Wavelet Filter Research Articles

A Hybrid Scattering Transform for Signals with Isolated Singularities.

The scattering transform is a wavelet-based model of Convolutional Neural Networks originally introduced by S. Mallat. Mallat's analysis shows that this network has desirable stability and invariance guarantees and therefore helps explain the observation that the filters learned by early layers of a Convolutional Neural Network typically resemble wavelets. Our aim is to understand what sort of filters should be used in the later layers of the network. Towards this end, we propose a two-layer hybrid scattering transform. In our first layer, we convolve the input signal with a wavelet filter transform to promote sparsity, and, in the second layer, we convolve with a Gabor filter to leverage the sparsity created by the first layer. We show that these measurements characterize information about signals with isolated singularities. We also show that the Gabor measurements used in the second layer can be used to synthesize sparse signals such as those produced by the first layer.

Evaluating generator damping for wind‐integrated power system in ambient conditions

This paper proposes a power system multimode generator energy loss factor (GELF) based on energy flow method under environmental excitation. This index can evaluate generator damping changes in different oscillation modes in power systems, timely discover the damping deterioration of the generator, and track the source of low-frequency oscillation. A signal expression method for electrical frequency domain under environmental excitation is derived. This method is combined with dissipated energy flow method to obtain a new type of GELF. In terms of signal processing, dynamic mode decomposition and Morlet wavelet filter extraction system mode components are used to improve computing accuracy. The proposed index enables online calculation with the support of phasor measurement unit and wide area measurement system. Simulation analysis is conducted in a standard 39 node system and wind-integrated power system. Test results show the effectiveness and generality of the proposed index and method.

DATA-DRIVEN LEARNING OF GEOMETRIC SCATTERING MODULES FOR GNNS.

We propose a new graph neural network (GNN) module, based on relaxations of recently proposed geometric scattering transforms, which consist of a cascade of graph wavelet filters. Our learnable geometric scattering (LEGS) module enables adaptive tuning of the wavelets to encourage band-pass features to emerge in learned representations. The incorporation of our LEGS-module in GNNs enables the learning of longer-range graph relations compared to many popular GNNs, which often rely on encoding graph structure via smoothness or similarity between neighbors. Further, its wavelet priors result in simplified architectures with significantly fewer learned parameters compared to competing GNNs. We demonstrate the predictive performance of LEGS-based networks on graph classification benchmarks, as well as the descriptive quality of their learned features in biochemical graph data exploration tasks.

Comparison of Single MRI vs. Multiparametric MRI in GBM Image Data

MRI is the standard imaging tool for diagnosis, monitoring and response evaluation for glioblastoma multiforme (GBM). The diagnostic image sequences typically include T1-weighted contrast-enhanced (T1-C), T1-weighted (T1), T2-fluid-attenuated inversion recovery (T2-Flair), standard T2-weighted (T2), and apparent diffusion coefficient (ADC) through diffusion-weighted imaging. Multiparametric MRI (mpMRI) integrates these image data to define spatially distinct regions with similar physiologies as habitats. This study tests the hypothesis of whether mpMRI, single MRI sequence, or combination sequences could improve prediction of GBM recurrence.A study cohort of 119 patients with GBM was used for evaluation. The primary outcome was recurrence which was defined as low risk if recurrence time was above the median recurrence time and otherwise as high-risk. For mpMRI, analysis was limited to 2 image sequence combinations from the above 5 image sequences, resulting in 10 sets of 2-image sequences for habitat features (e.g., T1C and T2-Flair, T1C and ADC, etc.). Analysis for single MRI sequences was divided into 14 subgroups by different filters (e.g., Wavelet, neighborhood, and intensity). Subgroups from two image sequences from same filter were combined for analysis, as well as the habitat features data from the same image sequences. Random forest method was used to evaluate performance in each group based on average test accuracy rate with a random split of 84 in training set and 35 in test set for 10 times of shuffling.The Wavelet subgroup performed better than other subgroups. Most of the average accuracy rates for two image sequences combinations in this subgroup were more than 75%, with the highest rate of 79% in the combination of T1 and ADC. The highest accuracy rate for the single MRI subgroup is 80% in the T2F's Wavelet subgroup. The mpMRI had an average test accuracy rate of 66%.This exploratory analysis indicates that the Wavelet filter could be an informative image marker in predicting GBM recurrence. Future large study cohorts are needed to verify the results.

