Hamed Azami

Dispersion Entropy: A Measure for Time-Series Analysis

One of the most powerful tools to assess the dynamical characteristics of time series is entropy. Sample entropy (SE), though powerful, is not fast enough, especially for long signals. Permutation entropy (PE), as a broadly used irregularity indicator, considers only the order of the amplitude values and hence some information regarding the amplitudes may be discarded. To tackle these problems, we introduce a new method, termed dispersion entropy (DE), to quantify the regularity of time series. We gain insight into the dependency of DE on several straightforward signal-processing concepts via a set of synthetic time series. The results show that DE, unlike PE, can detect the noise bandwidth and simultaneous frequency and amplitude change. We also employ DE to three publicly available real datasets. The simulations on real-valued signals show that the DE method considerably outperforms PE to discriminate different groups of each dataset. In addition, the computation time of DE is significantly less than that of SE and PE.

Improved multiscale permutation entropy for biomedical signal analysis: Interpretation and application to electroencephalogram recordings

Abstract Permutation entropy (PE) is a well-known and fast method extensively used in many physiological signal processing applications to measure the irregularity of time series. Multiscale PE (MPE) is based on assessing the PE for a number of coarse-grained sequences representing temporal scales. However, the stability of the conventional MPE may be compromised for short time series. Here, we propose an improved MPE (IMPE) to reduce the variability of entropy measures over long temporal scales, leading to more reliable and stable results. We gain insight into the dependency of MPE and IMPE on several straightforward signal processing concepts which appear in biomedical activity via a set of synthetic signals. We also apply these techniques to real biomedical signals via publicly available electroencephalogram (EEG) recordings acquired with eyes open and closed and to ictal and non-ictal intracranial EEGs. We conclude that IMPE improves the reliability of the entropy estimations in comparison with the traditional MPE and that it is a promising technique to characterize physiological changes affecting several temporal scales. We provide the source codes of IMPE and the synthetic data in the public domain.

Amplitude-aware permutation entropy

BACKGROUND AND OBJECTIVE Signal segmentation and spike detection are two important biomedical signal processing applications. Often, non-stationary signals must be segmented into piece-wise stationary epochs or spikes need to be found among a background of noise before being further analyzed. Permutation entropy (PE) has been proposed to evaluate the irregularity of a time series. PE is conceptually simple, structurally robust to artifacts, and computationally fast. It has been extensively used in many applications, but it has two key shortcomings. First, when a signal is symbolized using the Bandt-Pompe procedure, only the order of the amplitude values is considered and information regarding the amplitudes is discarded. Second, in the PE, the effect of equal amplitude values in each embedded vector is not addressed. To address these issues, we propose a new entropy measure based on PE: the amplitude-aware permutation entropy (AAPE). METHODS AAPE is sensitive to the changes in the amplitude, in addition to the frequency, of the signals thanks to it being more flexible than the classical PE in the quantification of the signal motifs. To demonstrate how the AAPE method can enhance the quality of the signal segmentation and spike detection, a set of synthetic and realistic synthetic neuronal signals, electroencephalograms and neuronal data are processed. We compare the performance of AAPE in these problems against state-of-the-art approaches and evaluate the significance of the differences with a repeated ANOVA with post hoc Tukeys test. RESULTS In signal segmentation, the accuracy of AAPE-based method is higher than conventional segmentation methods. AAPE also leads to more robust results in the presence of noise. The spike detection results show that AAPE can detect spikes well, even when presented with single-sample spikes, unlike PE. For multi-sample spikes, the changes in AAPE are larger than in PE. CONCLUSION We introduce a new entropy metric, AAPE, that enables us to consider amplitude information in the formulation of PE. The AAPE algorithm can be used in almost every irregularity-based application in various signal and image processing fields. We also made freely available the Matlab code of the AAPE.

