Entropy Analysis of Univariate Biomedical Signals:Review and Comparison of Methods

International audienc

Guest Editorial Special Issue on Cardiovascular System Monitoring and Therapy: Innovative Technologies and Internet of Things

The papers in this special section focus on cardiovascular system monitoring and therapy. The number of devices for the measurement and interpretation of biological systems that describe performance of the cardiovascular system is growing. Among others, this is due to the improvement of circuit and system design that renders the devices wearable and easy to use. Moreover, internetworking enables these devices to exchange data. Their true impact on patient care is highly dependent on the quality and relevancy of the data acquired. The design of circuits and systems to answer the growing demand and the necessity to have portable and connected devices lead to a focus on designing ultra-low power apparatus, mixed-signal devices, using nanoscale electronics. Microelectronic issues are therefore at the heart of the demand. All this requires inter-disciplinary collaborations between scientists, engineers, medical researchers, and practitioners. The interconnection of these embedded devices, known as Internet of Things, is expected to usher in the medical field, among others to study the cardiovascular system of patients. Data processing and storage will also take place in the healthcare information technology. Furthermore, key issues such as data security and privacy will be determinants of the utility of these systems and impact in healthcare monitoring and management. This special issue aimed to provide a forum for both established experts and newinvestigators to share their developments, knowledge, and insights for the further design of circuits and systems aiming at being integrated in sensors to monitor or treat the cardiovascular system

Fuzzy Entropy Metrics for the Analysis of Biomedical Signals: Assessment and Comparison

Fuzzy entropy (FuzEn) was introduced to alleviate limitations associated with sample entropy (SampEn) in the analysis of physiological signals. Over the past decade, FuzEn-based methods have been widely used in various real-world biomedical applications. Several fuzzy membership functions (MFs), including triangular, trapezoidal, Z-shaped, bell-shaped, Gaussian, constant-Gaussian, and exponential functions have been employed in FuzEn. However, these FuzEn-based metrics have not been systematically compared yet. Since the threshold value r used in FuzEn is not directly comparable across different MFs, we here propose to apply a defuzzication approach using a surrogate parameter called \u27center of gravity\u27 to re-enable a fair and direct comparison. To evaluate these MFs, we analyze several synthetic and three clinical datasets. FuzEn using the triangular, trapezoidal, and Z-shaped MFs may lead to undened entropy values for short signals, thus providing a very limited advantage over SampEn. When dealing with an equal value of the center of gravity, the Gaussian MF, as the fastest algorithm, results in the highest Hedges\u27 g effect size for long signals. Our results also indicate that the FuzEn based on exponential MF of order four better distinguishes short white, pink, and brown noises, and yields more signicant differences for the short real signals based on Hedges\u27 g effect size. The triangular, trapezoidal, and Z-shaped MFs are not recommended for short signals. We propose to use FuzEn with Gaussian and exponential MF of order four for characterization of short (around 50400 sample points) and long data (longer than 500 sample points), respectively. We expect FuzEn with Gaussian and exponential MF as well as the concept of defuzzication to play prominent roles in the irregularity analysis of biomedical signals. The MATLAB codes for the FuzEn with different MFs are available at https://github.com/HamedAzami/FuzzyEntropy_Matlab

Multivariate refined composite multiscale entropy analysis

International audienceMultiscale entropy (MSE) has become a prevailing method to quantify signals complexity. MSE relies on sample entropy. However, MSE may yield imprecise complexity estimation at large scales, because sample entropy does not give precise estimation of entropy when short signals are processed. A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. Nevertheless, RCMSE is for univariate signals only. The simultaneous analysis of multi-channel (multivariate) data often over-performs studies based on univariate signals. We therefore introduce an extension of RCMSE to multivariate data. Applications of multivariate RCMSE to simulated processes reveal its better performances over the standard multivariate MSE

