Hybridizing β-hill climbing with wavelet transform for denoising ECG signals

Abstract

This paper introduces βHCWT, a hybrid of the β-hill climbing metaheuristic algorithm and wavelet transform (WT), as a new method for denoising electrocardiogram (ECG) signals. ECG signals are non-stationary signals that provide a graphical measure of electrical activities in human heart muscles. However, given their non-stationarity, these signals frequently encounter noise and a low signal-to-noise ratio (SNR). The selection of wavelet parameters is a challenging task that is usually performed based on empirical evidence or experience. Therefore, in this paper, β-hill climbing is applied to find the optimal wavelet parameters that can obtain the minimum mean square error (MSE) between the original and denoised ECG signals. The proposed method was tested on a standard ECG dataset from MIT-BIH while its performance was evaluated by using percentage root mean square difference (PRD) and SNR as criteria. Meanwhile, the effect of β-hill climbing on the performance of WT was tested by comparing the proposed method with WT. The proposed method was then compared with the genetic algorithm in consideration of the performance of the WT parameters and adaptive thresholding methods. The proposed method demonstrated an outstanding performance in removing noise from non-stationary signals, and the quality of the output signal was deemed favorable for medical diagnosis.

Introduction

An electrocardiogram (ECG) is a graphical recording of electrical activities in human heart muscles that is commonly used in cardiology tests, in which electrodes are placed on the skin for a certain period (generally around 10 s depending on the condition of the patient) [49] to detect whether the heart muscle has produced any electrical change on the skin in each heartbeat [32]. Thus, ECG signals are non-stationary signals [32] that frequently encounter noise and a low signal-to-noise ratio (SNR).

Accordingly, researchers have proposed various methods for reducing signal noise. Wavelet transform (WT) is a widely used signal processing tool [17], [22], [23], [31], [40], [46] that represents signals in the time-frequency domain and uses five parameters to obtain a smooth signal, including wavelet function name, decomposition level, thresholding methods, thresholding selection rule, and threshold rescaling methods, with each parameter having several types or values as shown in Table 1.

WT is considered the most effective solution to the signal denoising problem, particularly in biomedical signal processing [38], [40], [46]. Several other techniques have also been proposed for denoising ECG signals in biological signal processing, with most techniques adopting Donoho’s universal theory [5], [36], [39], [40], [46]. Sayadi et al. in [46] proposed bionic WT, which denoises ECG signals via the adaptive thresholding of WT. Novak et al. in [36] applied a detection algorithm to identify different noise levels in the wavelet domain and adopted soft thresholding in which they computed the thresholding value based on the noise in each signal decomposing level. Singh et al. in [50] proposed a method for selecting mother wavelet basis functions for denoising ECG signals in the wavelet domain. El-Dahshan in [19] proposed a hybrid of the genetic algorithm and WT for denoising ECG signals, in which the genetic algorithm was applied to find the best set of wavelet parameters and the performance of the hybrid was tested on an MIT-BIH dataset to test its performance. Srivastava et al. in [53] proposed a signal denoising method that involved (1) selecting the number of decomposition levels, (2) adopting a new approach for estimating the thresholding value, (3) adopting positive and negative thresholding values based on the wavelet coefficients, (4) denoising in the approximation part, and (5) adjusting the noise thresholding level. Nguyen et al. in [35] proposed a new ECG signal denoising method based on adaptive genetic algorithm-based thresholding and ensemble empirical mode decomposition. They tested this method on an MIT-BIH dataset [20], where the original ECG signal was corrupted with white Gaussian noise (WGN) and different SNR input noise levels. This method, which performance was evaluated based on mean squared error (MSE) and SNR, successfully removed white Gaussian noise from the ECG signal.

The above techniques have been adopted to achieve a high SNR, which corresponds to a low noise level in the output ECG signal. However, two factors, namely, high SNR and low percentage root mean square difference (PRD), must be also considered to guarantee an efficient system. An increase in SNR indicates the smooth denoising of signals, while a decrease in PRD indicates the efficient denoising of the original ECG signal. The survival of the fittest principle must be considered in the optimization to achieve a better ECG signal denoising performance. The β-hill climbing algorithm is a novel optimization algorithm with a local search area nature that can easily, rapidly, and efficiently find the local optimal solution [2]. This algorithm is initiated by a single provisional solution, x, which is changed iteratively by using a neighborhood structure (i.e.,$\mathcal{N}$(x)) and a β-operator until a locally optimized solution is obtained. Before finding a precise local optimal solution, the β-hill climbing algorithm fine-tunes the search space in which all solutions converge. However, this algorithm goes through a trajectory without scanning the entire search space [2]. Nevertheless, given its many advantages, the β-hill climbing algorithm has been successfully applied to solve many optimization problems, such as in Sudoku [3], text clustering [1], multiple-reservoir scheduling [6], and signal processing [8], [9].

In this paper, the β-hill climbing algorithm is hybridized with WT to solve the ECG signal denoising problem. The β-hill climbing algorithm initially locates the optimal wavelet parameters that will minimize the MSE between the original and denoised signals. Afterward, the WT uses the optimal parameters to solve the ECG signal denoising problem. Selecting the best combination of wavelet parameters is a challenging task because the optimal wavelet denoising parameters are not determined by applying a certain technique but rather by referring to experience or empirical evidence. The proposed hybrid method involves three phases. In the first phase (Initialization), the noisy ECG signal and wavelet denoising parameters are initialized. In the second phase (tuning WT parameters by β-hill climbing algorithm), the β-hill climbing algorithm is applied to search the ECG signal space for the optimal wavelet parameters that can obtain the minimum MSE. The third phase (ECG denoising using WT with ${\mathit{x}}_{opt}^{\prime }$) involves the Decomposition of the ECG signal by using discrete wavelet transform (DWT), Thresholding based on the noise level coefficients, and Reconstruction of the denoising signal via inverse DWT (iDWT).

The proposed hybrid method was tested on a standard ECG dataset from MIT-BIH,¹ evaluated by using PRD and SNR as criteria, and compared with the genetic algorithm, which is a population-based optimization technique [19], [35]. The proposed method showed an outstanding performance in denoising ECG signals, and the quality of the denoised signal was deemed appropriate for clinical diagnosis.

This paper is organized as follows. Section 2 describes the denoising of ECG signals based on the optimal wavelet parameters. Section 3 describes the wavelet denoising principle. Section 4 presents the β-hill climbing algorithm. Section 5 explains the proposed denoising method. Section 6 presents an example of an ECG signal denoising process. Section 7 discusses the experiments and results. Section 7.1 explains the effect of the β-hill climbing algorithm on the performance of WT. Section 7.2 compares the β-hill climbing algorithm with the genetic algorithm. Section 8 concludes the paper.