Image enhancement in wavelet domain based on histogram equalization and median filter

During the acquisition of a new digital image, noise may be introduced as a result of the production process. Image enhancement is used to alleviate problems caused by noise. In this work, the purpose is to propose, apply, and evaluate enhancement approaches to images by selecting suitable filters to produce improved quality and performance results. The new method proposed for image noise reduction as an enhancement process employs threshold and histogram equalization implemented in the wavelet domain. Different types of wavelet filters were tested to obtain the best results for the image noise reduction process. Also, the effect of canceling one or more of the high-frequency bands in the wavelet domain was tested. The mean square error and peak signal to noise ratio are used for measuring the improvement in image noise reduction. A comparison made with two related works shows the superiority of the methods proposed and implemented in this research. The proposed methods of applying the median filter before and after the histogram equalization methods produce improvement in performance and efficiency compared to the case of using discrete wavelet transform only, even with the cases of multiresolution discrete wavelet transform and the cancellation step.

Improving UNIWARD distortion function via isotropic construction and hierarchical merging

Distortion function is designed for evaluating the cost of modifications in adaptive steganography. UNIWARD is a successful and popular distortion scheme which achieves high performance both for spatial and JPEG images. In this paper, we analyze the UNIWARD scheme with some empirical rules of distortion function designation. Based on that we propose our scheme to improve UNIWARD distortion. In our scheme, we focus on the symmetric characteristic of UNIWARD, and suggest that not only use original wavelet filters but also their flippings to calculate sub-models of UNIWARD distortion to maintain its isotropic properties. Moreover, we design several schemes to merge sub-models, which could maintain its invariance regard to flipping or rotation and improve its security against steganalysis detection. Experimental results show our revised UNIWARD achieves better performance for spatial and JPEG image in comparison with original UNIWARD.

Lifting dual tree complex wavelets transform

We describe the lifting dual tree complex wavelet transform (LDTCWT), a type of lifting wavelets remodeling that produce complex coefficients by employing a dual tree of lifting wavelets filters to get its real part and imaginary part. Permits the remodel to produce approximate shift invariance, directionally selective filters and reduces the computation time (properties lacking within the classical wavelets transform). We describe a way to estimate the accuracy of this approximation and style appropriate filters to attain this. These benefits are often exploited among applications like denoising, segmentation, image fusion and compression. The results of applications shrinkage denoising demonstrate objective and subjective enhancements over the dual tree complex wavelet transform (DTCWT). The results of the shrinkage denoising example application indicate empirical and subjective enhancements over the DTCWT. The new transform with the DTCWT provide a trade-off between denoising computational competence of performance, and memory necessities. We tend to use the PSNR (peak signal to noise ratio) alongside the structural similarity index measure (SSIM) and the SSIM map to estimate denoised image quality.

Application of Wavelet Filtering to Vibrational Signals from the Mining Screen for Spring Condition Monitoring

