Investigation of Fault-Tolerant Adaptive Filtering for Noisy ECG Signals

Transcription

1 Investigation of Fault-olerant Adaptive ing for Noisy ECG Signals Nian Zhang, Member IEEE South Dakota School of Mines and echnology Department of Electrical and Computer Engineering 5 E. St. Joseph Street, Rapid City, SD 577 USA Nian.Zhang@sdsmt.edu Abstract- Studies shos that Electrocardiogram (ECG computer programs perform at least equally ell as human observers in ECG measurement and coding, and can replace the cardiologist in epidemiological studies and clinical trials []. Hoever, in order to also replace the cardiologist in clinical settings, such as for out patients, better systems are required in order to reduce ambient noise hile maintaining signal sensitivity. herefore the objective of this ork as to develop an adaptive filter to remove the contaminating signal in order to better obtain and interpret the electrocardiogram (ECG data. o achieve reliability, the real-time computing systems must be fault-tolerant. his paper proposed a fault-tolerant adaptive filter for noise cancellation of ECG signals. Comparison of the performance and reliability of non-fault-tolerant and fault-tolerant adaptive filters are performed. Experimental results shoed that the fault-tolerant adaptive filter not only successfully extract the ECG signals, but also is very reliable. Keyords: ECG, adaptive filter, noise cancellation, fault tolerant. I. INRODUCION Electrocardiogram is the body-surface manifestation of the electrical potentials produced by the heart. he ECG is acquired by placing electrodes on the patient s skin. In a resting setting, the principal technical issue in interpreting ECG aveforms arise from the existence of ambient or background noise emanating from other electromagnetic sources, including ( signals generated by the other organs, muscles and systems of the body, hether from movement or the performance by those organs of their bodily functions, and ( signals generated by sources external to the body, such as electronic equipment, lights or engines. Cardiologists can identify irregularities in the heart s rate and rhythm, knon as arrhythmia, by examining changes in the.67 to 4 Hz frequency range. Because of the relatively large amplitudes of these aveforms in this range, cardiologists can easily identify arrhythmia notithstanding the existence of electromagnetic ambient noise from other sources. Hoever, it is very difficult for cardiologists to distinguish physiological signals from ambient noise in the broader frequency ranges used to identify different types of heart disease, including cardiac ischemia, hypertrophy and the existence of past or presently occurring heart attacks. he reason for this difficulty is that the physiological signals associated ith these other heart diseases are of a much loer amplitude or strength in the loer.5 to.67 Hz and upper 4 to 5 Hz portions of the frequency range, meaning that they do not stand-out from the ambient noise in these portions and therefore cannot be easily discriminated from that ambient noise. In order to minimize ambient noise in the clinical setting, ECGs are normally taken in the hospital or physician offices. Cardiologists instruct the patient to lie in the supine position, being as still as possible hile a reading is taken to reduce ambient noise caused by physical movement. Another method to reduce ambient noise is to reduce the sensitivity of the monitoring equipment, although this alternative results in a loss of signal quality and the ability to read certain signal intricacies. Although diagnostic criteria have been improved by computerization, many of these techniques have not been idely applied, due to the described limitations []. herefore, adaptive filtering [] to remove artifact noise ithout distorting the actual signal is crucial to enable computer based clinical ECG. Subsequently advances in filtering techniques ill also improve ambulatory ECG recording routinely used to detect infrequent, and asymptomatic arrhythmias [4], [5] and to trace heart activities in fetals [6], [7]. Furthermore, it ill enhance ECG editing [8] used to supplement advances in other technologies such as computer tomography used for cardiology [9]. Microprocessorbased even recorders have been commonly developed and used that carry out online signal processing, data reduction, and arrhythmia detection []. Computational poer of the microprocessor makes them feasible to implement digital filters for noise cancellation and arrhythmia detection []. Adaptive filtering technique using neural netorks has been shon to be useful in many biomedical applications []. he basic idea behind adaptive filtering has been summarized by Widro et al. []. It reduces the meansquared error beteen a primary input, hich is the noisy ECG, and a reference input, hich is either noise that is correlated in some ay ith the noise in the primary input or a signal that is correlated only ith ECG in the primary input []. Adaptive filters permit to detect time-varying potentials and to track the dynamic variations of the signal. hese types of filters learn the deterministic signal and remove the noise. Besides, they modify their behavior according to the input signal. herefore, they can detect shape variations in the ensemble and thus can obtain a better signal estimation /7/$5. 7 IEEE 77

