A SUPERVISED LEARNING APPROACH BASED ON THE

CONTINUOUS WAVELET TRANSFORM FOR R SPIKE

DETECTION IN ECG

G. de Lannoy

1,2

, A. de Decker

and M. Verleysen

Machine Learning Group, Universit

e catholique de Louvain

pl. du Levant 3, 1348 Louvain-la-Neuve, Belgium

Departement of physiology and pharmacology, Universit

e catholique de Louvain

av. Hippocrate 54, 1200 Bruxelles, Belgium

Keywords:

Continuous wavelet transform, automatic ECG annotation, R spike detection, supervised learning.

Abstract:

One of the most important tasks in automatic annotation of the ECG is the detection of the R spike. The

wavelet transform is a widely used tool for R spike detection. The time-frequency decomposition is indeed

a powerful tool to analyze non-stationary signals. Still, current methods use consecutive wavelet scales in

an a priori restricted range and may therefore lack adaptivity. This paper introduces a supervised learning

algorithm which learns the optimal scales for each dataset using the annotations provided by physicians on a

small training set. For each record, this method allows a speciﬁc set of non consecutive scales to be selected,

based on the record characteristics. The selected scales are then used on the original long-term ECG signal

recording and a hard thresholding rule is applied on the derivative of the wavelet coefﬁcients to label the R

spikes. This algorithm has been tested on the MIT-BIH arrhythmia database and obtains an average sensitivity

rate of 99.7% and average positive predictivity rate of 99.7%.

1 INTRODUCTION

In the framework of biomedical engineering, the anal-

ysis of the electrocardiogram (ECG) is one of the

most widely studied topics. The easy recording and

visual interpretation of the non-invasive electrocar-

diogram signal is a powerful way for medical pro-

fessionals to extract important information about the

clinical condition of their patients.

The ECG is a measure of the electrical activity as-

sociated with the heart. It is characterized by a time-

variant cyclic occurrence of patterns with different

frequency content (QRS complexes, P and T waves).

The P wave corresponds to the contraction of the atria,

the QRS complex to the contraction of the ventricles

and the T wave to their repolarization. Because the

ventricles contain more muscle mass than the atria,

the QRS complex is more intensive than the P wave.

The QRS wave is therefore the most representative

feature of the ECG. Furthermore, once the QRS com-

plex has been identiﬁed, other features of interest can

be more easily detected.

Analyzing ECGs for a long time can lead to errors

and misinterpretations. This is the reason why au-

tomatic feature extraction of the ECG signal can help

physicians in their diagnosis for early detection of car-

diac troubles. The feature extraction mainly consists

in the automatic annotation of the different waves in

the recording, the most important of them being the

QRS. One of the main application of the QRS detec-

tion is the heart rate variability (HRV) analysis (Task

Force of the European Society of Cardiology and The

North American Society of Pacing and Electrophysi-

ology, 1996). HRV measures have been proven suc-

cessful in diagnosing cardiac abnormalities and neu-

ropathies or evaluating the actions of the autonomic

nervous system on the heart (Acharya et al., 2006).

However, HRV measures heavily rely on the accuracy

of the QRS feature detection on the digitalized ECG

signal.

Automatic feature extraction and especially R

spike detection is thus a milestone for ECG analy-

sis. However, it is a difﬁcult task in real situations:

(1) The physiological variations due to the patient and

its disease make the ECG a non-stationary signal. (2)

Other ECG components such as the P or T wave look-

ing like QRS complexes often lead to wrong detec-

tions. (3) There are many sources of noise that pol-

140

de Lannoy G., de Decker A. and Verleysen M. (2008).

A SUPERVISED LEARNING APPROACH BASED ON THE CONTINUOUS WAVELET TRANSFORM FOR R SPIKE DETECTION IN ECG.

In Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing, pages 140-145

DOI: 10.5220/0001062501400145

 SciTePress

lute the ECG signal such as power line interferences,

muscular artifacts, poor electrode contacts and base-

line wanderings due to respiration. These three prob-

lems highly compromise the detection of R spikes.

The detection of QRS complexes in the ECG has

been conducted by many researchers in the past years.

