Sample entropy (SpEn) is a measure of the underlying regularity or complexity of a system that is achieved by assessing the entropy of a time series recorded from the system. It is a powerful signal processing tool and has received increasing attention in recent years. SpEn has been successfully applied in biomedical measurements and other applications. In particular, many emerging applications require measuring the SpEn of signals in real-time embedded systems. However, the standard implementation of SpEn requires a computational complexity of $O(n^{2})$ , where $n$ is the data length, making it difficult to meet real-time constraints, especially for large $n$ . Moreover, power consumption and computation latency must be considered as well. The data length used in previous studies was approximately several hundred, and it remains a challenging task to operate on longer data lengths. In this article, we propose the assisted sliding box (SBOX) algorithm to accelerate the computation of SpEn without any approximation while maintaining a low memory overhead so that the algorithm can be executed in embedded systems for edge computing. We also develop an electroencephalogram (EEG)-based wearable device for comfortable overnight recording. The SBOX algorithm is then implemented in the system to measure the online SpEn of an overnight sleep EEG signal. The results show that, compared with the standard algorithm, the SBOX algorithm speeds up the computation time by a factor of 60, thereby reducing power consumption by 98% when measuring a 30-s epoch of sleep EEG with $n=7500$ and a 250-Hz sampling rate.

中文翻译：

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可穿戴嵌入式系统中样本熵的低成本实现：睡眠脑电图在线分析示例

样本熵 (SpEn) 是对系统潜在规律性或复杂性的度量，它是通过评估从系统记录的时间序列的熵来实现的。它是一种强大的信号处理工具，近年来受到越来越多的关注。SpEn 已成功应用于生物医学测量和其他应用。特别是，许多新兴应用需要在实时嵌入式系统中测量信号的 SpEn。然而，SpEn 的标准实现需要的计算复杂度为 $O(n^{2})$ ， 在哪里 $n$ 是数据长度，难以满足实时约束，特别是对于大 $n$ . 此外，还必须考虑功耗和计算延迟。先前研究中使用的数据长度约为数百，并且对更长的数据长度进行操作仍然是一项具有挑战性的任务。在本文中，我们提出了辅助滑动盒 (SBOX) 算法来加速 SpEn 的计算，同时保持较低的内存开销，以便该算法可以在嵌入式系统中执行以进行边缘计算。我们还开发了一种基于脑电图 (EEG) 的可穿戴设备，用于舒适的夜间记录。然后在系统中实施 SBOX 算法来测量夜间睡眠 EEG 信号的在线 SpEn。结果表明，与标准算法相比，SBOX算法的计算速度提高了60倍， $n=7500$ 和 250 Hz 的采样率。