The main task of mineral processing plants is to further process the raw material extracted in the mining faces into a concentrate with the highest possible concentration of the final product. In practice, it is a complex process in which several stages can be distinguished. After the ore has been transported to the surface by the skip shaft, one of the first steps is sieving the ore, which is typically performed using vibrating mining screens. In a typical Ore Enrichment Plant, the screening process is carried out by several such machines. This is a typical bottleneck in the technological chain. For this reason, the main challenge for users is to achieve the highest reliability and efficiency of these technical facilities. The solution is to focus on predictive maintenance strategies based on the development of monitoring and advanced diagnostic procedures capable of estimating the time of safe operation. This work was developed as part of an advanced diagnostic system ensuring comprehensive technical conditioning and early fault detection of components such as the engine, transmission, bearings, springs, and screen. This article focuses on vibration data. The problem of damage detection in the presence of periodically impulsive components resulting from falling feed material on the screen and its further screening process has been considered. These disturbances are of a non-Gaussian noise nature, the elimination of which is essential to extract the fault-related signal of interest. One solution may be to properly smooth and filter the raw signal. In this article, a wavelet filtering technique is applied. First, the wavelet filtering procedure is described. In the next step, the performance of a wavelet filter is investigated depending on its parameters. Then, the results of wavelet filtering are compared with such methods as low-pass filtering and smoothing using a moving average. Finally, the impact of wavelet filtering on the calculation of screen trajectories is investigated.

Image Focus Enhancement Using Focusing Filter and DT-CWT Based Image Fusion

Combining multi-model images of the same scene that have different focus distances can produce clearer and sharper images with a larger depth of field. Most available image fusion algorithms are superior in results. However, they did not take into account the focus of the image. In this paper a fusion method is proposed to increase the focus of the fused image and to achieve highest quality image using the suggested focusing filter and Dual Tree-Complex Wavelet Transform. The focusing filter consist of a combination of two filters, which are Wiener filter and a sharpening filter. This filter is used before the fusion operation using Dual Tree-Complex Wavelet Transform. The common fusion rules, which are the average-fusion rule and maximum-fusion rule, were used to obtain the fused image. In the experiment, using the focus operators, the performance of the proposed fusion algorithm was compared with the existing algorithms. The results showed that the proposed method is better than these fusion methods in terms of the focus and quality.

Systematic fatigue spectrum editing by fast wavelet transform and genetic algorithm

AbstractFatigue testing is critical in order to establish the service life of load‐bearing components and structures. The extensive time associated with full fatigue spectrum testing can lead to prohibitive costs. A significant need exists for a fatigue load spectrum editing methodology, based on the mechanics of fatigue, that produces load spectra that can replicate service damage in laboratory testing and can lead to compressed testing times and reduced costs. In this work, a wavelet genetic (WAVEGEN) algorithm is developed to edit fatigue loading spectra using wavelet analysis to greatly reduce the length of a spectrum while retaining the same damage accumulation characteristics. In addition, an optimization protocol using a genetic algorithm is included within this process to automatically select the best wavelet editing parameters. The algorithm is designed to identify the most suitable wavelet type, filter, and level to optimally edit a given fatigue spectrum and ensure equivalence between edited and unedited spectra from a damage perspective. The algorithm was applied to two well‐known aircraft fatigue spectra: Fighter Aircraft Loading Standard for Fatigue evaluation (FALSTAFF) and Transport Wing Standard (TWIST). The proposed approach has demonstrated that both spectra can be compressed significantly even while ensuring equivalence from a damage perspective.

Hybrid of the Lee-Carter Model with Maximum Overlap Discrete Wavelet Transform Filters in Forecasting Mortality Rates

This study implements various, maximum overlap, discrete wavelet transform filters to model and forecast the time-dependent mortality index of the Lee-Carter model. The choice of appropriate wavelet filters is essential in effectively capturing the dynamics in a period. This cannot be accomplished by using the ARIMA model alone. In this paper, the ARIMA model is enhanced with the integration of various maximal overlap discrete wavelet transform filters such as the least asymmetric, best-localized, and Coiflet filters. These models are then applied to the mortality data of Australia, England, France, Japan, and USA. The accuracy of the projecting log of death rates of the MODWT-ARIMA model with the aforementioned wavelet filters are assessed using mean absolute error, mean absolute percentage error, and mean absolute scaled error. The MODWT-ARIMA (5,1,0) model with the BL14 filter gives the best fit to the log of death rates data for males, females, and total population, for all five countries studied. Implementing the MODWT leads towards improvement in the performance of the standard framework of the LC model in forecasting mortality rates.

