Deep learning image processing models have had remarkable success in recent years in generating high quality images. Particularly, the Improved Denoising Diffusion Probabilistic Models (DDPM) have shown superiority in image quality to the state-of-the-art generative models, which motivated us to investigate their capability in the generation of the synthetic electrocardiogram (ECG) signals. In this work, synthetic ECG signals are generated by the Improved DDPM and by the Wasserstein GAN with Gradient Penalty (WGAN-GP) models and then compared. To this end, we devise a pipeline to utilize DDPM in its original $2D$ form. First, the $1D$ ECG time series data are embedded into the $2D$ space, for which we employed the Gramian Angular Summation/Difference Fields (GASF/GADF) as well as Markov Transition Fields (MTF) to generate three $2D$ matrices from each ECG time series, which when put together, form a $3$-channel $2D$ datum. Then $2D$ DDPM is used to generate $2D$ $3$-channel synthetic ECG images. The $1D$ ECG signals are created by de-embedding the $2D$ generated image files back into the $1D$ space. This work focuses on unconditional models and the generation of \emph{Normal Sinus Beat} ECG signals exclusively, where the Normal Sinus Beat class from the MIT-BIH Arrhythmia dataset is used in the training phase. The \emph{quality}, \emph{distribution}, and the \emph{authenticity} of the generated ECG signals by each model are quantitatively evaluated and compared. Our results show that in the proposed pipeline and in the particular setting of this paper, the WGAN-GP model is consistently superior to DDPM in all the considered metrics.

翻译：深度学习图像处理模型近年来在生成高质量图像方面取得了显著成功。特别是改进的去噪扩散概率模型（DDPM）在图像质量上已展现出优于当前最先进生成模型的性能，这促使我们探究其在合成心电图（ECG）信号生成中的能力。本研究通过改进的DDPM和带梯度惩罚的Wasserstein GAN（WGAN-GP）模型生成合成ECG信号并进行了比较。为此，我们设计了一套流水线，以利用DDPM原始的二维（$2D$）形式。首先，将一维（$1D$）ECG时间序列数据嵌入到二维空间中，我们采用格拉姆角求和/差分场（GASF/GADF）以及马尔可夫转移场（MTF），从每条ECG时间序列生成三个$2D$矩阵，组合后形成三通道$2D$数据。随后使用$2D$ DDPM生成$2D$三通道合成ECG图像。通过将生成的$2D$图像文件反嵌入回$1D$空间，重建出$1D$ ECG信号。本研究聚焦于无条件模型，并专门生成正常窦性心律ECG信号，训练阶段使用了MIT-BIH心律失常数据集中的正常窦性心律类别。我们对各模型生成的ECG信号的“质量”、“分布”和“真实性”进行了定量评估与比较。结果显示，在所提出的流水线及本文特定设置下，WGAN-GP模型在所有评估指标上均一致优于DDPM。