Wavelet Transform Research Articles

Besov‐Type Spaces Associated With Dunkl Wavelet Transform on ℝ$$ \mathbb{R} $$

ABSTRACTWe define the Besov‐type spaces related to Dunkl transform. We extend the concept of continuous wavelet transform on space and derive continuity of Dunkl wavelet transform on Besov‐type spaces. We characterize the Besov–Dunkl space by using Dunkl wavelet coefficients. Lastly, boundedness results in a generalized Besov space and Lizorkin–Triebel space are discussed.

Impact of Texture Feature Count on the Accuracy of Osteoporotic Change Detection in Computed Tomography Images of Trabecular Bone Tissue

The aim of this study is to compare the classification accuracy depending on the number of texture features used. This study used 400 computed tomography (CT) images of trabecular spinal tissue from 100 patients belonging to two groups (50 control patients and 50 patients diagnosed with osteoporosis). The descriptors of texture features were based on a gray level histogram, gradient matrix, RL matrix, event matrix, an autoregressive model, and wavelet transformation. From the 290 obtained texture features, the features with fixed values were eliminated and structured according to the feature importance ranking. The classification performance was assessed using 267, 200, 150, 100, 50, 20, and 10 texture features to build classifiers. The classifiers applied in this study included Naive Bayes, Multilayer Perceptron, Hoeffding Tree, K-nearest neighbors, and Random Forest. The following indicators were used to assess the quality of the classifiers: accuracy, sensitivity, specificity, precision, negative predictive value, Matthews correlation coefficient, and F1 score. The highest performance was achieved by the K-Nearest Neighbors (K = 1) and Multilayer Perceptron classifiers. KNN demonstrated the best results with 50 features, attaining a highest F1 score of 96.79% and accuracy (ACC) of 96.75%. MLP achieved its optimal performance with 100 features, reaching an accuracy and F1 score of 96.50%. This demonstrates that building a classifier using a larger number of features, without a selection process, allows us to achieve high classification effectiveness and holds significant diagnostic value.

Vibroarthrographic Signal Classification for Knee Joint Disorder Detection using Tunable Q-factor Wavelet Transform based on Entropy Measures

Research on Vibroarthrographic (VAG) signals presents a promising means for the early diagnosis of knee joint disorders. However, the classification problem for these signals faces serious issues due to their complex and dynamic nature. This study proposes a novel method for decomposing and analyzing VAG signals based on a Tunable Q-factor Wavelet Transform (TQWT) and entropy-based measures. TQWT is used to preprocess and decompose VAG signals recorded during knee motion into subbands. Different entropy metrics, such as approximate entropy, sample entropy, fuzzy entropy, slope entropy, and so on, were computed over different subbands of the signal to capture significant signal features. Effective features were selected using Recursive Feature Elimination (RFE) and then classified using ensemble classifiers such as XGBoost, Ensemble Random Forest (ERF), and RF-logistic regression. The classification accuracy of the proposed sample entropy method was 87.64% and had 90% sensitivity, 86.36% specificity, and 0.88 AUC-ROC. These results demonstrate the ability of the TQWT-based approach to discriminate knee joint abnormalities. Future work will explore performance scaling with larger datasets and apply it to other joint disorders.

Implementation of a Deep Learning ANN-based Algorithm utilizing the IEEE 34 Bus Test System to Investigate the Effects of Distributed Generation on Fault Diagnosis in Distribution Networks

