sufficiently long straight parts of the R and T waves) to remove the interference components. They are stored as phase locked corrections and further subtracted from the signal wherever nonlinear segments are encountered, e.g. QRS complexes or other high and steep waves. Several criteria for linearity have been tested and implemented depending on the purpose. In general, they are based on the second difference of the signal (mathematical evaluation of the curvature).
Filtering out the tremor is a priori partially successful since it has a relatively wide spectrum, which covers the useful ECG frequency band. One of the first recommendations for ECG instruments [20] suggests a lowpass filter with minimum 35 Hz cutoff. However, in this way the amplitudes of sharp QRS waves are reduced. The moving averaging (comb filter with linear phase characteristic) gives similar results [21].
The time averaging is one of the classic methods for ECG noise suppression. It is based on the assumption that the ECG signal is repeatable [22]. As the variability of the ECG morphology is also suppressed, some authors [23, 24] proposed adaptive triggered filtering. Another way to preserve the ECG individuality is to reduce the number of the averaged beats but thus the effect of noise suppression is decreased. The variable ECG morphology, which is related to the respiration, may be compensated in multilead recordings by spatial transformations [24]. However, they can not be applied in the case of single channel time alignment.
Kotas [25] published projective filtering of timealigned ECG beats. This is an extension of time averaging, which preserves the variability of the beat morphology. The method employs the rules of principal component analysis for the desired ECG reconstruction and aims to retain to some extent the deviations from the averaged component changes, in the same time, rejecting deviations caused by noise. However, the nonlinear projective filtering is computationally intensive and is known to be sensitive to noise changes.
Adaptive filtration has been also attempted but with limited success because the QRS complexes disturb the adaptation process up to the end of the Twaves [14]. Luo and Tompkins [8] obtained faster convergence using additional EMG channel as reference input. Bensadoun et al [9] proposed a multidimensional method but the reduction of sharp Qwaves amplitudes is too high.
Clifford et al [26] reported a modelbased filtering method. P, Q, R, S and Twaves are defined by a Gaussian with three parameters: amplitude, width and relative position with respect to the Rpeak. Twave is described by T^{+} and T^{} because of its asymmetric turning point. Nonlinear leastsquares optimization is applied to fit this ECG model to the observed signal. The authors present one cleanly recorded PQRST interval superimposed by electrode motion noise. The result shows almost total noise suppression but also significant waveform distortions. However, the locations of the wave peaks match the uncorrupted signal; the errors around the isoelectric line and the ST segment are negligible. Thus, much of the clinical information of the beats is captured after the noise removal. Nevertheless, the error tolerance has to be tested over a set of databases, since nonparameterized beat will be considered to be an artefact, while some artefacts may closely resemble a known beat. An important advantage of the method is the almost total elimination of series of pulses (artefacts).
Sameni et al [27] proposed a nonlinear Bayesian filtering framework consisting of Extended Kalman Filter (EKF), Extended Kalman Smoother (EKS) and Unscented Kalman Filter (UKF) as suboptimal filtering schemes. They are based on modified dynamic ECG model thus utilizing a priori information about the underlying dynamics of ECG signals. Recordings taken from the MITBIH Normal Sinus Rhythm Database are superimposed by artificially generated noise. They are used for offline testing EKF, EKS and UKF together with Wavelet denoising technique, adaptive and FIR filtering. A best SNR improvement (difference between output and input SNR) of about 10 dB is obtained with the framework filters. The authors found that brady or tachycardia do not considerably affect the filter performance, while other abnormalities appearing in some of the ECG cycles may lead to large errors in the Gaussian functions locations. Besides, neither the model nor the measurement is reliable for filtering signals with low input SNR. Therefore, an accurate denoising of abnormal ECGs with high morphological changes remains an open problem.
Christov and Daskalov [10] applied an adopted by Savitzky and Golay [28] smoothing procedure, which uses least square approximation and a special 'wings' function for defining the weighting coefficients. The obtained suppression ration of the EMG artefact is about 6. Low reduction of R and S waves is reported depending of the wave shape.
Nikolaev and Gotchev [11] denoised ECG signals by applying wavelet domain Wiener filtering. They mixed original signals with EMG noise with a SNR = 14 dB. Twostage algorithm improves the traditional technique by involving timefrequency dependent threshold for calculating the first stage pilot estimate. A SNR over 20 dB is obtained together with less than 10% QRS amplitudes reduction. In another paper Nikolaev et al [12] reported an SNR improvement of more than 10 dB.