2 Different filter structures are presented to eliminate the diverse form of noise: baseline ander, 6 Hz poer line interference, muscle noise, and motion artifact [4], [5]. 6 Hz poerline interference cancellation is a simple but important application. In the paper, this kind of noise source is used to demonstrate the effectiveness of the adaptive filters e introduced. he first aim of this paper is to construct an adaptive filter and demonstrate its application in noise cancellation. We combine a tapped delay lines to a tapped delay line ith an ADALINE netork to create an adaptive filter. he adaptive filter eights are updated by using the Least Mean Square algorithm. he constructed filter is proved and demonstrated ith a single frequency noise source. he second aim is to introduce a fault-tolerant adaptive filter and demonstrate its improved reliability. A parallel construction is adopted for the fault-tolerant adaptive filter hose reliability is compared ith that of the nonfault-tolerant adaptive filter. II. ADAPIVE NOISE CANCELLAION When doctors are examining a patient on-line and ant to revie the electrocardiogram (ECG of the patient in real-time, there is a good chance that the ECG signal has been contaminated by a 6-Hz noise source. o allo doctors to vie the best signal that can be obtained, e need to develop an adaptive filter to remove the contaminating signal in order to better obtain and interpret the ECG data. A. Adaptive ithout Fault olerance he adaptive filter ithout fault tolerance is designed to remove the contaminating signal, as shon in Fig.. he ECG signal, s is the original uncontaminated input signal to the netork. he desired output is the contaminated ECG signal t. he adaptive filter ill do its best to reproduce this contaminated signal, but it only knos about the original 6 Hz noise source, v. hus, it can only reproduce the part of t that is linearly correlated ith v, hich is m. In effect, the adaptive filter ill attempt to mimic the noise path filter, so that the output of the filter a ill be close to the contaminating noise m. In this ay the error e ill be close to the original uncontaminated ECG signal s. We call (sm the primary input, and a the reference signal. Patient 6-Hz ECG Signal, s m Path v Contaminated Signal, t Adaptive Fig. Cancellation System - a Restored Signal, e Error Since the adaptive filter output is a and the error is e = ( s m a, then the mean square error (MSE is e = (( s m a = ( s m ( s m a a = ( m a s s m s a ( Since signal and noise are uncorrelated, the MSE is E [ e ] = ( m a ] s ] ( Minimizing the MSE results in a filter error that is the best least squares estimate of the signal s. he adaptive filter extracts the signal, or eliminates noise, by iteratively minimizing the MSE beteen the primary and the reference inputs. B. he Least Mean Square (LMS Algorithm he LMS algorithm is an iterative technique for minimizing the mean square error (MSE beteen the primary input and the reference signal [8]. he adaptive filter eights are updated by using the LMS algorithm. he LMS algorithm can be ritten in matrix notation: W ( k = W ( α e( p ( ( and b ( k = b( α e( (4 here W ( = [ ( ( L ( ] is a set of i filter eights at time k, and ( is the ith ro of the i eight matrix. p ( = [ p( p( L p ( ] is the i input vector at time k of the samples from the reference signal. he error is e ( = t( a( = ( a(, here t is the desired primary input from the ECG to be filtered, and a( is the filter output that is the best least-squared estimate of t(. For simplicity, e use a single sine ave noise source. In this case a neuron ith to eights and no bias is sufficient to implement the adaptive filer. he inputs to the filter are the current and previous values of the noise source. Such a to-input filter can attenuated and phaseshift the noise v in the desired ay. he adaptive filter is shon in Fig.. Inputs ADALINE D, n( a(, a( =,, k Fig.. Adaptive for Sine Wave Source 78

3 C. Proof of Concept We ill first need to find the input correlation matrix R and the input/target cross-correlation vector h: R = zz ] and h = tz]. (5 In our case the input vector is given by the current and previous values of the noise source: z ( =, (6 k hile the target is the sum of the current signal and filtered noise: t ( =. (7 No expand the expressions for R and h to give v ( k R =, k v ( k (4 and ] h =. (8 k ] o obtain specific values for these to quantities e must define the noise signal v, the ECG signal s and the filtered noise m. We ill assume: the ECG signal is a hite (uncorrelated from one time step to the next random signal uniformly distributed beteen the values -. and., the noise source (6-Hz sine ave sampled at 8 Hz is given by k =. sin(, (9 and the filtered noise that contaminates the ECG is the noise source attenuated by a factor of and shifted in phase by / : k m ( = sin(. ( No calculate the elements of the input correlation matrix R: k v ( ] = (sin( k = = (sin sin sin sin sin sin = ( = ( E [ v ( k ] = v ( ] = ( k ( k k ] = (sin (sin k = = (sin sin sin sin sin sin = ( (.75 = ( hus R is.7.6 R =. (4.6.7 he terms of h can be found in a similar manner. We ill consider the top term in Eq. (8 first: E [ ] = ] [ ] Here the first term on the right is zero because and are independent and zero mean. he second term is also zero: sin( (sin( ( k k ] = k = = (sin( sin sin( sin( sin( sin (5 = ( =.485 =.469 Next consider the second element of h: k ] = k ] k ] As ith the first element of h, the first term on the right is zero because and k- are independent and zero mean. he second term is evaluated as follos: k ( k k = sin( sin k = sin( sin (6 = (sin( sin sin( sin = ((.885 ( 5 = (.944 = 7 hus, h is.469 h = (7 7 he minimum mean square error solution for the eights is given by: * x = R h = = (8.9 o find the minimum mean square error, consider the performance index: t F( x = c x h x Rx (9 We have just found c: * x, h and R, so e only need to find 79