Electrical distribution systems are undergoing significant modifications since the application of new technologies. New possibilities for automated, dependable, and efficient electrical power grids have been made possible by the technological advancement. While new technologies might improve electrical network performance and offer creative solutions to future network difficulties, they can also have unintended consequences that need to be carefully studied and considered. A recent technological advancement that enhances power grid performance is Distributed Generation (DG). While DG unit integration has measurable benefits for electrical grids, its significant effects on power network protection systems create many questions and difficulties about the proper way to identify and isolate distribution network faults. The DLANN-based approach looks into the ways the integration of DGs affects fault identification and location. This method involves two steps: first, three-phase currents are constantly analyzed for detection, and Discrete Wavelet Transform (DWT) is utilized to extract the currents' features. The second step is classification employing Artificial Neural Networks (ANNs) to pinpoint the defective stages. Counting the shorted phases will reveal the sort of short circuit. The MATLAB programming environment is utilized in the development of the fault identification and classification technique. The fault type (one, two, or three phases), fault resistance, fault location bus, fault distance, and the DG type (upstream or downstream) are all considered. The methodology is used on a modified IEEE 34-bus test system, and four scenarios, one with combined DGs units, one with IBDGs, one with SBDGs, and one without DGs, are modeled. As per the simulation results, 100% fault detection and classification accuracy were obtained, whereas the average fault location accuracy attained without DGs, with IBDGs, SBDGs and combined DGs for selected nodes were 99.94%, 99.91%, 99.86%, and 99.88%, respectively

Using stacking ensemble learning to predict multi-step wind speed based on wavelet transformation, two-steps feature selection method, and neural networks

Using stacking ensemble learning to predict multi-step wind speed based on wavelet transformation, two-steps feature selection method, and neural networks

A Method of EEG Signal Feature Extraction Based on Hybrid DWT and EMD

The processing and recognition of electroencephalogram (EEG) signal is the most important part of brain-computer interface (BCI) system, and the quality of signal processing and recognition is directly related to the effectiveness of BCI system. Aiming at the problems of incomplete removal of artifacts and inadequate retention of active components in EEG signal, a fusion method of wavelet transform (WT) and Fast Independent Component Analysis (FastICA) is utilized to preprocess the raw EEG signals. The fusion method can remove noise artifacts while preserving effective information. Aiming at the problems of poor time-frequency resolution and low classification accuracy of the traditional feature extraction method, a feature extraction algorithm on the basis of hybrid Discrete Wavelet Transform (DWT) and Empirical Mode Decomposition (EMD) is proposed. Firstly, DWT is used to analyze the pre-processed EEG signal to obtain a series of sub-band signals. Then, EMD decomposition is applied to subband signal and eigenmode function is extracted to complete feature integration. Finally, the feature extraction results are input into the Support Vector Machine (SVM) for classification. Comparative experiments show that the classification accuracy of the proposed method reaches 91.32%, which is significantly higher than other algorithms.

A combined wavelet analysis-quantile mapping (WA-QM) method for bias correction: capturing the intra-annual temporal patterns in climate model precipitation simulations and projections

Abstract Despite recent improvements, global climate models (GCMs) still have biases that prevent their direct application. Quantile mapping (QM) has been widely used in bias correction (BC) due to its effectiveness in aligning the cumulative density function of climate model data with observations. However, QM has a significant limitation: it fails to consider the temporal correspondence between the model data and observations, which restricts its ability to represent intra-annual temporal patterns. To address this issue, this study integrated wavelet analysis (WA) into QM to develop a combined method termed WA-QM, which aimed to preserve QM’s efficacy in overall BC and preservation of climate change signals, while capturing the intra-annual temporal patterns. The effectiveness of WA-QM was investigated using monthly precipitation data from five Coupled Model Intercomparison Project Phase 6 models in the Pan Third Pole region, which includes Central Asia (CA), Southeast Asia, and the Tibetan Plateau. Quantile delta mapping (QDM) and scaled distribution mapping (SDM) served as the benchmark methods for assessment. The results indicated that integrating WA into QDM or SDM did not compromise the ability of QDM or SDM to correct overall biases and preserve the model’s climate change signal. Furthermore, WA could be an effective tool to overcome QM’s limitation in capturing intra-annual temporal patterns. The WA approach employed discrete wavelet transformation to decompose GCM data into various frequency bands and then adjusted their standard deviations and signs to ensure that their relative relationships were consistent with those in observations. Compared to the standalone QM approach, WA-QM showed greater accuracy in monthly statistical metrics. In the CA region, WA-SDM reduced the monthly root mean square error of the mean by 25.2%, the standard deviation by 17.6%, and the 90th percentile by 26.7% compared to SDM. The effectiveness of WA-QM was demonstrated across different data periods, spatial areas, and GCMs.