However, none of the current algorithms are able to

automatically learn their parameters using pre-labeled

beats provided by physicians. The aim of this paper

is to introduce a new algorithm for R peak detection

that does not blindly detect beats but learns and prop-

agates the annotations provided by physicians on a

small portion of the signal, which is often wanted in

real situations. Our contribution consists in the de-

sign and experiment of a supervised learning algo-

rithm for an optimal and automatic signal decompo-

sition for further optimal R spike detection. The as-

sociated detection method by hard thresholding rule

is also presented. The algorithm does not require any

pre-processing of the signal and can also be adapted

for the detection of other features such as the P or T

wave.

The following of this paper is structured as fol-

lows. After this introduction, section 2 gives a brief

literature review about the state of the art on ECG

feature detection and especially the QRS detection.

Section 3 provides a summary of the theory about the

continuous wavelet transform used in this paper. Sec-

tion 4 introduces the methodology followed by the al-

gorithm and section 5 shows the experiments and re-

sults obtained on a real public database.

2 STATE OF THE ART

Due to the non-stationarity of the ECG signal, the

physiological conditions and the presence of many

artifacts, ﬁnding a robust and general algorithm for

ECG feature detection is a tough task. A lot of work

has been published in the literature about the detec-

tion of various interesting ECG features such as P

waves, QRS waves, T waves, QT intervals or abnor-

mal beats by numerous techniques (Addison, 2005;

Sahambi et al., 2000; Senhadji et al., 1995). This pa-

per focuses on R spike detection only.

For this purpose, several approaches using dif-

ferent signal processing methods have been reported

previously: template matching (Dobbs et al., 1984),

mathematical models (Pahlm and Sornmo, 1984), sig-

nal envelop (Nygards and Sornmo, 1983), matched

ﬁlters (Koeleman et al., 1985), ECG slope crite-

rion (Algra and Zeelenberg, 1987), dynamic time

warping (Vullings et al., 1998), syntactic methods

(Kohler et al., 2002), hidden Markov models (Clavier

et al., 2002), beat detection by neural networks

(Xue et al., 1992; Shyuand et al., 2004), adapta-

tive thresholding (Madeiro et al., 2007; Christov,

2004), time-frequency decompositions by wavelet

transforms (Addison, 2005), and geometrical ap-

proach (Surez et al., 2007).

Among all these methods, the time-frequency de-

compositions by wavelet transform (WT) seem the

most intuitive tool for ECG analysis. The WT is natu-

rally appropriate for analyzing non-stationary signals

because it allows precise time-frequency representa-

tion of the signal with a low computational complex-

ity. A lot of work has been published in past years

on the use of the WT for QRS detection. In 1995,

(Li et al., 1995) used an algorithm based on ﬁnding

the maxima larger than a threshold obtained from the

pre-processed initial beats. Later, (Kadambe et al.,

1999) produced a method allocating a R peak at a

point being the local maxima of several consecutive

dyadic wavelet scales. In both these methods, a post-

processing allowed to eliminate false R detections.

Based on these two publications, a lot of other re-

searches were published on the beat detection based

on the WT (Shyuand et al., 2004; Fard et al., 2007;

Martinez et al., 2004; Addison, 2005; Chen et al.,

2005; Chen et al., 2006).

The main problem of the WT is that one has to

choose the mother wavelet and the scales used to an-

alyze the signal on an empirical basis. While the

mother wavelet can easily be chosen based on its char-

acteristics and ressemblance with a QRS wave, the

ideal scale(s) at which the QRS are matched is harder

to guess a priori. Current algorithms blindly search

for QRS complexes in a limited number of consecu-

tive scales selected in a range of a priori ﬁxed scales.

However, the shape of the QRS pattern can be varying

between patients but also with time. One or several

consecutive ﬁxed wavelet scales may not be enough

to match all complexes at once in a dataset. In this

paper, we propose a new supervised learning algo-

rithm based on the continuous wavelet transform that

overcomes these issues. It only relies on the anno-

tations provided by physicians on a small portion of

the signal in order to select the optimal subset of non-

consecutive scales for each dataset.

