A Low-Cost Implementation of Sample Entropy in Wearable Embedded Systems: An Example of Online Analysis for Sleep EEG
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 app...
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description | 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. |
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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 <inline-formula> <tex-math notation="LaTeX">O(n^{2}) </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> is the data length, making it difficult to meet real-time constraints, especially for large <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">n=7500 </tex-math></inline-formula> and a 250-Hz sampling rate.]]></description><identifier>ISSN: 0018-9456</identifier><identifier>EISSN: 1557-9662</identifier><identifier>DOI: 10.1109/TIM.2020.3047488</identifier><identifier>CODEN: IEIMAO</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Algorithms ; Complexity ; Computation time ; Correlation ; Edge computing ; Electroencephalography ; Embedded systems ; Entropy ; microcontroller (MCU) ; Power consumption ; Power management ; Real time ; Real-time systems ; sample entropy (SpEn) ; Signal processing ; Sleep ; sleep electroencephalogram (EEG) ; Time series analysis ; wearable device ; Wearable technology</subject><ispartof>IEEE transactions on instrumentation and measurement, 2021, Vol.70, p.1-12</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c380t-e76d394981aeec240dfdbd2c2bd9dc9a52685e144c43a73976b2615dc74907873</citedby><cites>FETCH-LOGICAL-c380t-e76d394981aeec240dfdbd2c2bd9dc9a52685e144c43a73976b2615dc74907873</cites><orcidid>0000-0001-8773-6819 ; 0000-0002-4828-3316 ; 0000-0002-6347-5017 ; 0000-0002-2873-4087</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/9312616$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,4024,27923,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/9312616$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Wang, Yung-Hung</creatorcontrib><creatorcontrib>Chen, I-Yu</creatorcontrib><creatorcontrib>Chiueh, Herming</creatorcontrib><creatorcontrib>Liang, Sheng-Fu</creatorcontrib><title>A Low-Cost Implementation of Sample Entropy in Wearable Embedded Systems: An Example of Online Analysis for Sleep EEG</title><title>IEEE transactions on instrumentation and measurement</title><addtitle>TIM</addtitle><description><![CDATA[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 <inline-formula> <tex-math notation="LaTeX">O(n^{2}) </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> is the data length, making it difficult to meet real-time constraints, especially for large <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">n=7500 </tex-math></inline-formula> and a 250-Hz sampling rate.]]></description><subject>Algorithms</subject><subject>Complexity</subject><subject>Computation time</subject><subject>Correlation</subject><subject>Edge computing</subject><subject>Electroencephalography</subject><subject>Embedded systems</subject><subject>Entropy</subject><subject>microcontroller (MCU)</subject><subject>Power consumption</subject><subject>Power management</subject><subject>Real time</subject><subject>Real-time systems</subject><subject>sample entropy (SpEn)</subject><subject>Signal processing</subject><subject>Sleep</subject><subject>sleep electroencephalogram (EEG)</subject><subject>Time series analysis</subject><subject>wearable device</subject><subject>Wearable technology</subject><issn>0018-9456</issn><issn>1557-9662</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kE1Lw0AQhhdRsFbvgpcFz6n7lf3wVkqshUoPrXgMm-wEUpJs3E3R_ntTWjwNvLzPzPAg9EjJjFJiXnarjxkjjMw4EUpofYUmNE1VYqRk12hCCNWJEam8RXcx7gkhSgo1QYc5XvufZOHjgFdt30AL3WCH2nfYV3hrTxHOuiH4_ojrDn-BDbY4ZW0BzoHD22McoI2veN7h7PcMjOima-oOxtA2x1hHXPmAtw1Aj7NseY9uKttEeLjMKfp8y3aL92S9Wa4W83VSck2GBJR03AijqQUomSCucoVjJSuccaWxKZM6BSpEKbhV3ChZMElTVyphiNKKT9HzeW8f_PcB4pDv_SGML8WcCaU1T4WWY4ucW2XwMQao8j7UrQ3HnJL8JDcf5eYnuflF7og8nZEaAP7rhtPxvuR_dtV0qA</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Wang, Yung-Hung</creator><creator>Chen, I-Yu</creator><creator>Chiueh, Herming</creator><creator>Liang, Sheng-Fu</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0001-8773-6819</orcidid><orcidid>https://orcid.org/0000-0002-4828-3316</orcidid><orcidid>https://orcid.org/0000-0002-6347-5017</orcidid><orcidid>https://orcid.org/0000-0002-2873-4087</orcidid></search><sort><creationdate>2021</creationdate><title>A Low-Cost Implementation of Sample Entropy in Wearable Embedded Systems: An Example of Online Analysis for Sleep EEG</title><author>Wang, Yung-Hung ; Chen, I-Yu ; Chiueh, Herming ; Liang, Sheng-Fu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c380t-e76d394981aeec240dfdbd2c2bd9dc9a52685e144c43a73976b2615dc74907873</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algorithms</topic><topic>Complexity</topic><topic>Computation time</topic><topic>Correlation</topic><topic>Edge computing</topic><topic>Electroencephalography</topic><topic>Embedded systems</topic><topic>Entropy</topic><topic>microcontroller (MCU)</topic><topic>Power consumption</topic><topic>Power management</topic><topic>Real time</topic><topic>Real-time systems</topic><topic>sample entropy (SpEn)</topic><topic>Signal processing</topic><topic>Sleep</topic><topic>sleep electroencephalogram (EEG)</topic><topic>Time series analysis</topic><topic>wearable device</topic><topic>Wearable technology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Yung-Hung</creatorcontrib><creatorcontrib>Chen, I-Yu</creatorcontrib><creatorcontrib>Chiueh, Herming</creatorcontrib><creatorcontrib>Liang, Sheng-Fu</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>IEEE transactions on instrumentation and measurement</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Wang, Yung-Hung</au><au>Chen, I-Yu</au><au>Chiueh, Herming</au><au>Liang, Sheng-Fu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Low-Cost Implementation of Sample Entropy in Wearable Embedded Systems: An Example of Online Analysis for Sleep EEG</atitle><jtitle>IEEE transactions on instrumentation and measurement</jtitle><stitle>TIM</stitle><date>2021</date><risdate>2021</risdate><volume>70</volume><spage>1</spage><epage>12</epage><pages>1-12</pages><issn>0018-9456</issn><eissn>1557-9662</eissn><coden>IEIMAO</coden><abstract><![CDATA[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 <inline-formula> <tex-math notation="LaTeX">O(n^{2}) </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> is the data length, making it difficult to meet real-time constraints, especially for large <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">n=7500 </tex-math></inline-formula> and a 250-Hz sampling rate.]]></abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TIM.2020.3047488</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0001-8773-6819</orcidid><orcidid>https://orcid.org/0000-0002-4828-3316</orcidid><orcidid>https://orcid.org/0000-0002-6347-5017</orcidid><orcidid>https://orcid.org/0000-0002-2873-4087</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Algorithms Complexity Computation time Correlation Edge computing Electroencephalography Embedded systems Entropy microcontroller (MCU) Power consumption Power management Real time Real-time systems sample entropy (SpEn) Signal processing Sleep sleep electroencephalogram (EEG) Time series analysis wearable device Wearable technology |
title | A Low-Cost Implementation of Sample Entropy in Wearable Embedded Systems: An Example of Online Analysis for Sleep EEG |
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