Electrocardiogram Signal Denoising: Comparison
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心电图The electrocardiogram （ECG） 在医学上被广泛使用，因为它可以提供有关不同类型心脏病的基本信息。(ECG) is widely used in medicine because it can provide basic information about different types of heart disease. 

  • disentangled representation learning
  • autoencoder
  • ECG signal denoising

1. 引言

目前，心血管疾病是人类生命健康的主要威胁之一，心血管疾病导致的死亡人数每年都在增加[1]。心电图（

Introduction

At present, cardiovascular disease is one of the major threats to human life and health, and the number of deaths due to cardiovascular disease is increasing every year [1]. The electrocardiogram (ECG) is an important tool for cardiology research, and it is also a powerful basis for doctors to directly analyze the cardiac status of patients. Compared with other methods, ECG is often highly efficient and non-invasive and has low costs [2]. As a bioelectric signal source, the signal intensity of the heart must be directly related to the number of active cells, and the number of heart cells constituting the atrium and ventricle is the largest. Therefore, a surface ECG waveform mainly reflects changes in the action potentials of the atrial and ventricular cells [3]. Figure 1 shows a complete ECG）是心脏病学研究的重要工具，也是医生直接分析患者心脏状态的有力依据。与其他方法相比，心电图通常高效、无创且成本低[2]。作为生物电信号源，心脏的信号强度必须与活性细胞的数量直接相关，而构成心房和心室的心脏细胞数量最大。因此，表面心电图波形主要反映心房和心室细胞动作电位的变化[3]。图 cycle in 1which 显示了一个完整的心电图周期，其中the P 波、wave, QRS 束和 T 波是最重要的特征波。这些波及其基础上形成的PR间期、QT间期、ST段是心电图最重要的特征信息[4]，可以从多方面反映心脏的传导系统以及心脏本身是否有病变。因此，在采集心电图数据的过程中，确保心电图不受噪声干扰尤为重要。
bundle, and T wave are the most important characteristic waves. These waves and the PR interval, QT interval, and ST segment formed on their basis are the most important characteristic information of the ECG [4] and can reflect the conduction system of the heart and whether the heart itself has lesions from many aspects. Therefore, in the process of collecting ECG data, it is particularly important to ensure that the ECG is not disturbed by noise.
图Figure 1.完整的心电图周期。 A complete ECG cycle.
心电图具有低频、能量集中的特点，信号微弱，易受噪声干扰，还具有准周期性[5]。心电图取样通常伴有大量噪声，主要是肌肉伪影（ The ECG has the characteristics of low frequency and energy concentration, and the signal is weak, easily disturbed by noise, and also has quasi-periodicity [5]. ECG sampling is often accompanied by a lot of noise, mainly muscle artefacts (MA）[6]、电极运动伪影（) [6], electrode motion artefacts (EM）[7]和基线漂移（) [7], and baseline wander (BW）[8]。肌肉伪影是一种常见的高频噪声，通常在) [8]. Muscle artefacts are a common type of high-frequency noise, usually between 30 到and 300 Hz 之间。这种噪音的来源来自身体肌肉的震颤，因此在图像上表现为肌肉图像与实际情况之间的差异。为了减少这种噪声对图像质量的影响，医学成像专业人员必须使用适当的技术来减少其影响。电极运动伪影是由皮肤和电极接触不良引起的瞬时噪声。基线漂移是低频噪声，主要由呼吸引起，电极滑移是由低频干扰引起的。这些噪音对临床医生诊断疾病性质的能力有重大影响，这可能会导致误诊。因此，对采样的心电图数据进行降噪尤为重要。. The source of this noise comes from the tremor of the body’s muscles and therefore appears on the image as a discrepancy between the muscle image and the actual situation. In order to reduce the impact of this noise on the image quality, medical imaging professionals must use appropriate techniques to reduce its effects. Electrode motion artefacts are instantaneous noise caused by poor contact between the skin and the electrodes. Baseline wander is low-frequency noise, mainly caused by breathing, and electrode slippage is caused by low-frequency interference. These noises have a major impact on a clinician’s ability to diagnose the nature of a disease, which is likely to lead to a false diagnosis. Therefore, it is particularly important to denoise sampled ECG data.