Another technique for applying the subtraction procedure in the case of tremor is reported by Christov [16]. The approach introduces adaptive criterion for linearity detection based on the ratio R between the linear segments length in a selected epoch and its total length usually chosen about 1 s. Normally, the criterion threshold M is a constant, which is set from 100 to 160 μV [19]. In the referred publication [16], M starts from a low value of 50 μV and increases until R reaches a preselected value, e.g. 0.9 that corresponds to QRS complex and free of noise RR interval with normal dimensions. The results obtained show a reasonable compromise between tremor suppression and QRS amplitudes reduction.
Gotchev et al [29] applied SavitzkyGolay filter inside the QRS complexes and wavelet shrinkage outside them. The first technique gives a good preservation of the RS amplitude of about 30 μV but with low tremor suppression, while the second one offers good suppression with 440 μV decreasing in the RS amplitude. The combined method incorporates the features of both approaches. They are switched depending on the value W of the 'wings' function. W < 10 is taken as dynamic order of the SavitzkyGolay filter; a higher value calls the wavelet subroutine.
When the comb filter is used as a step of the subtraction procedure [19], the signal inside the QRS complexes is not subjected to moving averaging. Thus, the QRS peaks are preserved but in the presence of tremor the complexes become corrupted and the linear segments are not detected correctly, the last leading to: i) unsuppressed disturbance in false nonlinear segments, and ii) rare recalculation of the phase corrections, which can not follow the changes of the interference amplitudes. These problems are overcome to some extent by Dotsinsky and Christov [17], who introduced a parallel buffer. The comb filtering is applied there over the entire signal, thus allowing precise location of the linear segments. However, the possibility of denoising the QRS complexes by inappropriate tremor components as a part of the calculated phase corrections still remains.
Aim of the study
The purpose of this work was to develop realtime going method and algorithm for suppressing both tremor and PL interference in single or multilead ECG regardless of SNR, wave shapes and morphology changes.
Methods and materials
The developed method for tremor suppression in ECG implements the following three procedures:

Contaminated ECG signals are subjected to moving averaging (comb filter with linear phase characteristic) with first zero set at 50 Hz to suppress tremor and PL interference together.

The reduced peaks of the processed signal are then restored by an introduced by us procedure called linearlyangular, thus the useful high frequency components are preserved in the range specified by the embedded in the ECG instrument filter, usually up to 125 Hz.

Finally, a SavitzkyGolay smoothing filter is applied for supplementary tremor suppression outside the QRS complexes.
About 80 episodes consisting of several RR intervals are extracted from 51 AHA database recordings [30]. They are preliminary moving averaged to suppress any undefined inherent noise. The obtained signals are called 'conditionally clean'. The sampling rate is 250 Hz, the resolution is 5 μV/bit.
In the first part of the study the conditionally clean signals are used for developing the recovery procedure and evaluation of its correctness. For this purpose clean signals are comb filtered and then restored. Input and output signals are compared to assess the distortions introduced by the recovery.
In the second part of the study the clean signals are mixed with synthesized 50 Hz PL interference and tremor obtained by two ECG electrodes placed on one forearm. The mixed signals are subjected to all procedures. The obtained results are analysed to evaluate the tremor suppression and PL interference cancellation.
In the third part of the study the procedures are applied directly on noisy recordings taken from the AHA database and MITBIH Noise Stress Database.
Signal recovery
Basic relations between filtered and nonfiltered samples
Here m is integer, n is equal to the sampling rate divided by the rated interference frequency; i stands for the position of the ongoing averaged sample Y _{ i }, which is obtained over m surrounding nonaveraged samples.
The polynomial inside the parentheses is a second difference, represents one of the possible versions of the linear criterion [19] and is further denoted as
The mean signal velocities on the left and the right hand side of the ongoing sample X _{ i }are ${v}_{i,ij}=\frac{{X}_{i}{X}_{ij}}{j}$ and ${v}_{i+j,i}=\frac{{X}_{i+j}{X}_{i}}{j}$. They are averaged within the intervals [ij, i] and [i, i+j], since they correspond to the timecoordinates i+j/2 and ij/2.
Background of the linearlyangular recovery procedure
The coefficient η is intended to consider the real signal shapes. For the time being, this study presumes that η is very close to 1.
The influence of k on the back filtering error is assessed by experiments with k = 1, 2, 3, 4, 5; n = 5 and M = 0,12 mV. The error committed is minimal with k = 2, which value is further used. Lower value of k contributes to better shape recovery of rounded peaks, while the steeper ones are subcompensated. Higher k value restores well steep peaks, but the rounded ones become overcompensated.
