Contributed articleMyopotential denoising of ECG signals using wavelet thresholding methods
Introduction
A good electrocardiogram (ECG) signal is shown in the stylized representation in Fig. 1. The ECG is mainly used for cardiac arrhythmia detection, where the P, R, and T waves constitute the most critical signal components representing atrial and ventricular contractions respectively. In practice, wideband myopotentials from pectoral muscle contractions will cause a noisy overlay with this ECG signal where:
In the above Eq. (1), the myopotential component of a signal corresponds to additive noise, so obtaining the true ECG signal from noisy observations can be formulated as the problem of signal estimation or signal denoising. Actual views of sampled ECGs with clearly defined clean and noisy regions can be seen in Fig. 2, Fig. 3, Fig. 4. Fig. 2 shows the ECG recording with myopotential noise. In this example, the noise occurs between sample no. 8000 and sample no. 14000. Note that the sampling rate is 1 kHz and the total number of samples in the ECG under consideration is 16,384.
Our objective is to investigate applicability of several wavelet-based denoising methods to the problem of myopotential denoising. It can be readily seen from the data in Figs 2–4 that myopotential denoising of ECG signals is a challenging problem because of the following.
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The useful signal (ECG) itself is non-stationary.
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The myopotential noise is applied only to localized sections of a signal.
Consequently, we can expect that standard (linear) filtering methods for signal denoising are not appropriate for this application. On the other hand, wavelet methods are more suitable for denoising non-stationary signals.
The paper is organized as follows. Section 2 provides background on wavelet thresholding methods, and relates signal denoising to function estimation (learning) from samples. Section 3 describes VC-based signal denoising methodology. Section 4 describes and compares applications of several wavelet thresholding methods to myopotential denoising using real-life data sets. Finally, a summary is given in Section 5.
Section snippets
Signal denoising and function estimation
The traditional approach to signal estimation from noisy samples is rooted in the function approximation framework. Under this approach, a given function (signal) with certain smoothness/frequency characteristics is represented (approximated) as a linear combination of orthogonal basis functions (i.e., Fourier, wavelets etc.). Even though in practical applications signals are represented by finite samples rather than continuous functions, this framework still (approximately) holds, because of
VC-based signal denoising
In Signal Processing, signals are estimated as a linear combination of orthogonal basis functions:Where x denotes a continuous input variable (i.e., time) for univariate signals, or a 2-dimensional input variable (for 2-D signals or images). The bias term w0 is often omitted since signals are zero mean.
Cherkassky, 1998, Cherkassky and Shao, 2001 identify three factors that are important for accurate signal estimation (denoising).
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The type of orthogonal basis functions gi(x
Empirical comparisons
This section describes application of several denoising methods to ECG signals.
Data sets used. All of the experiments presented in this paper are done with an ECG sampled at 1 kHz and a resulting digitized signal with 16,384 (214) samples. For sections where ‘clean’ and ‘noisy’ regions are analyzed, a slice of this larger sample is taken with 4096 (212) samples. These sample regions correspond to samples 261 through 4356 (clean region) and 8000 through 12095 (noisy region) respectively. For the
Denoising results
Denoising with linear filters. Standard approaches to signal denoising use mainly linear filtering based on Fourier analysis. The exact filter design is up to the engineer, but the methodology is fairly standard. The process here includes taking a Fourier transform of a clean segment of the ECG signal and a noisy section of the ECG. A bandpass/lowpass can then be identified that optimally filters the noisy regions. Filtering and denoising tools are readily available in packages such as Matlab.
Summary
Currently, everyone in the industry simply lives with myopotential noise, as there has been no workable method to filter it. The possible applications of these wavelet-denoising methods are obviously very broad. One implementation is in post-processing of an ECG. Myopotentials can be filtered out as described with an automatic implementation of the algorithm in software. An implementation in hardware could even be used to process the ECG signal in an implantable device for real-time arrhythmia
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