3 THEORY OF THE

CONTINUOUS WAVELET

TRANSFORM

The continous wavelet transform (CWT) is a tool

which produces a time-frequency decomposition of a

A SUPERVISED LEARNING APPROACH BASED ON THE CONTINUOUS WAVELET TRANSFORM FOR R SPIKE

DETECTION IN ECG

141

signal x(t) by the convolution of this signal with a so-

called wavelet function.

A wavelet function ψ(t) is a function with several

properties. It must be a function of ﬁnite energy, that

E =

+∞

−∞

|ψ(t)|

dt < ∞, (1)

and it must have a zero mean.

From a wavelet function, one can obtain a family

of time-scale waveforms by translation and scaling

a,b

(t) =

√



t −b



(2)

where a > 0 represents the scale factor, b the transla-

tion and a, b ∈ R. When a = 1 and b = 0, the wavelet

is called the mother wavelet.

The wavelet transform of a function x (t) ∈ L

(R)

is a projection of this function on the wavelet basis

{ψ

a,b

} :

T (a, b) =

+∞

−∞

x(t)ψ

a,b

(t)dt. (3)

For each a, the wavelet coefﬁcients T (a,b) are signals

(that depend on b) which represent the matching de-

gree between wavelet ψ

a,b

(t) and the analyzed func-

tion x(t).

The signal energy at a speciﬁc scale and position

can be calculated as

E(a, b) = |T (a, b)|

. (4)

The two-dimensional wavelet energy density function

is called the scalogram.

The CWT is a suitable tool for ECG analysis be-

cause of this time-frequency representation of the sig-

nal. With the multiscale feature of WTs, the QRS

complex can be distinguished from high P or T waves,

noise, baseline drift, and artifacts. The important

time aspect of the non-stationary ECG signal is kept.

Moreover, very efﬁcient implementations of the al-

gorithm exist and a low computational complexity is

required, allowing real-time analysis. With the aim of

a QRS detection, an appropriate mother wavelet must

be chosen. It must match nicely with a QRS complex,

in order to emphasizes these complexes and to ﬁlter

the useless noise. For more details on the wavelet

transform and on the standard wavelet functions avail-

able, the interested reader can consult (Mallat, 1999;

Addison, 2005; Daubechies, 1992).

4 METHOD DESCRIPTION

4.1 General Description

The detection of R spikes is a tough task due to the

complexity of the ECG signal. The aim of the algo-

rithm introduced here is to automatically ﬁnd the best

subset of wavelet scales for optimal R detection. For

each dataset, this subset is selected on a short train-

ing sample by a supervised learning procedure. The

CWT at the selected scales is then computed on the

complete dataset. Finally, R spikes are detected by a

hard thresholding rule on the selected wavelet coefﬁ-

cients.

4.2 Training

The algorithm uses a supervised learning approach: it

will use the labeled information that is provided and

learn the best way to adapt to the problem. Here, the

labeled information that is provided is the location of

the R peaks in a training dataset.

Each dataset consists in a long-term ECG signal

recording (for example 24 hours). With such long

recording, the problem is that a manual extraction of

the R peaks cannot be performed, as detailed in the In-

troduction. However, asking a specialist to annotate a

small part of the signal by indicating the R peaks is

perfectly feasible; this annotated part will consist in

labeled segments of one minute each, taken at ran-

dom locations over the entire dataset. Choosing ran-

dom locations along the signal is a way to obtain a

representative training set maximizing the probability

to include all types of beats contained in the record-

ings. The CWT is then computed on the training set

in a wide (therefore non restrictive) range of 50 ﬁxed

scales deﬁned as {s

}, 1 ≤i ≤50. The mother wavelet

ψ(t) that was used in our experiments is the mexican

hat wavelet, for its similarity with the regular mor-

phology of the QRS complex. It is deﬁned as the

second derivative of the gaussian probability density

function:

ψ(t) = (1 −t

. (5)

In order to select the appropriate scales among the

wide range of wavelet scales, one needs a criterion. A

natural criterion is the percentage of correct R peaks

detection on the annotated parts of the signal using the

coefﬁcients of the wavelet transform at the trial scales

in the set {s

}. A stepwise forward method automat-

ically selects the best subset {a

} ⊂ {s

} of scales on

the basis of the detection rate. It involves starting with

an empty subset, trying out at each step the trial scales

one by one and including them to the model if the de-

tection rate is improved. The procedure stops when

no scale left in {s

} can improve the detection rate. In

addition, at each step, the scales previously selected

in {a

} are individually challenged: if their removal

does not decrease the detection rate, the scale is now

useless and therefore removed from the model.

