Source Localization of EEG Brainwaves Activities via Mother Wavelets Families for SWT Decomposition

A Brain-Computer Interface (BCI) is a system used to communicate with an external world through the brain activity. The brain activity is measured by electroencephalography (EEG) signal and then processed by a BCI system. EEG source reconstruction could be a way to improve the accuracy of EEG classification in EEG based brain-computer interface (BCI). The source localization of the human brain activities can be an important resource for the recognition of the cognitive state, medical disorders, and a better understanding of the brain in general. In this study, we have compared 51 mother wavelets taken from 7 different wavelet families, which are applied to a Stationary Wavelet Transform (SWT) decomposition of an EEG signal. This process includes Haar, Symlets, Daubechies, Coiflets, Discrete Meyer, Biorthogonal, and reverse Biorthogonal wavelet families in extracting five different brainwave subbands for source localization. For this process, we used the Independent Component Analysis (ICA) for feature extraction followed by the Boundary Element Model (BEM) and the Equivalent Current Dipole (ECD) for the forward and inverse problem solutions. The evaluation results in investigating the optimal mother wavelet for source localization eventually identified the sym20 mother wavelet as the best choice followed by bior6.8 and coif5.

Continuous Empirical Wavelets Systems

The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a well-suited formalism and then investigate some general properties of empirical wavelet systems. In particular, we provide some sufficient conditions to the existence of a reconstruction formula. In the second part of the paper, we propose the construction of empirical wavelet systems based on some classic mother wavelets.

Stochastic wavelets from minimizers of an uncertainty principle: An example

This paper proposes a method through which a family of wavelets can be obtained. This is done by choosing each member based on a random variable. The method is preferred in situations where a single mother wavelet proves inadequate and an evolving sequence of mother wavelets is needed but a priori the next member in the sequence is uncertain. The adopted approach is distinct from the way spatiotemporal wavelets are used or even the way stochastic processes have been studied using spatiotemporal wavelets.

Using a boundary-corrected wavelet transform coupled with machine learning and hybrid deep learning approaches for multi-step water level forecasting in Lakes Michigan and Ontario

<p>Accurate water level (WL) forecasting is important for water resources management and planning purposes in the Great Lakes. The objectives of this research are two-fold.  The first objective is to apply machine learning (ML) (i.e., random forest (RF) and support vector regression (SVR)) and hybrid convolutional neural network(CNN)-long-short term memory (LSTM) deep learning (DL) models for multi-step (i.e., one-, two- and three-monthly step ahead) WL forecasting in the Great Lakes (Michigan and Ontario). The second objective is to integrate the boundary corrected (BC) maximal overlap discrete wavelet transform (MODWT) with SVR, RF, and CNN-LSTM models to improve the performance of the individual models. By employing a BC-wavelet decomposition method, the ‘future data’ issue (i.e., data from the future that is not available), often overlooked in the literature and a major barrier to achieving realistic forecasting performance is overcome. </p><p>For Lakes Michigan and Ontario, 1212 monthly WL (m) records (spanning Jan 1918–Dec 2018) were used to develop the models. For the non-wavelet-based models (SVR, RF, and CNN-LSTM), candidate model inputs included the WL recorded over the previous 12 months.  For the BC-MODWT-based models (BC-MODWT-SVR, BC-MODWT-RF, and BC-MODWT-CNN-LSTM), the lagged input time series were decomposed into BC-wavelet and scaling coefficients by using different mother wavelets (Haar, Daubechies, Symlets, Fejer-Korovkin and Coiflets), filter lengths (from two up to 12) and decomposition levels (from one up to seven).  For each method (SVR, RF, and CNN-LSTM), mother wavelet, and decomposition level a model was generated.  For both wavelet- and non-wavelet-based models, the particle swarm optimization (PSO) method was used to select the most appropriate inputs to include in the proposed multi-step WL forecasting models.</p><p>The datasets were partitioned into calibration and validation subsets. After calibrating the models, various performance evaluation metrics, e.g., coefficient of determination (R<sup>2</sup>), root mean square error (RMSE), mean absolute error (MAE), root mean square percentage error (RMSPE), mean absolute percentage error (MAPE) and the Nash-Sutcliffe efficiency coefficient (NSC) were used to assess model accuracy.</p><p>Of the ML models, the SVR outperformed RF while the DL models outperformed the ML models for each forecast lead time (one-, two-, and three-step(s) ahead). Results from this case study indicate that not all wavelet families and decomposition levels perform equally and in some cases, the wavelet-based models do not improve performance over the non-wavelet-based models. However, the BC-MODWT-CNN-LSTM using suitable mother wavelets (e.g., Haar) outperforms the individual ML and BC-MODWT-ML-based models. More accurate forecasts were obtained for Lake Michigan although the performance in both Great Lakes was accurate. The outcomes of this research indicate that the BC-MODWT-CNN-LSTM model is a promising tool for generating accurate WL forecasts.</p>