Coupled SWAT, Stationary Wavelet Transform, and Interpretable Machine Learning to Improve Watershed Streamflow Simulation

Coupled SWAT, Stationary Wavelet Transform, and Interpretable Machine Learning to Improve Watershed Streamflow Simulation

Analysis of Different Noise Reduction Effects of Ground Penetrating Radar Image of Cavity Behind Tunnel Primary Support Based on Singular Value Decomposition and Wavelet Transform

The cavity behind the lining structure is a typical disease in tunnel engineering. Cavity seriously affects the interaction between lining and surrounding rock, resulting in uneven bearing of lining structure and stress concentration, which can easily induce lining concrete cracking, water leakage and other diseases. Accurate identification of lining structure cavities is the key to ensure the normal operation of the tunnel. However, the ground penetrating radar detection images of lining cavities often contain interference signals such as background noise, which seriously affects the accuracy and clarity of cavity detection. The application effects of wavelet transform and singular value decomposition in image denoising and resolution of tunnel lining cavity ground penetrating radar are studied. Under this background, the model test of regular and irregular cavity detection behind tunnel lining is carried out, in which the irregular cavity is located in the surrounding rock environment of filling soil to simulate the real situation of tunnel. The measured images of lining cavity under different working conditions are obtained, and the image denoising analysis is carried out. The results show that singular value decomposition can effectively suppress noise. The ground penetrating radar image after singular value decomposition denoising is clearer, and the image resolution is effectively improved, thus realizing the accurate identification of cavity diseases behind the primary support of the tunnel

Automated classification of cardiac arrhythmia using short-duration ECG signals and machine learning

Accurate detection of cardiac arrhythmias is crucial for preventing premature deaths. The current study employs a dual-stage Discrete Wavelet Transform (DWT) and a median filter to eliminate noise from ECG signals. Subsequently, ECG signals are segmented, and QRS regions are extracted for further preprocessing. The study considers five cardiac arrhythmias: normal beats, Premature Ventricular Contractions (PVC), Premature Atrial Contractions (PAC), Right Bundle Branch Block (R-BBB), and Left Bundle Branch Block (L-BBB) for classification. Nine distinct temporal features are extracted from the segmented QRS complex. These features are then applied to six different classifiers for arrhythmia classification. The classifiers' performance is evaluated using the MIT-BIH Arrhythmia Database (MIT-BIH AD). Support Vector Machine (SVM) and Ensemble Tree classifiers demonstrate superior performance in classifying the five different classes. Particularly, the Support Vector Machine classifier achieves high sensitivity (97.44%), specificity (99.36%), positive predictive value (97.44%), and accuracy (98.97%) with a Gaussian kernel. This comprehensive approach, integrating preprocessing, and feature extraction, holds promise for improving automatic cardiac arrhythmia classification in clinical trials.

STIT-Net- A Wavelet based Convolutional Transformer Model for Motor Imagery EEG Signal Classification in the Sensorimotor Bands.

Motor Imagery (MI) electroencephalographic (EEG) signal classification is a pioneer research branch essential for mobility rehabilitation. This paper proposes an end-to-end hybrid deep network "Spatio Temporal Inception Transformer Network (STIT-Net)" model for MI classification. Discrete Wavelet Transform (DWT) is used to derive the alpha (8-13) Hz and beta (13-30) Hz EEG sub bands which are dominant during motor tasks to enhance the performance of the proposed work. STIT-Net employs spatial and temporal convolutions to capture spatial dependencies and temporal information and an inception block with three parallel convolutions extracts multi-level features. Then the transformer encoder with self-attention mechanism highlights the similar task. The proposed model improves the classification of the Physionet EEG motor imagery dataset with an average accuracy of 93.52% and 95.70% for binary class in the alpha and beta bands respectively, and 85.26% and 87.34% for three class, for four class 81.95% and 82.66% were obtained in the alpha and beta band respective EEG based motor signals which is better compared to the results available in the literature. The proposed methodology is further evaluated on other motor imagery datasets, both for subject-independent and cross-subject conditions, to assess the performance of the model.