2. 传统的心电图去噪方法The Traditional ECG Denoising Method

心电图采集过程往往伴随着大量的噪声，严重影响了医生对患者的准确诊断。因此，从心电数据中去除噪声的技术研究一直是热点。许多研究人员提出了不同的研究算法。The ECG acquisition process is often accompanied by a large amount of noise, which seriously affects a doctor’s accurate diagnosis of a patient. Therefore, technical research on removing noise from ECG data has always been a hot topic. Many researchers have proposed different research algorithms. In 2015年，[9]的作者提出使用多变量经验模态分解（, the authors of [9] proposed the use of multivariate empirical mode decomposition (MEMD）来消除) to remove baseline wander in ECG数据中的基线漂移。MEMD技术是EMD的多变量扩展，最近在许多应用中引起了研究人员的关注[10]。该方法的基本思想是将信号转换为多通道信号，并使用 data. MEMD technology was a multivariate extension of EMD, which had recently attracted the attention of researchers for many applications [10]. The basic idea of this method was to transform a signal into a multi-channel signal and use the MEMD算法同时处理多通道信号。从心电图中去除最后一个本征模态函数 algorithm to process the multi-channel signal at the same time. The last intrinsic mode function (IMF) or the last two （IMF）IMFs obtained by decomposition were removed from the ECG as the baseline wander to obtain a baseline-corrected ECG. Simulation results showed that this method can remove the baseline wander in ECG data and retain the morphological characteristics of ECG data. Empirical mode decomposition technology was a data-driven adaptive threshold method that was very suitable for non-stationary signals such as ECG data [11]. However, it could not 或通过分解获得的最后两个select IMF 作为基线漂移，以获得基线校正的心电图。仿真结果表明，该方法能够消除心电数据中的基线漂移，保留心电数据的形态特征。经验模态分解技术是一种数据驱动的自适应阈值方法，非常适合心电数据等非平稳信号[11]。然而，它无法有效和适应性地选择货币基金组织，这导致了信息的丢失。[12]的作者提出了一种基于经验模态分解结合小波阈值的自适应心电基线漂移噪声去除方法。对包含efficiently and adaptively, which led to the loss of information. The authors of [12] proposed a noise removal method based on empirical mode decomposition combined with a wavelet threshold for adaptive ECG baseline wander. ECG data containing BW噪声的 noise were denoised. First, they were decomposed into high-frequency signals and low-frequency signals using empirical mode decomposition. Then, the low-frequency signals were wavelet-transformed, and the high-frequency signals were combined to reconstruct the ECG data, thereby achieving the effect of removing baseline wander noise. The technology based on the wavelet transform was also more popular and widely used because of its ability to characterize the time–frequency domain information of time-domain signals [13]. The noise reduction method based on wavelets was widely used because it had good localization properties and could fully highlight the detailed features of ECG数据进行去噪。首先，采用经验模态分解方法将其分解为高频信号和低频信号;然后，对低频信号进行小波变换，将高频信号组合起来重构心电数据，从而达到去除基线漂移噪声的效果。基于小波变换的技术也因其能够表征时域信号的时频域信息而更加流行和广泛使用[13]。基于小波的降噪方法具有较好的定位特性，能够充分突出心电数据在时域和频域的细节特征，因此被广泛应用。然而，由于小波基函数和阈值的选择，去噪后 data in the time domain and frequency domain. However, due to the selection of the wavelet basis function and threshold, the amplitudes of the R波和 wave and S波的振幅可能有所降低[14]。因此，如何选择合适的小波基函数和小波分解电平来消除输入信号中的噪声仍然是一个问题[15]。在小波去噪方法中，使用两个阈值[16]来增强心电图数据。 wave may have been reduced after denoising [14]. Therefore, how to select the appropriate wavelet basis function and wavelet decomposition level to remove the noise in the input signal was still a problem [15]. In the wavelet denoising method, two thresholds [16] were used to enhance the ECG data. Tan Xue e等[17]提出了一种改进的小波阈值函数去噪方法，避免了传统软硬阈值函数中信号处理后阈值连续性差的缺陷。t al. [17] proposed an improved wavelet-threshold-function denoising method that avoided the defect of poor continuity at the threshold after processing the signal in the traditional soft and hard threshold function. Das等[18]对小波变换进行了比较，提出了一种基于 et al. [18] compared the wavelet transform and proposed an ECG denoising method based on the S变换的-transform. Because of the sparse characteristics of the ECG去噪方法。由于心电图本身的稀疏特性[19]，近年来对基于稀疏表示的方法进行了大量研究。然而，稀疏降噪后引入了一些梯形分量[20]，使得降噪后信号不均匀，大多数稀疏表示使用 itself [19], a method based on sparse representation had been studied a lot in recent years. However, some ladder components were introduced after sparse noise reduction [20], which made the signal uneven after noise reduction, and most sparse representations use the L1范数作为惩罚项，导致对原始信号的低估[21]。 norm as a penalty term, which leads to the underestimation of the original signal [21]. 在深度学习领域，基于自编码器模型的In the field of deep learning, an ECG去噪方法[22]更为流行。 denoising method based on the autoencoder model [22] was more popular. An autoencoder composed of eight convolution blocks and eight deconvolution blocks was proposed by Eleni等[23]提出了一种由24个卷积块和25个反卷积块组成的自动编码器，可以有效地学习 et al. [23], which can effectively learn the characteristics of ECG的特征并去除噪声。作为深度学习技术的众多突破之一，生成对抗网络（s and remove noise. As one of the many breakthroughs in deep learning technology, a generative adversarial network (GAN）已被广泛使用。自从) had been widely used. Since Goodfellow[2015]首次引入这种方法以来，已经开发了许多生成对抗网络的变体。 [24] first introduced this method, many variants of generative adversarial networks have been developed. Radford et al. [25] proposed a deep convolutional generative ad等[26]在27年提出了深度卷积生成对抗网络（versarial network (DCGAN）。) in 2015. The DCGAN使用卷积层替换全连接层，并用相同步长的卷积替换原来的池化层。 used a convolutional layer to replace the fully connected layer and replaced the original pooling layer with a convolution of the same step size. Pratik Singh和 and Gayahar Pradhan[<>]提出了一种用于 [26] proposed a generative adversarial network architecture for ECG去噪的生成对抗网络架构。对基于卷积神经网络的 denoising. The GAN模型进行有效训练，进行心电噪声滤波，利用干净噪声的心电数据进行端到端的GAN模型训练。Zhu等[<>]提出了一种生成对抗网络，该网络是由双向长短期记忆（ model based on convolutional neural networks was effectively trained for ECG noise filtering, and end-to-end GAN model training was performed using clean and noisy ECG data. Zhu et al. [27] proposed a generative adversarial network, which was a Bi-LSTM）和卷积神经网络（-CNN）组成的Bi-LSTM-CNN网络。该模型包括一个生成器和一个鉴别器。生成器使用两层 network composed of bidirectional long short-term memory (LSTM) and a convolutional neural network (CNN). The model included a generator and a discriminator. The generator used a two-layer Bi-LSTM网络，判别器基于卷积神经网络。 network, and the discriminator was based on a convolutional neural network.