A hybrid evolutionary approach to segmentation of non-stationary signals

Automatic segmentation of non-stationary signals such as electroencephalogram (EEG), electrocardiogram (ECG) and brightness of galactic objects has many applications. In this paper an improved segmentation method based on fractal dimension (FD) and evolutionary algorithms (EAs) for non-stationary signals is proposed. After using Kalman filter (KF) to reduce existing noises, FD which can detect the changes in both the amplitude and frequency of the signal is applied to reveal segments of the signal. In order to select two acceptable parameters of FD, in this paper two authoritative EAs, namely, genetic algorithm (GA) and imperialist competitive algorithm (ICA) are used. The proposed approach is applied to synthetic multi-component signals, real EEG data, and brightness changes of galactic objects. The proposed methods are compared with some well-known existing algorithms such as improved nonlinear energy operator (INLEO), Varri@?s and wavelet generalized likelihood ratio (WGLR) methods. The simulation results demonstrate that segmentation by using KF, FD, and EAs have greater accuracy which proves the significance of this algorithm.

An intelligent approach for variable size segmentation of non-stationary signals

In numerous signal processing applications, non-stationary signals should be segmented to piece-wise stationary epochs before being further analyzed. In this article, an enhanced segmentation method based on fractal dimension (FD) and evolutionary algorithms (EAs) for non-stationary signals, such as electroencephalogram (EEG), magnetoencephalogram (MEG) and electromyogram (EMG), is proposed. In the proposed approach, discrete wavelet transform (DWT) decomposes the signal into orthonormal time series with different frequency bands. Then, the FD of the decomposed signal is calculated within two sliding windows. The accuracy of the segmentation method depends on these parameters of FD. In this study, four EAs are used to increase the accuracy of segmentation method and choose acceptable parameters of the FD. These include particle swarm optimization (PSO), new PSO (NPSO), PSO with mutation, and bee colony optimization (BCO). The suggested methods are compared with other most popular approaches (improved nonlinear energy operator (INLEO), wavelet generalized likelihood ratio (WGLR), and Varri’s method) using synthetic signals, real EEG data, and the difference in the received photons of galactic objects. The results demonstrate the absolute superiority of the suggested approach.

Refined Composite Multiscale Dispersion Entropy and its Application to Biomedical Signals

Objective: We propose a novel complexity measure to overcome the deficiencies of the widespread and powerful multiscale entropy (MSE), including, MSE values may be undefined for short signals, and MSE is slow for real-time applications. Methods: We introduce multiscale dispersion entropy (DisEn—MDE) as a very fast and powerful method to quantify the complexity of signals. MDE is based on our recently developed DisEn, which has a computation cost of O(N), compared with O(N2) for sample entropy used in MSE. We also propose the refined composite MDE (RCMDE) to improve the stability of MDE. Results: We evaluate MDE, RCMDE, and refined composite MSE (RCMSE) on synthetic signals and three biomedical datasets. The MDE, RCMDE, and RCMSE methods show similar results, although the MDE and RCMDE are faster, lead to more stable results, and discriminate different types of physiological signals better than MSE and RCMSE. Conclusion: For noisy short and long time series, MDE and RCMDE are noticeably more stable than MSE and RCMSE, respectively. For short signals, MDE and RCMDE, unlike MSE and RCMSE, do not lead to undefined values. The proposed MDE and RCMDE are significantly faster than MSE and RCMSE, especially for long signals, and lead to larger differences between physiological conditions known to alter the complexity of the physiological recordings. Significance : MDE and RCMDE are expected to be useful for the analysis of physiological signals thanks to their ability to distinguish different types of dynamics. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/1982.

