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This paper introduces a new method for R wave's locations using the multiscale wavelet analysis, that is based on Mallat's and Hwang's approach for singularity detection via local maxima of the wavelet coefficients signals. Using a first derivative Gaussian function as prototype wavelet, we apply the pointwise product of the wavelet coefficients (PWCs) over some successive scales, in order to enhance the peak amplitude of the modulus maxima line and to reduce noise. The R wave corresponds to two modulus maximum lines with opposite signs (min-max) of multi-scale product. The proposed algorithm does not include regularity analysis but only amplitude-based criteria. We evaluated the algorithm on two manually annotated databases, such as MIT-BIH Arrhythmia and QT.

QRS complex detectors are extremely useful tools for the analysis of ECG signals. They are used for finding the fiducial points for averaging methods and to calculate the RR time series in Heart Rate Variability techniques. There are currently a number of QRS detection algorithms available which use a variety of signal analysis methods. The most common of these are based on signal matched filters or time-frequency decomposition methods. In contrast to conventional techniques, the wavelet transform provides a new dimension to signal processing and event detection. The ability of wavelet transform to extract electrocardiogram (ECG) features has been demonstrated by several researchers. The majority of them are based on singularity detection via local maxima of the wavelet coefficients signal; therein the correspondence between singularities of a function and local maxima in its wavelet transform is investigated. It is shown that singularities correspond to pairs of modulus maxima across several scales [

The QRS detection technique proposed by Li et al. [

We present here a new method for R wave’s locations using the multiscale wavelet analysis, that is based on Mallat’s and Hwang’s approach for singularity detection via local maxima of the wavelet coefficients signals. Using a first derivative Gaussian function as prototype wavelet, we apply the pointwise product of the wavelet coefficients (hereafter PWC) over some successive scales. That allows us to enhance the peak amplitude of the modulus maxima line and to reduce noise.

This paper is organized as follows. In Section

Wavelet Transform [

The continuous wavelet transform of signal

The idea of this study is to detect singularity not via local maxima of the wavelet coefficients signals but via the product of the wavelet coefficients. Rosenfeld and coworkers suggested forming multiscale pointwise products [

In this section, we introduce a new method of QRS detection based on multiscale product.

We decompose the ECG signal into five scales, labelled Scale_{1}, Scale_{2}, Scale_{3}, Scale_{4}, and Scale_{5}. We specify that none pretreatment is applied to the origin signal.

Then, the product of wavelet coefficients over three categories of successive scales, say P_{123}, P_{234}, and P_{345}, is calculated for all time samples. The choice of an odd levels number preserves the sign of the singularity, that is, couples of maximum modules (minimum/maximum) characterizing one QRS complex. The ECG signal plotted in Figures

ECG signal followed by its wavelet transforms for different values of scale.

ECG signal followed by its multiscale products.

We apply a threshold rule to select the modulus maxima from large to small PWC product scales. The R wave corresponds to two modulus maximum lines with opposite signs (min-max) of multiscale product. Firstly, find all of the modulus maxima larger than a threshold TH_{3} from multiscale products P_{345} to obtain the location set of modulus maxima _{2} on the neighborhood of _{123} are found. Then, the location sets

We eliminate the redundant modulus maxima lines, for some dual R waves or noise in the neighborhood of a modulus maxima lines. Suppose _{123}(

Next, we eliminate the redundant modulus maximum lines. Usually, a given R wave corresponds to a modulus maxima pair with opposite signs (minima and maxima) of wavelet transforms. But in some ectopic beats or in the presence of noise, two or more modulus maxima can occur, of which only one is useful.

If two negative minima Min1 and Min2 are near a positive maximum, with

_{123} between negative minima and positive maxima. Our algorithm does not include regularity analysis, but only amplitude-based criteria. Moreover, the threshold is not updated for each beat, but for each excerpt of _{3}, TH_{2}, and TH_{1}) are proportional to the RMS value of the WT coefficients at the corresponding scale.

We used the MIT-BIH Arrhythmia [

To assess the R detector, we calculated the sensitivity

The detection results on the MITDB and QTDB obtained by our PWC-based R detection and other published detectors are given in Table

R wave’s detection results on MITDB and QTDB.

Database | QRS detector | % error | ||
---|---|---|---|---|

MITDB | Arzeno et al. [ | 99.29 | 99.24 | — |

99.57 | 99.59 | — | ||

98.07 | 99.18 | — | ||

Huabin and Jiankang [ | 99.68 | 99.59 | — | |

Fard et al. [ | — | — | 0.3 | |

Josko [ | 99.86 | 99.91 | 0.23 | |

Zhang and Yong [ | 99.87 | 99.82 | — | |

Mahmoodabadi et al. [ | 99.18 | 98 | — | |

Martinez et al. [ | 99.80 | 99.86 | 0.34 | |

Li et al. [ | 99.89 | 99.94 | 0.17 | |

QTDB | ||||

Martinez et al. [ | 99.92 | 99.88 | 0.20 |

We have presented in this paper a new method for R wave’s locations using the multiscale wavelet analysis and the pointwise product of the wavelet coefficients (PWCs) over some successive scales, in order to enhance the peak amplitude of the modulus maxima line and to reduce noise. The algorithm has been validated using two standard databases, MIT and QT, with different sampling rates and a wide diversity for QRS forms.

Our method achieves very good detection performance on the two studied databases. This algorithm attains