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The increase in the occurrence of cardiovascular diseases in the world has made electrocardiogram an important tool to diagnose the various arrhythmias of the heart. But the recorded electrocardiogram often contains artefacts like power line noise, baseline noise, and muscle artefacts. Hence denoising of electrocardiogram signals is very important for accurate diagnosis of heart diseases. The properties of wavelets and multiwavelets have better denoising capability compared to conventional filtering techniques. The electrocardiogram signals have been taken from the MIT-BIH arrhythmia database. The simulation results prove that there is a 29.7% increase in the performance of multiwavelets over the performance of wavelets in terms of signal to noise ratio (SNR).

In modern medicine, there are many methods to diagnose heart disease such as electrocardiogram (ECG), ultrasound, magnetic resonance imaging (MRI), and computer tomography (CT). Among these methods, diagnosis using electrocardiogram has the advantages of convenience and low cost so that it can be used in a wide area. However, certain arrhythmia (a fast, slow, or irregular heartbeat) which can cause abnormal symptoms may occur only sporadically or may occur only under certain conditions such as stress. Arrhythmia of this type is difficult to obtain on an electrocardiogram tracing that runs only for a few minutes. The electrocardiogram is the record of variation of bioelectric potential with respect to time as the human heart beats. Due to its ease of use and noninvasiveness, electrocardiogram plays an important role in patient monitoring and diagnosis.

The change in solar activity including electrocardiographic data with variations in galactic cosmic rays, geomagnetic activity, and atmospheric pressure suggests the possibility of links among these physical environmental variations and health risks, such as myocardial infarctions and ischemic strokes. An increase in the incidence of myocardial infarction in association with magnetic storms has been reported by Cornélissen et al. [

Magnetic storms are found to decrease heart rate variability (HRV) indicating a possible mechanism since a reduced HRV is an important factor for coronary artery disease and myocardial infarction. An increase of 5% in mortality during years of maximal solar activity is found when compared with years of minimal solar activity. These chronodiagnostics are particularly important for those venturing into regions away from hospitals.

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A wavelet is simply a small wave which has energy concentrated in time. It is compactly supported and has finite energy function. It can satisfy admissibility condition and could be amendable for multiresolution analysis. The wavelet transform is a mathematical tool for decomposing a signal into a set of orthogonal waveforms localized both in time and frequency domains. The wavelet transform is a suitable tool to analyse the electrocardiogram signal, which is characterized by a cyclic occurrence of patterns with different frequency content (

Wavelet analysis is done by the breaking up of a signal into a shifted and scaled version of the original wavelet. A continuous wavelet transform can be defined as the sum of overall time of the signal multiplied by a scaled and shifted version of the wavelet function. The greater the scale factor “

The wavelet transform is designed to address the problem of nonstationary signals such as electrocardiogram signals. It involves representing a time function in terms of simple, fixed building blocks, and termed wavelets. The next step is the selection of number of decomposition levels of signal

Diagram of multiresolution analysis of signal

For analysis the following mother wavelet was used:

In the first step threshold values for detail coefficients at every level of decomposition are determined according to the following relationship:

The final step of the analysis is reconstruction of signal

The advantages of wavelet methods are possibility of receiving good quality signal for beat to beat analysis and possibility of having high quality signal while averaging technique is impossible, as causing morphology distortion of electrocardiogram signals, it provides a way for analysing waveforms bounded in both frequency and duration, it allows signals to be stored more efficiently than by the Fourier transform, it can lead to better approximate real-world signals and it is well-suited for approximating data with sharp discontinuities. The disadvantage of wavelet method is that the wavelet transforms ignore polynomial components of the signal up to the approximation order of the basis.

The wavelet transform equation is given by

Multiwavelets constitute a new chapter which has been added to wavelet theory in recent years. Recently, much interest has been generated in the study of the multiwavelets where more than one scaling functions and mother wavelet are used to represent a given signal. The first construction for polynomial multiwavelets was given by Albert, who used them as a basis for the representation of certain operators. Later, Geronimo, Hardin, and Massopust constructed a multiscaling function with 2 components using fractal interpolation.