Quality evaluation of metal surfaces treatment by wavelet analysis

Purpose. Analyze the effectiveness of using wavelet analysis to assess the quality of metal surfaces. Investigate the possibility of using wavelet analysis in ultrasonic flaw detection. Determine the optimal wavelet families and their criteria for assessing the quality of metal surface processing.
 Research methods. Orthogonal wavelets are considered: Daubechies wavelet, Simlet wavelet and Coiflet wavelet, which provide the possibility of performing a discrete wavelet transform procedure. The criteria influencing the effectiveness of ultrasonic signal filtering by methods using wavelet analysis are considered. Ultrasonic signals were filtered using wavelet functions.
 Results. It has been determined that for successful signal filtering, the selected wavelet method must provide a discrete wavelet transformation and have a similarity in the wavelet function shape in the local features of the ultrasonic signals flaw detector. During the work, a rigid threshold for limiting the detail coefficients of wavelet analysis was chosen, as it is the best for filtering tasks. The filtering efficiency is confirmed by the relatively high signal to noise ratio, as well as by the fact that the shape of the pulse extracted from the defect remained almost unchanged.
 Scientific novelty. When using the Daubechies and Coiflet wavelets as basic functions, as a result of wavelet filtering, it was possible to increase the signal to noise ratio by 20 dB and confidently isolate the useful signal against the background noise, which indicates the prospects of using this kind of transformations in filtering problems.
 Practical value. The obtained solutions can be used for implementation in signal filtering algorithms in digital processing units of automated non-destructive ultrasonic control systems.

Data-Driven Radar Processing Using a Parametric Convolutional Neural Network for Human Activity Classification

The paper proposes a data-driven pre-processing optimization for radar data using a parametric convolutional neural network. The proposed method is applied on human activity classification as a use case. Present radar-based activity recognition system exploit micro-Doppler signature by generating Doppler spectrograms or a temporal series of range-Doppler maps, followed by deep neural networks or machine learning approaches for classification. Those radar data representations are typically generated on the basis of short-time Fourier transformations. A Fourier transformation equally resolves the frequency space, which may be sub-optimal in some applications. Although deep convolutional neural networks (DCNN) have been shown to implicitly learn features from raw sensor data in other fields, such as speech recognition, yet, for the case of radar-based DCNNs, pre-processing is required to develop a scalable and robust classification or regression application. In this paper, we propose a parametric convolutional neural network that mimics the radar pre-processing across fast-time and slow-time radar data through 2D sinc filter or 2D wavelet filter kernels to extract features for classification of various human activities. During training only the filter parameters of the 2D sinc filters or 2D wavelets are learned, leading to optimized feature representation for the classification task. It is demonstrated that our proposed solution shows improved results compared to equivalent DCNN architectures that rely on Doppler spectrograms or radar data cubes as input data.

Sparsity enhancing wavelets design for ECG and fetal ECG compression

This paper details the design of a set of wavelet filters that are bi orthogonal in nature. The designed wavelets are experimented in publicly available MIT data base. In Compressed Sensing (CS) paradigm reconstruction quality can be improved by improving the sparsity. From experiments it was found that ECG records especially fetal ECGs have a better sparse representation in the newly designed domain as compared to commonly used wavelets. This paper also details the fundamentals of CS in a much easier way and briefly reviews some state of art methods in CS based on ECG reconstruction scenarios. The best state of art method in terms of reconstruction quality is selected for testing the designed wavelets. The designed wavelet is named as ‘dew2’.The design details of this bi orthogonal wavelet system are detailed in different sections with the help of standard wavelet system design rules.

Repeatability of image features extracted from FET PET in application to post-surgical glioblastoma assessment.