4 c = t ( ] = ( ] ( = E [ s ( ] ] m ( ] he middle term is zero because and are independent and zero mean. he first term, the expected value of the random signal, can be calculated as follos:.. E [ s ( ] = s ds = s. =..4. (.4 ( he mean square value of the filtered noise is k k m ( = ( sin( (sin( ] k = = (sin( sin( ( sin( sin( sin( sin( = ( =.5 = so that c=. =. 8 t F( x = c x h x Rx.469 [ ] =.8,, 7, [,, ], =.8.498,.46,, [,,,, ], =.8.498,.46, (,,, (,,, =.8.498,.46,,,,,,, = ,,,,,, * Substituting x, h and R, e find that the minimum mean square error is * F( x = ( (.9 (.4487(.9 =. he minimum mean square error is the same as the mean square value of the ECG signal. his is hat e expected, since the error of this adaptive noise canceller is in fact the reconstructed ECG signal. Fig. illustrates the mean square error performance index surface contour Mean Square Error Performance Index Surface Contour Fig.. Mean Square Error Performance Index Surface Contour D. Adaptive ith Fault olerance Real-time computing systems must be fault-tolerant: they must be able to continue operating despite the failure of a limited subset of their hardare or softare. A fault is a physical defect, imperfection or fla that occurs ithin some hardare or softare component. A fault can be caused by specification mistakes, implementation mistakes, component defects or external disturbance. Fault tolerance is the ability of a system to continue to perform its tasks after the occurrence of faults. he fault tolerant adaptive filter is shon in Fig. 4. ECG Signal, s Patient 6-Hz Path v m E. Reliability Analysis of Fault olerant Adaptive he reliability at time t, R(t, is the conditional probability that the system performs correctly during the period [,t], given that the system as performing correctly at time. he unreliability, F(t, is equal to - R(t. Often referred to as the probability of failure. No e compare the reliability of a non-fault-tolerant adaptive filter and that of a fault-tolerant adaptive filter. R = F ( - Contaminated Signal, t Adaptive Adaptive Restored Signal e - Error a Fig. 4 Fault olerant Cancellation System 8

5 For a parallel construction, as shon in Fig. 4, to parts are considered to be operating in parallel if the combination is considered failed hen both parts fail. he combined system is operational if either is available. From this it follos that the combined availability is - (both parts are unavailable. he combined availability is shon by the equation belo: R = F F = ( R ( R (4 When the redundancy of a parallel construction is N, the reliability is R = F F K F N N N = F = R i = i ( i = i (5 he reliability of fault-tolerant adaptive filter is R = ( R ( R (6 here R is the reliability of adaptive filter. is the reliability of adaptive filter, and R Assume the reliability of the to filters are equal, the reliability of the fault-tolerant adaptive filter is simplified as R = ( R = ( ( R ( ( R = R ( R (7 R = R R (8 Since R, so R. In other ord, the reliability of fault-tolerant adaptive filter is greater than or equal to that of the non-fault-tolerant adaptive filter. III. EXPERIMENAL RESULS In the first experiment, the input signal is a hite (uncorrelated from one time step to the next random signal uniformly distributed beteen the values -. and., the noise source (6-Hz sine ave sampled at 8 Hz. A non-fault-tolerant adaptive filter is used. In order to judge the performance of the noise canceller, the original random signals, noise, contaminated signals (i.e. random signals noise, and the restored signals (i.e. filtered signals ere plotted in Fig. 5. From the fourth subplot, e can see that: at first the restored signal is a poor approximation of the original random signals. It takes about. second for the filter to adjust to give a reasonable restored signal. he fifth subplot compares the original random signals and the restored signal. It shos that the restored signal favorably matches the original signal. In the second experiment, MI-BIH Arrhythmia Database data as used as the input: reference annotation (.atr, data file (.dat, and header file (.hea. he result is shon in Fig. 6. A non-fault-tolerant adaptive filter is used. At the 5th time step, the eights of adaptive filter ere all set to s. From the fourth subplot e can see that: the filtered ECG decayed to zero at about the 55th time step. he fifth subplot compares the original ECG signal and the restored signal. It shos that the adaptive filter cannot give the right response after the 55th time step. In the third experiment, the same MI-BIH Arrhythmia Database data as used as the input: reference annotation (.atr, data file (.dat, and header file (.hea. he result is shon in Fig. 7. his time a fault-tolerant adaptive filter is used. At the 5th time step, the eights of adaptive filter ere all set to s. Hoever, from the fourth subplot e can see that: the system as not affected by the failure of the first adaptive filter and operated normally. he fifth subplot compares the original ECG signal and the restored signal. It shos that the restored ECG signal exactly matches the original ECG signal. Adaptive Cancellation for Random Signals ithout Fault olerance Original Random Signals Random Signals ed Signals Comparison of Original and Restored Random Signals Fig. 5. Adaptive Cancellation for Ran dom Signal ithout Fault olerance Adaptive Cancellation for ECG Signals ithout Fault olerance Original ECG ECG ed ECG Comparison of Original and Restored ECG Signals Fig. 6. Adaptive Cancellation for ECG Signal ithout Fault olerance 8