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

142

The set {a

} of scales coming from the selection

is thus made of the scales giving the best R detection

when combined together. The selected set of scales is

then used for R spike detection on the complete orig-

inal long-term recording. Figure 1 shows an original

ECG segment and the coefﬁcients of the ﬁrst selected

wavelet scale.

4.3 R Detection

The learning procedure extracted {a

} ⊂ {s

}, the

best subset of scales on the training set. Note that

the scales in the subset are not necessarily consecu-

tive, which means that different QRS shapes can be

matched at different scale levels. The CWT is com-

puted on the whole signal at the scales {a

Because of the non-stationarity of the signal, a

moving window of 5 seconds length with an over-

lap of one second is used to cut T (a

, b) into J parts,

1 ≤ j ≤ J. For each a

and b

, the R spikes are de-

tected on T (a

, b

) by a hard thresholding rule, where

index b

scans the jth window. Let us deﬁne

D(a

, b

) =



d|T (a

, b



. (6)

A threshold th(a

, j) is estimated as the mean of

D(a

, b

). As D(a

, b

) has sharp peaks in the slopes

of the QRS complexes, the intervals I(a

, j) satisfying

D(a

, b

) > th(a

, j) (7)

belong to QRS complexes. The R spikes are then

deﬁned as the maxima of |T (a

, b

in each of the

I(a

, j) intervals. All the R spikes obtained at each

scale k are then merged together.

4.4 Post-processing

A last step of post-processing makes sure that T waves

or Q and S spikes have not been wrongly labeled as a

R. If two or more R spikes were detected in a window

smaller than 250ms (two heartbeats cannot physiolog-

ically happen in less than 250ms (Christov, 2004)),

the algorithm keeps only the peak which has the high-

est value on the original ECG.

5 RESULTS AND VALIDATION

The learning of the model on the training set and the

assessment of performances must be done using an

annotated database. The public standard MIT-BIH ar-

rhythmia database (Goldberger et al., 2000) was used

in this work. It contains 48 half-hour recordings of

annotated ECG with a sampling rate of 360Hz and

11-bit resolution over a 10-mV range. The recorded

signals contain different wave types and only a ro-

bust algorithm can perform well on all datasets to-

gether. Some datasets include very few artifacts and

clear R peaks, but others make the detection of the

R spike more difﬁcult because of (1) abnormal QRS

shapes or P and T waves, (2) low signal-to-noise ra-

tio, (3) heavy baseline drifts, (4) lots of non normal

beats such as premature ventricular contraction, left

bundle branch block beat, atrial premature contraction

etc... Among the 48 available datasets, the four ones

including paced beats were a priori rejected because

they consist in a special case. After visual inspection

of the data, datasets 207 and 208 were also rejected.

The reason is that a representative training set of ﬁve

times one minute would be hard to extract randomly

as several minutes of these two datasets contain only

non-labeled parts looking like a sinus wave.

The performances were assessed by evaluating

two parameters as suggested in (Kohler et al., 2002).

The sensitivity is measured as

T P

T P + FN

(8)

and the positive predictivity as

T P

T P + FP

, (9)

where TP is the number of true positive detections,

FN the number of false negatives and FP the number

of false positives. The error rate is also reported. It is

computed by

FN + FP

QRS

, (10)

where n

QRS

is the total number of QRS labeled in a

dataset. On the database, the algorithm obtains an av-

erage sensitivity rate of 99.7% and average positive

predictivity rate of 99.7%. The average error rate is

below one percent. To our knowledge, only three R

Figure 1: Example of an original ECG segment (upper plot),

the ﬁrst selected wavelet scale (middle plot) and its squared

derivative (lower plot).

A SUPERVISED LEARNING APPROACH BASED ON THE CONTINUOUS WAVELET TRANSFORM FOR R SPIKE

DETECTION IN ECG

143

spike detectors based on WT reported in the literature

obtained comparable results with a sensitivity and a

positive predictivity of around 99.8% (Martinez et al.,

2004; Li et al., 1995; Chen et al., 1997). Our algo-

rithm achieves comparable performances without the

need for a more advanced post-processing stage such

as those used in these articles.