Prediction and decoding of metaverse coin dynamics: a granular quest using MODWT-Facebook’s prophet-TBATS and XAI methodology

Abstract The growing media buzz and industry focus on the emergence and rapid development of Metaverse technology have paved the way for the escalation of multifaceted research. Specific Metaverse coins have come into existence, but they have barely seen any traction among practitioners despite their tremendous potential. The current work endeavors to deeply analyze the temporal characteristics of 6 Metaverse coins through the lens of predictive analytics and explain the forecasting process. The dearth of research imposes serious challenges in building the forecasting model. We resort to a granular prediction setup incorporating the Maximal Overlap Discrete Wavelet Transformation (MODWT) technique to disentangle the original series into subseries. Facebook's Prophet and TBATS algorithms are utilized to individually draw predictions on granular components. Aggregating components-wise forecasted figures achieve the final forecast. Facebook's Prophet is deployed in a multivariate setting, applying a set of explanatory features covering macroeconomic, technical, and social media indicators. Rigorous performance checks justify the efficiency of the integrated forecasting framework. Additionally, to interpret the black box typed prediction framework, two explainable artificial intelligence (XAI) frameworks, SHAP and LIME, are used to gauge the nature of the influence of the predictor variables, which serve several practical insights.

Wavelet‐Based Stochastic Model for the Generation of Fully Nonstationary Bidirectional Seismic Accelerograms

ABSTRACTA new stochastic methodology is proposed for the generation of bidirectional horizontal components of artificial, fully nonstationary, site‐ and spectrum‐compatible seismic accelerograms through a nonseparable process. The model operates in the time‐frequency domain and combines spectral representation techniques with signal processing tools. The basis of the methodology involves the generation of spectrum‐compatible stationary artificial accelerogram signals whose nonstationarity is then modeled with a time‐frequency modulating function that is based on a seed ground motion record. At the core of the proposed methodology lies the use of the Continuous Wavelet Transform (CWT). Specifically, the CWT method is used to perform time‐frequency analysis and to define the nonstationary component. The proposed methodology provides any required number of seismic accelerograms whose temporal and spectral modulation is consistent with the characteristics of the site of interest. Furthermore, the model is extended to the case of pairs of bidirectional horizontal components. This is accomplished by probabilistically generating two orthogonal spectra whose geometric mean spectrum is compatible with a target spectrum. This procedure also takes into account the correlation structure of spectral acceleration pairs in orthogonal directions at different periods based on empirical models. The bidirectional components are then generated with the proposed site and spectrum‐based methodology. An online tool that implements the proposed methodology is freely provided.

A wavelet packet transform-based domain adaptation method for rolling bearings fault diagnosis with fusion of local and global time–frequency features

Abstract Fault diagnosis transfer learning models commonly employ deep neural networks (DNN) to analyze time-frequency features. However, excessively deep neural networks can result in diminished generalization capabilities, leading to subpar performance of the model across various working conditions. Furthermore, inappropriate domain adaptation strategies significantly constrain the accuracy of the model. To address this issue, a Robustly Optimized Residual-Network and Vision Transformer Domain Adaptation Model (RoReViTDAM) is proposed in this article, combining Wavelet Packet Transform (WPT), residual networks, and self-attention mechanisms. Firstly, the WPT is utilized to construct Multi-band Wavelet Coefficient Matrix (MWCM) and corresponding Multi-band Wavelet Coefficient Time-Frequency Feature Matrix (MWSM) with small size and feature aggregation. Subsequently, a shallow Robustly Optimized Residual Network (RoResNet) is designed to effectively extract features from MWCM, considering the spatial distance dependencies of features. Additionally, ViT (Vision Transformer) is employed for time-frequency global feature extraction from MWSM. Furthermore, Domain Adversarial Neural Network (DANN) and Multi-Kernel Maximum Mean Discrepancy (MK-MMD) are employed to extract domain-invariant features from signals of different operating conditions and fault types. At last, three fault diagnosis experiments are conducted in multi-condition scenarios of bearings. The experimental results illustrate the superiority and effectiveness of the proposed model.