In spite of many theoretical results on multiwavelet, their successful applications to various problems in signal processing are still limited. Unlike scalar wavelets in which Mallet’s pyramid algorithm have provided a solution for good signal decomposition and reconstruction, a good framework for the application of the multiwavelet is still not available. Nevertheless, several researchers have proposed method of how to apply a given multiwavelet filter to signal and image decomposition.

The concept of multiresolution analysis can be extended from the scalar case to general dimension

The Fourier transform fails to analyze the nonstationary signal, whereas wavelet transform allows the components of a nonstationary signal to be analyzed.

Wavelet transform holds the property of multiresolution to give both time and frequency domain information in a simultaneous manner.

A set of wavelets which are complementary can decompose the given data without gaps or overlap so that the decomposition process becomes mathematically reversible.

Multiwavelets contain multiple scaling functions, whereas scalar wavelets contain one scaling function and one wavelet. This leads to more degrees of freedom in constructing wavelets. Therefore, opposed to scalar wavelets, properties such as compact support, orthogonality, symmetry, vanishing moments, and short support can be gathered simultaneously in multiwavelets which are fundamental in signal processing.

The increase in degree of freedom in multiwavelets is obtained at the expense of replacing scalars with matrices, scalar functions with vector functions, and single matrices with block of matrices. However, prefiltering is an essential task which should be performed for any use of multiwavelet in signal processing.

MIT-BIH arrhythmia database consists of 48-half-hour electrocardiogram recordings. The recordings were digitized at 360 Hz (samples per second per channel) with 11-bit resolution over 10 mV. The simulations were carried out in MATLAB environment R2010b. Various benchmark records from the MIT-BIH database were considered for this study.

Wavelet denoising for ECG record no 103 m using Biorthogonal 1D wavelet.

Original and denoised signals for ECG record no 103 m using Biorthogonal wavelet.

Wavelet denoising for ECG record no 114 m using Biorthogonal 1D wavelet.

Original and denoised signals for ECG record no 114 m using Biorthogonal wavelet.

Multiwavelet denoising for ECG record no 103 m using Biorthogonal 1D wavelet.

Multiwavelet denoising for ECG record no 114 m using Biorthogonal 1D wavelet.

Comparison of signal to noise ratio for wavelet and multiwavelet based denoising techniques for various electrocardiogram records.

The inference from Tables

Performance comparison of wavelet and multiwavelet for record 100 m.

Wavelet family | SNR (dB) | |
---|---|---|

Record no 100 m | ||

Wavelet | Multiwavelet | |

Bio 6.8 | 11.5708 | 29.8328 |

Db 3 | 2.7306 | 21.7829 |

Db10 | 0.561 | 7.3489 |

Coif 4 | 2.466 | 3.6112 |

Sym 4 | 9.0630 | 21.956 |

Performance comparison of wavelet and multiwavelet for record 103 m.

Wavelet family | SNR (dB) | |
---|---|---|

Record no 103 m | ||

Wavelet | Multiwavelet | |

Bio 6.8 | 32.2094 | 35.5220 |

Db 3 | 15.827 | 27.7849 |

Db10 | 19.1099 | 33.1183 |

Coif 4 | 24.1340 | 29.7007 |

Sym 4 | 24.6220 | 36.0964 |

Performance comparison of wavelet and multiwavelet for record 114 m.

Wavelet family | SNR (dB) | |
---|---|---|

Record no 114 m | ||

Wavelet | Multiwavelet | |

Bio 6.8 | 9.184 | 13.4022 |

Db 3 | 28.6913 | 31.0045 |

Db10 | 18.2315 | 28.5193 |

Coif 4 | 19.3813 | 36.6501 |

Sym 4 | 29.6574 | 30.8971 |

Performance comparison of wavelet and multiwavelet for record 201 m.

Wavelet family | SNR (dB) | |
---|---|---|

Record no 201 m | ||

Wavelet | Multiwavelet | |

Bio 6.8 | 11.5636 | 32.3220 |

Db 3 | 20.1344 | 29.3001 |

Db10 | 21.2696 | 33.7040 |

Coif 4 | 17.8031 | 21.2874 |

Sym 4 | 24.0735 | 25.1638 |

The authors declare that they have no conflict of interests regarding the publication of this paper.