6 CONCLUSIONS

In this paper, a supervised learning algorithm for

the automatic detection of R peaks in ECG is in-

troduced. It uses the multiscale feature of the con-

tinuous wavelet transform (CWT) to emphasize the

QRS complex over high P or T waves, noise, base-

line drift and artifacts. The CWT keeps the important

time aspect of the non-stationary ECG signal. More-

over, very efﬁcient implementations of the CWT exist

and a low computational complexity is required, al-

lowing real-time analysis. This algorithm learns and

propagates the annotations provided by a physician

on a small annotated segment. For this purpose, the

method selects the best subset of wavelet scales on a

representative training set by a stepwise forward pro-

cedure. The forward procedure allows to select scales

that are not necessarily consecutive and it does not

a priori restrict the range of computed scales on an

empirical basis. It allows a complete different set

of scales to be selected for each ECG signal, based

on its characteristics. The selected scales are then

used on the original long-term ECG signal recording

and a hard thresholding rule is applied on the deriva-

tive of the wavelet coefﬁcients to label the R spikes.

The method is robust and does not require any pre-

processing stage. The selection procedure can be gen-

eralized in order to detect other ECG features such as

the P and T wave.

Experiments on the public annotated MIT-BIH

database lead to a sensitivity of 99.7% and a posi-

tive predictivity of 99.7% without the need of an ad-

vanced post-processing stage on the detected peaks.

To our knowledge, only three R spike detectors based

on WT reported in the literature obtained comparable

results, while requiring a more complex post process-

ing stage.

Further works will include: (1) The development

of a more advanced thresholding rule that takes the

peaks detected so far into account; (2) the use of

a more advanced post-processing stage to eliminate

wrong detections; (3) the design of an automatic se-

lection of the best mother wavelet by the same learn-

ing methodology; (4) the generalization of the method

for the detection of other ECG features such as P or T

wave.

ACKNOWLEDGEMENTS

This work was partly supported by the Bel-

gian “R

egion Wallonne” ADVENS convention 4994

project and by the Belgian “R

egion de Bruxelles-

Capitale” BEATS project.

REFERENCES

Acharya, U. R., Joseph, K. P., Kannathal, N., Lim, C., and

Suri, J. (2006). Heart rate variability: a review. Med-

ical and Biological Engineering and Computing, Nov

17.

Addison, P. D. (2005). Wavelet transform and the ecg: a

review. Physiological Measurement, 26:155–199.

Algra, A. and Zeelenberg, H. (1987). An algorithm for com-

puter measurement of qt intervals in the 24 h ecg. Pro-

ceedings of the IEEE Computer Society Press, page

1179.

Chen, S., Chen, H., and Chan, H. (1997). Dsp implementa-

tion of wavelet transform for real time ecg waveforms

detection and heart rate analysis. Computer Methods

and program in Biomedicine, 55(1):35–44.

Chen, S., Chen, H., and Chan, H. (2006). A real-time qrs

detection method based on moving-averaging incor-

porating with wavelet denoising. Comput Methods

Programs Biomed., 82(3):187–95.

Chen, Y., Yan, Z., and He, W. (2005). Detection of qrs-wave

in electrocardiogram: Based on kalman and wavelets.

Conf Proc IEEE Eng Med Biol Soc., 3:2758–60.

Christov, I. I. (2004). Real time electrocardiogram qrs de-

tection using combined adaptive threshold. BioMedi-

cal Engineering OnLine, 3(1):28.

Clavier, L., Boucher, J.-M., Lepage, R., Blanc, J.-J., and

Cornily, J.-C. (2002). Automatic p-wave analysis of

patients prone to atrial ﬁbrillation. Med Biol Eng

Comp, 40:6371.

Daubechies, I. (1992). Ten Lectures on Wavelets (C B M S

- N S F Regional Conference Series in Applied Math-

ematics). Soc for Industrial & Applied Math.

Dobbs, S., Schmitt, N., and Ozemek, H. (1984). Qrs detec-

tion by template matching using real-time correlation

on a microcomputer. Journal of clinical engineering,

9(3):197–212.

