The QRS Detection Based On Wavelet Transform

The heart disease is one of the three most deadly diseases(heart dis-ease,cerebrovascular disease and cancer)that cause death.The research of heart disease is one of the main tasks in medical field for a long time. Electrocardio-gram(ECG) can reflect electrophysiology action of the heart,and most of the heart diseases that caused by different kinds of pathology problems are relative with the electric activity of the heart. So,for most of the time, electrocardiogram is a very important basis to diagnose heart disease and estimate the function of the heart.The research of computer aided ECG analysis and diagnose system began at the end of 1950s.Later,the automatic analysis technique is going to mature along with the development of the technology of computer and artificial intelligence,and is going to be used at clinic. But on the aspect of wildness and acceptability,the application of computer automatic analysis and diagnose system of ECG is not satisfactory,and it takes very small proportion in the field of ECG automatic analysis.So,the research of detection and recognition algorithms of ECG waves by domestic and foreign researchers is very active for a long time. There are significant realistic meanings to do some research in improving the accuracy rate and speed of the ECG detection.The key of ECG signal analysis and diagnose is parameter extraction and the recognition of characteristic waves,its accuracy and reliability decide the diagnose and cure effect of heart disease patient.The detection of QRS complex is the most important thing in the detection of ECG waves.This is because QRS complexes are not only the most important basis to diagnose arrhythmia,but also we can analyse other detail information of ECG only when the QRS complexes are detected,such as the HRV analysis,detecting the parameter of the ST segment and so on.The main algorithms to detect QRS complex are difference and filter method,the method based on neural network,the method based on graph recognition template matching method,morphological method and some other methods. In recent years,the wavelet theory has got the common attention of many sub-jects.Wavelet transform is the inheritance and development of traditional Fourier transform. Because the multi-resolution analysis of wavelet has nice characteristic of time-frequency localization, is very suitable for dealing with non-stationary signals such as image signal and it has became a new method which is used to deal with signal/image.This paper uses wavelet analysis method to decompose ECG signal on different scales ,and extract the characteristic information of ECG signal.Definition Suppose f(x)∈L²(R),Ψ(x)is basic wavelet,Ψ_a,b(x) = the Continuous wavelet transform of f(x) is as followsa is the scale factor,and b is the displacement factor.Generally,we use the traditional Mallat algorithm to decompose the ECG sig-nal.But,the Mallat algorithm has its problem:because of the two-extraction,after every step of decomposition,the data volume reduce a half. So,along with the reduction of resolution,the data volume of low frequency is getting smaller and smaller, and in this case,we can not get the panorama of the whole data.In real application,sometimes we wish to calculate the wavelet transform point by point,namely,increase the grid density of time axis. In this paper,we use the aTrous algorithm to decompose the ECG signal.Suppose C₀(t) be the original discrete time data sequence.the decomposition of the signal by aTrous algorithm is as follows:h(l)denotes discrete low-pass filter,C_i(t)is scale coefficient(approximate compo-nent)under the decomposition scale i.The detail signals W_i(t) under every scale can be represented by the difference of the scale coefficients:W_i(t)is wavelet coefficient(detail component)under the decomposition scale i.W₁(t),W₂(t)…, W_p(t)andC_p(t)are the discrete wavelet transform when the decomposition scale is p.The decomposition of the signal by aTrous algorithm is equal-length,so it has some unique characteristics.For the problems such as ECG signal detection,it can be resolved by the corresponding relations of the traditional signal's characteristic point and the coefficients of wavelet transform.There are many kinds of interference from the ECG signals are acquired to be transformed into numerical signals and sent into analysis equipment,such as power line interference,baseline drift,electromyogram interference,movement artifact and so on. And the chief interference are power line interference and baseline drift caused by different kinds of reasons.They will influence the accurate detection and parameter extraction of QRS complexes,and the baseline drift will also influence the calculate of the ST segment excursion.So it is very important to get rid of power line interference and restrain baseline drift.In this paper, the amplitude-frequency characteristics of three point,four point,and eight point smooth niters are analysed.Considering the effect of the filter and compute speed,at last we used four point smooth filter to get rid of power line interference from the ECG signal.The difference equation of four point smooth filter is as follows:and its amplitude-frequency characteristic is:So,we getThis filter has a 50Hz wave trap,and has nice effect on restraining the high frequency interference.To resolve the problem of baseline drift, we use two median filters to deal with the original ECG signal,the algorithm is as follows:1.First of all,we pass the original ECG signal S through the first 200-ms median filter,the effect of this filter is to eliminate QRS complex and P wave,then we get signal S₁.2.Pass the signal S₁ through a 600-ms median filter,the effect of this filter is to eliminate the T wave of signal S₁.Then we get the baseline drift signal S₂ that does not include QRS complex,P wave and T wave.3.Displace the signal S and minus signal S₂,then we get the ECG signal that eliminates the baseline drift.After denoising the ECG signal by preprocess,we can detect the characteristic waves.The energy of QRS complex mainly concentrates on the scale 2³,and most of the high frequency interference concentrates on the scale 2¹.On the scale 2⁴,the energy of P wave and T wave(especially T wave)is much bigger. So,on the scale 2¹ and 2⁴,the extreme value pairs that generated by interference and T wave can influence the extreme value pairs that caused by QRS complex.After detecting the real ECG signal that collected from hospital,we found that,compare with searching for all the extreme value pairs of all the four scales,the R wave detection accuracy that acquired from searching extreme value pairs on scale 2² and 2³ is almost the same,but the time that used is much more less,and the complexity of the algorithm is smaller.The concrete detection steps are as follows:1. Take three minutes data as one segment.First of all,we decide the threshold of positive maximum valueε_max3,i, and the threshold of negative minimum valueε_mtn3,i on the scale 2³.2.According toε_max3,i andε_mtn3,i,we roughly localize the module maximum pairs of this segment.3.Calculate the slopes of these module maximum pairs.and compare them with the slope threshold of this segmentif the slope of one module maximum pair is bigger than slope threshold,then we consider this module maximum pair is corresponding to a QRS complex;otherwise,we consider this pair is interference,and get rid of it.4. Calculate the threshold of positive maximum value and the threshold of negative minimum value on the scale 2².Suppose maximum point A and minimum point B compose a module maximum pair on scale 2³,point C is the zero-crossing point of this pair.Then we search if there are still maximum point and minimum point near point C that compose a module maximum pair on scale 2².If the search is successrul,then we consider this pair is corresponding to a QRS com- plex;otherwise,we consider this pair is interference,and get rid of it.5.Modify the zero-crossing point of the maximum pair that detected previ-ously,and then we get the position of R wave.6.According to the physiological characteristic,we use the given rules to re-examinate the R waves of this segment,the purpose of this step is to prevent undetected and wrong detection.7. Take next three minutes data,and go to step (1) to deal with the signal.After detected the R wave,we detected the begin point and end point of QRS complex,and pointed out the method to detect P wave and T wave.At last,we use real ECG datas to evaluate the algorithm that proposed in this paper,and we got some nice results.