A Low-Cost Implementation of Sample Entropy in Wearable Embedded Systems: An Example of Online Analysis for Sleep EEG

Abstract

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.