3. 解缠表示学习Disentangled Representation Learning

解缠表示学习[28]由Disentangled representation learning [28] was first proposed by Bengio于 in 2013年首次提出。正在训练的特征集可用于多个任务，这些任务可能具有不同的相关特征子集。因此，最可靠的特征学习方法是分离尽可能多的因素并丢弃尽可能少的信息。解纠缠表示学习的应用使得深度学习的黑盒项目更具可解释性，可以展示神经网络各层的具体含义和功能。传统的去噪自编码器在编码阶段将信号信息和噪声信息一起映射到隐空间，然后通过隐空间变量将其解码为信号。我们认为存在解码混淆的现象;即将一些噪声信息一起解码为信号信息，从而降低信号的降噪效果。因此，我们试图将隐藏空间中的噪声信息和信号信息解耦，消除信号信息和噪声信息的纠缠，进而解码干净的信号。. The feature sets being trained may be used for multiple tasks, which may have different relevant feature subsets. Therefore, the most robust method of feature learning was to separate as many factors as possible and discard as little information as possible. The application of disentangled representation learning makes the black box project of deep learning more interpretable and can show the specific meaning and function of each layer of the neural network. The traditional denoising autoencoder maps the signal information and noise information to the hidden space together in the encoding phase and then decodes them into signals through the hidden space variable. Researchers believe that there is a phenomenon of decoding confusion; that is, some noise information is decoded into signal information together, thus reducing the noise reduction effect of the signal. Therefore, researchers are trying to decouple the noise information and signal information in the hidden space, eliminate the entanglement of signal information and noise information, and then decode the clean signal.

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