6 Fault olerant Adaptive Cancellation for ECG Signals Original ECG ECG ed ECG Comparison of Original and Restored ECG Signals Fig. 7. Adaptive Cancellation for ECG Signal ith Fault olerance IV. CONCLUSIONS A reliable neural netork based fault-tolerant adaptive filter as designed. he filter does not need computation for voting and error detection. As a result, it requires very little computational poer or memory hile still maintaining the ability to handle complex signal processing. We analyzed the reliability of the non-faulttolerant and fault-tolerant adaptive filters. he experimental results shoed that the fault-tolerant adaptive filter is highly reliable after a permanent fault occurs. hus the adaptive filter approach as described herein can be applied to readily remove 6Hz artifact noise hile minimally distorting the true ECG signals. ACKNOWLEDGEMENS he author ould like to acknoledge the support of Governor's Individual Research Seed Grant. REFERENCES [] J. A. Kors, and G. V. Herpen, he Coming of Age of Computerized ECG Processing: Can it Replace the Cardiologist in Epidemiological Studies and Clinical rials?, MEDINFO, Amsterdam: IOS Press IMIA. [] E. A. Ashley, V. Raxal, A. Kaplan, and V. Froelicher, An Evidence Based Revie of the Resting ECG as a Screening echnique for Heart Disease, International Journal of BioElectroMagnetism, Number, Volume, [] F. Cademartiri, N. R. Mollet, G. Runza, et, al, Improving Diagnostic Accuracy of MDC Coronary Angiography in Patients ith Mild Heart Rhythm Irregularities Using ECG Editing, American Journal of Roentgenology, 6; 86:64-68 [4] Jeffrey C. Bauer, he Future of Cardiology: Opportunities to Exceed Expectations, Bon Secours Health System, Inc., White Paper, June, [5] N.V. hakor. From Holter monitors to automatic implantable defibrillators: Developments in ambulatory arrhythymia monitoring, IEEE rans. Biomed. Eng., BME-, pp , 998. [6] N. V. hakor, J. G. Webster, and W. J. ompkins, Design, implementation and evaluation of microcomputer-based ambulatory arrhythmia monitor, Med. Biol. Eng. Comput., vol., pp.5-59, 984. [7] A. Kam, A. Cohen, Maternal ECG elimination and foetal ECG detection-comparison of several algorithms, Proceedings of the th Annual International Conference of the IEEE, vol., pp , 998. [8] X. Zhou, P. Engler, M.G. Coblentz, Adaptive filter application in fetal electrocardiography, Fifth Annual IEEE Symposium on Computer-Based Medical Systems, pp , 99. [9] N. V. hakor, D. Moreau, Design and analysis of quantized coefficient digital filters: Application to biomedical signal processing ith microprocessors, Med. Biol. Eng. Comput., vol. 5, pp. 8-5, 987. [] M. A. Ahlstrom, W. J. ompkins, Digital filter for real-time ECG signal processing using microprocessors, IEEE rans. Biomed., Eng., vol BME-, pp.78-7, 985. [] B. Widro, J.R. Glover, J. M. McCool, et al., Adaptive noise cancelling: principles and applications, Proc. IEEE, vol. 6, pp , 975. [] Simon Haykin, Neural Netorks: A Comprehensive Foundation, Prentice Hall, nd edition, 998. [] N. V. hakor, Yi-Sheng Zhu, Applications of adaptive filtering to ECG analysis: cancellation and arrhythmia detection, IEEE rans. BioBiomed., Eng., vol. 8, pp , 99. [4] A. Kam, A. Cohen, Maternal ECG Elimination and foetal ECG detection comparision of several algorithms, Proceedings of the th Annual international conference of the IEEE engineering in Medicine and biology society, vol., pp , 998. [5] D. A. ong, K. A. Bartels, and K. S. Honeyager, Adaptive reduction of motion artifact in the electrocardiogram, Proceedings of the second joint EMBS/BMES conference, pp. 4-44,. 8