Positron emission tomography (PET) imaging using the amino acid tracer O-[2-(18F)fluoroethyl]-L-tyrosine (FET) has gained increased popularity within the past decade in the management of glioblastoma (GBM). Radiomics features extracted from FET PET images may be sensitive to variations when imaging at multiple time points. It is therefore necessary to assess feature robustness to test-retest imaging.Eight patients with histologically confirmed GBM that had undergone post-surgical test-retest FET PET imaging were recruited. In total, 1578 radiomic features were extracted from biological tumour volumes (BTVs) delineated using a semi-automatic contouring method. Feature repeatability was assessed using the intraclass correlation coefficient (ICC). The effect of both bin width and filter choice on feature repeatability was also investigated.59/106 (55.7%) features from the original image and 843/1472 (57.3%) features from filtered images had an ICC ≥ 0.85. Shape and first order features were most stable. Choice of bin width showed minimal impact on features defined as stable. The Laplacian of Gaussian (LoG, σ = 5 mm) and Wavelet filters (HLL and LHL) significantly improved feature repeatability (p ≪ 0.0001, p = 0.003, p = 0.002, respectively). Correlation of textural features with tumour volume was reported for transparency.FET PET radiomic features extracted from post-surgical images of GBM patients that are robust to test-retest imaging were identified. An investigation with a larger dataset is warranted to validate the findings in this study.

Defining of the Minimum Wavelet Filter Coefficients Bit-Width for 3D Medical Imaging

Medical imaging uses a variety of modalities to provide visual information about a patient. Various methods are used to process this data. Many of them are based on discrete wavelet transform (DWT). Its use will allow effective denoising and compression of 2D and 3D images. This paper proposes a new approach to linear time-invariant wavelet filtering using quantized filter coefficients when using which the computational errors have different signs and allow to partially compensate each other as a result of which the processed image is of high quality. The analysis of the quantization noise of the direct multilevel DWT filter coefficients is carried out. The derived formulas demonstrate the relationship between the quantization accuracy of these coefficients and the processing quality of digital 3D images. The derived formulas for calculating the minimum accuracy of the wavelet filter coefficients representation in the computing devices memory allow minimizing the effect of quantization noise on the result of 3D images processing. Modelling of 3D medical tomographic images DWT processing showed that a decrease in the ratio of the average voxel brightness to the maximum allowable value with increasing color depth of images leads to faster achievement of high quality compared to the results of theoretical analysis with an increase in the value of the scaling degree of the wavelet filter coefficients. The obtained theoretical and practical results open up the possibility for reducing the computational complexity of software and hardware implementation of wavelet processing of 3D medical visual data on modern microelectronic devices (field-programmable gate arrays, application-specific integrated circuits, etc.).

System for Neural Network Determination of Atrial Fibrillation on ECG Signals with Wavelet-Based Preprocessing

Today, cardiovascular disease is the leading cause of death in developed countries. The most common arrhythmia is atrial fibrillation, which increases the risk of ischemic stroke. An electrocardiogram is one of the best methods for diagnosing cardiac arrhythmias. Often, the signals of the electrocardiogram are distorted by noises of varying nature. In this paper, we propose a neural network classification system for electrocardiogram signals based on the Long Short-Term Memory neural network architecture with a preprocessing stage. Signal preprocessing was carried out using a symlet wavelet filter with further application of the instantaneous frequency and spectral entropy functions. For the experimental part of the article, electrocardiogram signals were selected from the open database PhysioNet Computing in Cardiology Challenge 2017 (CinC Challenge). The simulation was carried out using the MatLab 2020b software package for solving technical calculations. The best simulation result was obtained using a symlet with five coefficients and made it possible to achieve an accuracy of 87.5% in recognizing electrocardiogram signals.