Optimizing Image Watermarking with Dual-Tree Complex Wavelet Transform and Particle Swarm Intelligence for Secure and High-Quality Protection

Watermarking is a technique used to address issues related to the widespread use of the internet, such as copyright protection, tamper localization, and authentication. However, most watermarking approaches negatively affect the quality of the original image. In this research, we propose an optimized image watermarking approach that utilizes the dual-tree complex wavelet transform and particle swarm optimization algorithm. Our approach focuses on maintaining the highest possible quality of the watermarked image by minimizing any noticeable changes. During the embedding phase, we break down the original image using a technique called dual-tree complex wavelet transform (DTCWT) and then use particle swarm optimization (PSO) to choose specific coefficients. We embed the bits of a binary logo into the least significant bits of these selected coefficients, creating the watermarked image. To extract the watermark, we reverse the embedding process by first decomposing both versions of the input image using DTCWT and extracting the same coefficients to retrieve those corresponding bits (watermark). In our experiments, we used a common dataset from watermarking research to demonstrate the functionality against various watermarked copies and peak signal-to-noise ratio (PSNR) and normalized cross-correlation (NCC) metrics. The PSNR is a measure of how well the watermarked image maintains its original quality, and the NCC reflects how accurately the watermark can be extracted. Our method gives mean PSNR and NCC of 80.50% and 92.51%, respectively.

Time–Frequency Transformations for Enhanced Biomedical Signal Classification with Convolutional Neural Networks

Background: Transforming one-dimensional (1D) biomedical signals into two-dimensional (2D) images enables the application of convolutional neural networks (CNNs) for classification tasks. In this study, we investigated the effectiveness of different 1D-to-2D transformation methods to classify electrocardiogram (ECG) and electroencephalogram (EEG) signals. Methods: We select five transformation methods: Continuous Wavelet Transform (CWT), Fast Fourier Transform (FFT), Short-Time Fourier Transform (STFT), Signal Reshaping (SR), and Recurrence Plots (RPs). We used the MIT-BIH Arrhythmia Database for ECG signals and the Epilepsy EEG Dataset from the University of Bonn for EEG signals. After converting the signals from 1D to 2D, using the aforementioned methods, we employed two types of 2D CNNs: a minimal CNN and the LeNet-5 model. Our results indicate that RPs, CWT, and STFT are the methods to achieve the highest accuracy across both CNN architectures. Results: These top-performing methods achieved accuracies of 99%, 98%, and 95%, respectively, on the minimal 2D CNN and accuracies of 99%, 99%, and 99%, respectively, on the LeNet-5 model for the ECG signals. For the EEG signals, all three methods achieved accuracies of 100% on the minimal 2D CNN and accuracies of 100%, 99%, and 99% on the LeNet-5 2D CNN model, respectively. Conclusions: This superior performance is most likely related to the methods’ capacity to capture time–frequency information and nonlinear dynamics inherent in time-dependent signals such as ECGs and EEGs. These findings underline the significance of using appropriate transformation methods, suggesting that the incorporation of time–frequency analysis and nonlinear feature extraction in the transformation process improves the effectiveness of CNN-based classification for biological data.

Long-Term Forecasting of Solar Irradiation in Riyadh, Saudi Arabia, Using Machine Learning Techniques