Fard, P. J. M., Moradi, M., and Tajvidi, M. (2007). A novel

approach in r peak detection using hybrid complex

wavelet (hcw). International Journal of Cardiology,

In press(Available online 27 March 2007).

Goldberger, A., Amaral, L., Glass, L., Hausdorff, J., Ivanov,

P., Mark, R., Mietus, J., Moody, G., Peng, C.-K.,

and Stanley, H. (2000). PhysioBank, PhysioToolkit,

and PhysioNet: Components of a new research re-

source for complex physiologic signals. Circulation,

101(23):e215–e220.

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

144

Kadambe, S., Murray, R., and Boudreaux-Bartels, G.

(1999). Wavelet transform-based qrs complex detec-

tor. IEEE Transactions on Biomedical Engineering,

46:838–48.

Koeleman, A., Ros, H., and van den Akker, T. (1985).

Beat-to-beat interval measurement in the electrocar-

diogram. Med Biol Eng Comp, 23:2139.

Kohler, B., Hennig, C., and Orglmeister, R. (2002). The

principles of software qrs detection. IEEE Eng Med

Biol Mag., 2(1):42–57.

Li, C., Zheng, C., and Tai, C. (1995). Detection of ecg

characteristic points using wavelet transform. IEEE

Trans.Biomed, 42(1):21–28.

Madeiro, J., Cortez, P., Oliveira, F., and Siqueira, R. (2007).

A new approach to qrs segmentation based on wavelet

bases and adaptive threshold technique. Medical En-

gineering and Physics, 29:2637.

Mallat, S. (1999). A Wavelet Tour of Signal Processing, Sec-

ond Edition (Wavelet Analysis and Its Applications).

IEEE press, San Diego. ISBN 978-0124666061.

Martinez, J., Almeida, R., Olmos, S., Rocha, A., and La-

guna, P. (2004). A wavelet-based ecg delineator: eval-

uation on standard databases. IEEE Transactions on

Biomedical Engineering, 51:570–81.

Nygards, M. and Sornmo, L. (1983). Delineation of the qrs

complex using the envelope of the ecg. Med Biol Eng

Comp, 21:53847.

Pahlm, O. and Sornmo, L. (1984). Software qrs detection in

ambulatory monitoringa review. Med Biol Eng Comp,

22:28997.

Sahambi, J., Tandon, S., and Bhatt, R. (2000). An auto-

mated approach to beat-by-beat qt-interval analysis.

IEEE Eng. Med. Biol. Mag., 19(3):97–101.

Senhadji, L., Carrault, G., Bellanger, J., and Passariello,

G. (1995). Comparing wavelet transforms for recog-

nizing cardiac patterns. IEEE Eng. Med. Biol. Mag.,

149(2):167–173.

Shyuand, L.-Y., Wu, Y.-H., and Hu, W. (2004). Using

wavelet transform and fuzzy neural network for vpc

detection from the holter ecg. IEEE Transactions on

Biomedical Engineering, 51:1269–73.

Surez, K. ., Silva, J., Berthoumieu, Y., Gomis, P., and Na-

jim, M. (2007). Ecg beat detection using a geometrical

matching approach. IEEE Transactions on Biomedi-

cal Engineering, 54(4):641–50.

Task Force of the European Society of Cardiology and The

North American Society of Pacing and Electrophys-

iology (1996). Heart-rate variability: Standards of

measurement, physiological interpretation, and clin-

ical use. Circulation, 93(5):1043–65.

Vullings, H., Verhaegen, M., and Verbruggen, H. (1998).

Automated ecg segmentation with dynamic time

warping. Proceedings of the 20th Annual Interna-

tional Conference on IEEE Engineering in Medicine

and Biology Society, page 1636.

Xue, X., Hu, Y., and Tompkins, W. (1992). Neural-

network-based adaptive matched ﬁltering for qrs de-

tection. IEEE Transactions on Biomedical Engineer-

ing, 32(4):317–329.

A SUPERVISED LEARNING APPROACH BASED ON THE CONTINUOUS WAVELET TRANSFORM FOR R SPIKE

DETECTION IN ECG

145