Wavelets based estimation of trend in sub-divisional rainfall in India

Presence of long memory in climatic variables is frequently observed. The trend assessment becomes difficult in the presence of long-memory as the usual methods are not capable to take care of this property during trend estimation. In order to estimate the trend in presence of long memory, the non-parametric wavelet method has become popular in the recent time. The discrete wavelet transformation (DWT) re-expresses a time-series in terms of coefficients that are associated with a particular time and a particular scale. In the present study, DWT has been applied to estimate the monthly rainfall trend for the monsoon months: June-September in ten selected sub-divisions of India using “Haar” wavelet filter. The results from DWT were cross checked with the non-parametric Mann-Kendall (M-K) test. The investigation reveals that the monthly rainfall trend for the monsoon months of different sub-divisions in India are significantly decreasing over the years. However, in some of the sub-divisions, rainfall trend is increasing. DWT reveals significant trend in most of the sub-divisions whereas M-K test reveals that most of the trends are not significant at 5% level.

Automated Characterization of Cyclic Alternating Pattern Using Wavelet-Based Features and Ensemble Learning Techniques with EEG Signals.

Sleep is highly essential for maintaining metabolism of the body and mental balance for increased productivity and concentration. Often, sleep is analyzed using macrostructure sleep stages which alone cannot provide information about the functional structure and stability of sleep. The cyclic alternating pattern (CAP) is a physiological recurring electroencephalogram (EEG) activity occurring in the brain during sleep and captures microstructure of the sleep and can be used to identify sleep instability. The CAP can also be associated with various sleep-related pathologies, and can be useful in identifying various sleep disorders. Conventionally, sleep is analyzed using polysomnogram (PSG) in various sleep laboratories by trained physicians and medical practitioners. However, PSG-based manual sleep analysis by trained medical practitioners is onerous, tedious and unfavourable for patients. Hence, a computerized, simple and patient convenient system is highly desirable for monitoring and analysis of sleep. In this study, we have proposed a system for automated identification of CAP phase-A and phase-B. To accomplish the task, we have utilized the openly accessible CAP sleep database. The study is performed using two single-channel EEG modalities and their combination. The model is developed using EEG signals of healthy subjects as well as patients suffering from six different sleep disorders namely nocturnal frontal lobe epilepsy (NFLE), sleep-disordered breathing (SDB), narcolepsy, periodic leg movement disorder (PLM), insomnia and rapid eye movement behavior disorder (RBD) subjects. An optimal orthogonal wavelet filter bank is used to perform the wavelet decomposition and subsequently, entropy and Hjorth parameters are extracted from the decomposed coefficients. The extracted features have been applied to different machine learning algorithms. The best performance is obtained using ensemble of bagged tress (EBagT) classifier. The proposed method has obtained the average classification accuracy of 84%, 83%, 81%, 78%, 77%, 76% and 72% for NFLE, healthy, SDB, narcolepsy, PLM, insomnia and RBD subjects, respectively in discriminating phases A and B using a balanced database. Our developed model yielded an average accuracy of 78% when all 77 subjects including healthy and sleep disordered patients are considered. Our proposed system can assist the sleep specialists in an automated and efficient analysis of sleep using sleep microstructure.

Computer Simulation of Extended Neyman–Pearson Detector in Monostatic Pulse Radar

An extended Neyman–Pearson detector based on the combination of a traditional matched and wavelet filter in pulsed monostatic radar was proposed in this paper. Its properties were compared with properties of the cell average constant false alarm radar detector in the presence of white noise. The properties of detectors were examined in the receiver operating characteristic curves, parameter space. It consisted of false detection rate and the rate of true positive detected targets. In order to investigate the influence of temperature, the new parameter space was constructed: the temperature versus the rate of true positive detected targets. The traditional Neyman–Pearson detector based on a matched filter was fully operational and superior in the temperature range between 290[Formula: see text]K and 350[Formula: see text]K. Below this temperature range, its performance is completely degraded. It has been shown that by adding a wavelet filter, it can extend this temperature range between 260[Formula: see text]K and 350[Formula: see text]K. In the temperature range, where all detectors are fully operational, extended and classic Neyman–Pearson detectors had better performance than constant false alarm radar detector in the receiver operating characteristic curves’ parameter space.