Univariate and Multivariate Generalized Multiscale Entropy to Characterise EEG Signals in Alzheimer’s Disease

Alzheimer’s disease (AD) is a degenerative brain disorder leading to memory loss and changes in other cognitive abilities. The complexity of electroencephalogram (EEG) signals may help to characterise AD. To this end, we propose an extension of multiscale entropy based on variance (MSEσ2) to multichannel signals, termed multivariate MSEσ2 (mvMSEσ2), to take into account both the spatial and time domains of time series. Then, we investigate the mvMSEσ2 of EEGs at different frequency bands, including the broadband signals filtered between 1 and 40 Hz, θ, α, and β bands, and compare it with the previously-proposed multiscale entropy based on mean (MSEµ), multivariate MSEµ (mvMSEµ), and MSEσ2, to distinguish different kinds of dynamical properties of the spread and the mean in the signals. Results from 11 AD patients and 11 age-matched controls suggest that the presence of broadband activity of EEGs is required for a proper evaluation of complexity. MSEσ2 and mvMSEσ2 results, showing a loss of complexity in AD signals, led to smaller p-values in comparison with MSEµ and mvMSEµ ones, suggesting that the variance-based MSE and mvMSE can characterise changes in EEGs as a result of AD in a more detailed way. The p-values for the slope values of the mvMSE curves were smaller than for MSE at large scale factors, also showing the possible usefulness of multivariate techniques.

Extracellular spike detection from multiple electrode array using novel intelligent filter and ensemble fuzzy decision making.

BACKGROUND The information obtained from signal recorded with extracellular electrodes is essential in many research fields with scientific and clinical applications. These signals are usually considered as a point process and a spike detection method is needed to estimate the time instants of action potentials. In order to do so, several steps are taken but they all depend on the results of the first step, which filters the signals. To alleviate the effect of noise, selecting the filter parameters is very time-consuming. In addition, spike detection algorithms are signal dependent and their performance varies significantly when the data change. NEW METHODS We propose two approaches to tackle the two problems above. We employ ensemble empirical mode decomposition (EEMD), which does not require parameter selection, and a novel approach to choose the filter parameters automatically. Then, to boost the efficiency of each of the existing methods, the Hilbert transform is employed as a pre-processing step. To tackle the second problem, two novel approaches, which use the fuzzy and probability theories to combine a number of spike detectors, are employed to achieve higher performance. RESULTS, COMPARISON WITH EXISTING METHOD(S) AND CONCLUSIONS The simulation results for realistic synthetic and real neuronal data reveal the improvement of the proposed spike detection techniques over state-of-the art approaches. We expect these improve subsequent steps like spike sorting.

Spike detection approaches for noisy neuronal data: Assessment and comparison

Spike detection in extracellular recordings is a difficult problem, especially when there are several noise sources. In this paper, three new approaches based on fractal dimension (FD), smoothed nonlinear energy operator (SNEO) and standard deviation to detect the spikes for noisy neuronal data are proposed. These methods however do not perform well in some cases, especially when the noise level is high. To overcome these problems, we use five smoothing techniques, namely, discrete wavelet transform (DWT), Kalman filter (KF), singular spectrum analysis (SSA), Savitzgy-Golay filter, and empirical mode decomposition (EMD). Although filtering approach based on EMD is relatively slow, when SNRs>0dB, those approaches which use EMD have the best efficiency and accuracy. While SNRs<0 dB, it is demonstrated that for SSA followed by SNEO, the performance in terms of the average spikes detection accuracy and CPU time is the most desirable.

Automatic signal segmentation based on singular spectrum analysis and imperialist competitive algorithm

Electroencephalogram (EEG) is generally known as a non-stationary signal. Dividing a signal into the epochs within which the signals can be considered stationary, segmentation, is very important in many signal processing applications. Noise often influences the performance of an automatic signal segmentation system. In this article, a new approach for segmentation of the EEG signals based on singular spectrum analysis (SSA) and imperialist competitive algorithm (ICA) is proposed. As the first step, SSA is employed to reduce the effect of various noise sources. Then, fractal dimension (FD) of the signal is estimated and used as a feature extraction for automatic segmentation of the EEG. In order to select two acceptable parameters related to the FD, ICA that is a more powerful evolutionary algorithm than traditional ones is applied. By using synthetic and real EEG signals, the proposed method is compared with original approach (i.e. without using SSA and ICA). The simulation results show that the speed of SSA is much better than that of the discrete wavelet transform (DWT) which has been one of the most popular preprocessing filters for signal segmentation. Also, the simulation results indicate the performance superiority of the proposed method.