Forecasting of time series data presents some challenges because the data’s nature is complex and therefore difficult to accurately forecast. This study presents the design and development of a novel forecasting system that integrates efficient data processing techniques with advanced machine learning algorithms to improve time series forecasting across the sustainability domain. Specifically, this study focuses on solar irradiation forecasting in Riyadh, Saudi Arabia. Efficient and accurate forecasts of solar irradiation are important for optimizing power production and its smooth integration into the utility grid. This advancement supports Saudi Arabia in Vision 2030, which aims to generate and utilize renewable energy sources to drive sustainable development. Therefore, the proposed forecasting system has been developed to the parameters characteristic of the Riyadh region environment, including high solar intensity, dust storms, and unpredictable weather conditions. After the cleaning and filtering process, the filtered dataset was pre-processed using the standardization method. Then, the Discrete Wavelet Transform (DWT) technique has been applied to extract the features of the pre-processed data. Next, the extracted features of the solar dataset have been split into three subsets: train, test, and forecast. Finally, two different machine learning techniques have been utilized for the forecasting process: Support Vector Machine (SVM) and Gaussian Process (GP) techniques. The proposed forecasting system has been evaluated across different time horizons: one-day, five-day, ten-day, and fifteen-day ahead. Comprehensive evaluation metrics were calculated including accuracy, stability, and generalizability measures. The study outcomes present the proposed forecasting system which provides a more robust and adaptable solution for time-series long-term forecasting and complex patterns of solar irradiation in Riyadh, Saudi Arabia.

Estimation of Time Varying Boundaries and Filtering of Empirical Wavelet Transform with Application to Adaptive Nonstationary Signal Decomposition

Estimation of Time Varying Boundaries and Filtering of Empirical Wavelet Transform with Application to Adaptive Nonstationary Signal Decomposition

Extraction of wavelet-based damage-sensitive features for concrete moment-resisting frames

This paper aims to derive conventional wavelet-based damage-sensitive features (WB-DSFs) and refined wavelet-based damage-sensitive features (rWB-DSFs) for concrete moment-resisting frames (MRFs) and detection of the best mother wavelet. For this purpose, wavelet-based and refined wavelet-based damage-sensitive features extracted from the absolute acceleration responses of building models subjected to different ground motion records were evaluated by using the continuous wavelet transform. Three concrete moment-resisting frames with four-, eight- and twelve-story building frames were selected to implement wavelet-based and refined wavelet-based damage-sensitive features. The wavelet coefficients were calculated from the acceleration signals, and different damage-sensitive features were specified by wavelet energies based on the appropriate scales and times. Then, the conventional wavelet-based damage-sensitive features were modified to address the effects of higher mode contributions. The results confirmed the efficiency of wavelet-based and refined wavelet-based damage-sensitive features for damage diagnosis and migration of these damage-sensitive features during damage progress. Furthermore, the findings of this study showed that the mother wavelet family of bior3.3 yields more accurate damage diagnosis states for reinforced concrete moment-resisting frames. The results show that the damage pattern, as well as the damaged floor can be detected using the proposed wavelet-based damage-sensitive features.

Wavelet Transform Cluster Analysis of UAV Images for Sustainable Development of Smart Regions Due to Inspecting Transport Infrastructure

Sustainable development of the Smart Cities and Smart Regions concept is impossible without the development of a modern transport infrastructure, which must be maintained in proper condition. Inspections are required to assess the condition of objects in the transport infrastructure (OTI). Moreover, the efficiency of these inspections can be enhanced with unmanned aerial vehicles (UAVs), whose application areas are continuously expanding. When inspecting OTI (bridges, highways, etc.) the problem of improving the quality of image processing, and analysis of data collected by UAV, for example, is particularly relevant. The application of advanced methods for assessing the quantity of information and making decisions to reduce information uncertainty and redundancy for such systems is often complicated by the presence of noise there. To harmonize the characteristics of certain procedures in such conditions, authors propose conducting data processing using wavelet transform clustering in three main phases: determining the number of clusters, defining the coordinates of cluster centres, and assessing the quality and efficiency of clustering. We compared the efficiency and quality of existing clustering methods with one using wavelet transform. The research has shown that UAVs can be used for OTI inspecting; moreover, the clustering method with wavelet transform is characterised by an improved quality and efficiency of data processing. In addition, the quality assessment enables us to assess the degree of approximation of the clustering result to the ideal one. In addition, authors examined the specific challenges associated with planning UAV flights during inspections to obtain data that will enhance the accuracy of clustering and recognition. This is especially important for a comprehensive quantitative assessment of adaptation degree for image processing procedures to the tasks of inspecting OTI “Smart Cities/Regions” based on a pragmatic measure of informativeness.