Comparison of Various Mother Wavelets for Fault Classification in Electrical Systems

This paper presents a comparative study on mother wavelets using a fault type classification algorithm in a power system. The study aims to evaluate the performance of the protection algorithm by implementing different mother wavelets for signal analysis and determines a suitable mother wavelet for power system protection applications. The factors that influence the fault signal, such as the fault location, fault type, and inception angle, have been considered during testing. The algorithm operates by applying the discrete wavelet transform (DWT) to the three-phase current and zero-sequence signal obtained from the experimental setup. The DWT extracts high-frequency components from the signals during both the normal and fault states. The coefficients at scales 1–3 have been decomposed using different mother wavelets, such as Daubechies (db), symlets (sym), biorthogonal (bior), and Coiflets (coif). The results reveal different coefficient values for the different mother wavelets even though the behaviors are similar. The coefficient for any mother wavelet has the same behavior but does not have the same value. Therefore, this finding has shown that the mother wavelet has a significant impact on the accuracy of the fault classification algorithm.

Appropriate Mother Wavelets for Continuous Gait Event Detection Based on Time-Frequency Analysis for Hemiplegic and Healthy Individuals

Gait event detection is a crucial step towards the effective assessment and rehabilitation of motor dysfunctions. Recently, the continuous wavelet transform (CWT) based methods have been increasingly proposed for gait event detection due to their robustness. However, few investigations on determining the appropriate mother wavelet with proper selection criteria have been performed, especially for hemiplegic patients. In this study, the performances of commonly used mother wavelets in detecting gait events were systematically investigated. The acceleration signals from the tibialis anterior muscle of both healthy and hemiplegic subjects were recorded during ground walking and the two core gait events of heel strike (HS) and toe off (TO) were detected from the signal recordings by a CWT algorithm with different mother wavelets. Our results showed that the overall performance of the CWT algorithm in detecting the two gait events was significantly different when using various mother wavelets. By using different wavelet selection criteria, we also found that the accuracy criteria based on time-error minimization and F1-score maximization could provide the appropriate mother wavelet for gait event detection. The findings from this study will provide an insight on the selection of an appropriate mother wavelet for gait event detection and facilitate the development of adequate rehabilitation aids.

Identification and Representation of Multi-Pulse Near-Fault Strong Ground Motion Using Adaptive Wavelet Transform

In order to identify the horizontal seismic motion owning the largest pulse energy, and represent the dominant pulse-like component embedded in this seismic motion, we used the adaptive wavelet transform algorithm in this paper. Fifteen candidate mother wavelets were evaluated to select the optimum wavelet based on the similarities between the candidate mother wavelet and the target seismic motion, evaluated by the minimum cross variance. This adaptive choosing algorithm for the optimum mother wavelet was invoked before identifying both the horizontal direction owning the largest pulse energy and every dominant pulse, which provides the optimum mother wavelet for the continuous wavelet transform. Each dominant pulse can be represented by its adaptively selected optimum mother wavelet. The results indicate that the identified multi-pulse component fits well with the seismic motion. In most cases, mother wavelets in one multi-pulse seismic motion were different from each other. For the Chi-Chi event (1999-Sep-20 17:47:16 UTC, Mw = 7.6), 62.26% of the qualified pulse-like earthquake motions lay in the horizontal direction ranging from ±15° to ±75°. The Daubechies 6 (db6) mother wavelet was the most frequently used type for both the first and second pulse components.