Assessment of the recovery procedure
Starting and ending times of the AHA recordings used for assessment of the recovery procedure.
episode taken  episode taken  episode taken  

AHA recording  starting time, s  ending time, s  AHA recording  starting time, s  ending time, s  AHA recording  starting time, s  ending time, s 
1004d1  384  416  4001d2  1152  1176  6008d1  864  896 
1010d1  672  704  4005d1  192  224  6009d1  864  952 
1010d2  672  704  4005d2  192  288  6009d1  1056  1112 
2001d1  672  688  4006d1  384  400  6010d1  1056  1088 
2004d1  1056  1072  4006d1  768  784  6010d1  1152  1176 
2004d1  1152  1168  4006d2  384  400  7001d2  480  552 
2004d1  1248  11296  4006d2  768  784  7002d1  280  512 
2004d2  1056  1072  4009d1  288  336  7002d1  576  608 
2004d2  1152  1168  4009d2  288  336  7003d2  768  800 
2004d2  1248  11296  5001d1  9  65  7004d1  288  320 
2005d1  1  41  5001d1  768  824  7005d1  480  560 
2005d2  1  41  5003d1  864  920  7005d1  576  656 
2008d1  9  57  5003d1  960  1016  7005d2  480  512 
2008d1  864  888  5003d1  1056  1104  7005d2  576  608 
2008d1  1056  1080  5003d2  960  1040  7006d1  672  728 
2008d2  9  57  5004d2  288  312  7006d2  672  696 
2008d2  864  888  5009d2  576  624  7007d1  672  760 
2008d2  1056  1080  5010d1  864  896  7007d2  672  720 
2009d1  1152  1208  5010d1  960  992  7008d1  288  320 
2009d2  1152  1208  5010d1  1152  1184  7009d1  9  65 
3004d1  576  632  5010d2  960  992  7009d1  96  128 
3004d2  576  632  6002d1  288  328  7009d1  960  992 
4001d1  960  1016  6002d2  288  304  7010d1  672  752 
4001d1  1056  1088  6003d2  288  344  7010d1  768  824 
4001d1  1152  1176  6005d1  192  280  7010d1  864  896 
4001d2  960  1016  6007d1  1056  1080  7010d2  864  896 
4001d2  1056  1088  6007d2  1056  1080  7010d2  1152  1184 
The recovery is assessed without additional suppression outside the QRS complexes in order to have statistically the same residual noise all over the episode. Thus, a more accurate evaluation of the distortions within the complexes is possible.
Actually, the linear segments outside the ventricular beats (see for example Fig. 2 and 3) that represent physiological zeroline should be free of any distortions. Obviously, the 'error' there is due to noise components of the AHA recordings that have not been totally eliminated by the preliminary moving averaging, since the first lobe of the comb filter [21] has an equivalent highpass cutoff approximately at 24 Hz.
This impression may be reinforced by visual inspection of tremor episodes after moving averaging followed by some kind of additional filtering.
Consequently, the real errors own to the procedure are considerably smaller. One may speculate that the distortions introduced by the recovery inside the QRS complexes are within ± 50 μV (see Fig. 2, 3, 4, 5).
Additional tremor suppression in the linear segments
Filters with parameter s < 4 are unusable since their first zero is shifted too far towards the high frequencies that stultify the attempts for tremor suppression. In this study s = 15 is used as a compromise between good tremor suppression and preserving the Pwave shapes.
The observation of the traces in Fig. 7 suggests how to assess the suppression ratio of both procedures. It is quite possible that the maximum peak coupled to a relatively high frequency before filtering is well suppressed after filtering while a lower amplitude lower frequency peak before may practically preserve its amplitude after that. Therefore, the suppression ratio could be defined as the quotient of the maximum peaks in signals before and after processing. For the moving averaging such ratio is over 6 times. It becomes about 25 after additional SavitzkyGolay filtering.
Results
Evaluation of the noise suppression in conditionally clean signals mixed with PL interference and tremor
Tremor suppression in originally noisy recordings
Discussion and conclusion
The proposed method for tremor suppression in one or multilead ECG is based on moving averaging of the ECG signal followed by a linearlyangular procedure for restoring the affected amplitudes of QRS complexes and other relatively high and steep ECG waves. Thus, the useful high frequency components are preserved in the range specified by the embedded in the ECG instrument filter, usually up to 125 Hz. Finally, the signal portions outside the QRS complexes are additionally processed to reduce the tremor level by applying a SavitzkyGolay smoothing procedure. The results prove the efficiency of the developed method. The recovery error of about 50 μV is below the level that may provoke wrong diagnostic. The interference is totally eliminated. The tremor is suppressed approximately 25 times. The residual tremor does not lead to false ECG interpretation. The procedure efficiency is independent on arrhythmia and any other wave shape variations. The algorithm is suitable for realtime implementation. For the time being the individual shape of the restored waves (the coefficient η) is not taken in consideration. This possibility will be further checked up.
Declarations
Authors’ Affiliations
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 American Heart Association (AHA) arrhythmia ECG database Emergency care Research Institute 5200 Butler Pike, Plymouth Meeting, PA 19462 USA
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