Color Texture Analysis: A Survey

International audienc

Centered and Averaged Fuzzy Entropy to Improve Fuzzy Entropy Precision

International audienceSeveral entropy measures are now widely used to analyze real-world time series. Among them, we can cite approximate entropy, sample entropy and fuzzy entropy (FuzzyEn), the latter one being probably the most efficient among the three. However, FuzzyEn precision depends on the number of samples in the data under study. The longer the signal, the better it is. Nevertheless, long signals are often difficult to obtain in real applications. This is why we herein propose a new FuzzyEn that presents better precision than the standard FuzzyEn. This is performed by increasing the number of samples used in the computation of the entropy measure, without changing the length of the time series. Thus, for the comparisons of the patterns, the mean value is no longer a constraint. Moreover, translated patterns are not the only ones considered: reflected, inversed, and glide-reflected patterns are also taken into account. The new measure (so-called centered and averaged FuzzyEn) is applied to synthetic and biomedical signals. The results show that the centered and averaged FuzzyEn leads to more precise results than the standard FuzzyEn: the relative percentile range is reduced compared to the standard sample entropy and fuzzy entropy measures. The centered and averaged FuzzyEn could now be used in other applications to compare its performances to those of other already-existing entropy measures

Evaluation of Systems’ Irregularity and Complexity: Sample Entropy, Its Derivatives, and Their Applications across Scales and Disciplines

n/

Multivariate Generalized Multiscale Entropy Analysis

Multiscale entropy (MSE) was introduced in the 2000s to quantify systems’ complexity. MSE relies on (i) a coarse-graining procedure to derive a set of time series representing the system dynamics on different time scales; (ii) the computation of the sample entropy for each coarse-grained time series. A refined composite MSE (rcMSE)—based on the same steps as MSE—also exists. Compared to MSE, rcMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy for short time series. The multivariate versions of MSE (MMSE) and rcMSE (MrcMSE) have also been introduced. In the coarse-graining step used in MSE, rcMSE, MMSE, and MrcMSE, the mean value is used to derive representations of the original data at different resolutions. A generalization of MSE was recently published, using the computation of different moments in the coarse-graining procedure. However, so far, this generalization only exists for univariate signals. We therefore herein propose an extension of this generalized MSE to multivariate data. The multivariate generalized algorithms of MMSE and MrcMSE presented herein (MGMSE and MGrcMSE, respectively) are first analyzed through the processing of synthetic signals. We reveal that MGrcMSE shows better performance than MGMSE for short multivariate data. We then study the performance of MGrcMSE on two sets of short multivariate electroencephalograms (EEG) available in the public domain. We report that MGrcMSE may show better performance than MrcMSE in distinguishing different types of multivariate EEG data. MGrcMSE could therefore supplement MMSE or MrcMSE in the processing of multivariate datasets

The Multiscale Entropy Algorithm and Its Variants: A Review

Multiscale entropy (MSE) analysis was introduced in the 2002 to evaluate the complexity of a time series by quantifying its entropy over a range of temporal scales. The algorithm has been successfully applied in different research fields. Since its introduction, a number of modifications and refinements have been proposed, some aimed at increasing the accuracy of the entropy estimates, others at exploring alternative coarse-graining procedures. In this review, we first describe the original MSE algorithm. Then, we review algorithms that have been introduced to improve the estimation of MSE. We also report a recent generalization of the method to higher moments

Centered and Averaged Fuzzy Entropy to Improve Fuzzy Entropy Precision

Several entropy measures are now widely used to analyze real-world time series. Among them, we can cite approximate entropy, sample entropy and fuzzy entropy (FuzzyEn), the latter one being probably the most efficient among the three. However, FuzzyEn precision depends on the number of samples in the data under study. The longer the signal, the better it is. Nevertheless, long signals are often difficult to obtain in real applications. This is why we herein propose a new FuzzyEn that presents better precision than the standard FuzzyEn. This is performed by increasing the number of samples used in the computation of the entropy measure, without changing the length of the time series. Thus, for the comparisons of the patterns, the mean value is no longer a constraint. Moreover, translated patterns are not the only ones considered: reflected, inversed, and glide-reflected patterns are also taken into account. The new measure (so-called centered and averaged FuzzyEn) is applied to synthetic and biomedical signals. The results show that the centered and averaged FuzzyEn leads to more precise results than the standard FuzzyEn: the relative percentile range is reduced compared to the standard sample entropy and fuzzy entropy measures. The centered and averaged FuzzyEn could now be used in other applications to compare its performances to those of other already-existing entropy measures