Wavelet Variance Research Articles

Deep learning with adaptive convolutions for classification of retinal diseases via optical coherence tomography

Optical coherence tomography (OCT) uses interferometry to capture high-resolution cross-sectional images of the retina to diagnose retinal diseases. Convolutional neural networks (CNNs) have become essential for developing efficient computer-aided diagnostic algorithms, but noisy images can hinder their performance. This study introduces an innovative image preprocessing strategy that involves a new method of representing images to reduce image noise and a new adaptive convolution layer. The adaptive convolution layer aims to replace traditional convolution layers for OCT image classification by relying on local’Feature Content’. The proposed image representation is based on Zeckendorf's theorem, which states that every positive integer may be split into a unique sum of distinct, non-adjacent Fibonacci numbers. The proposed approach enables the generation of two separate images, known as the ‘base’ and ‘fine,’ where the ‘base’ image is the denoised image. We assessed our methodology by evaluating against ten filters, comprising a Low-pass filter, Gaussian filter, Wiener filter, Wavelet filter, Guided filter, Lee filter, Frost filter, Kuan filter, Detail Preserving Anisotropic Diffusion (DPAD) filter, and Non-Local Means (NLM) filter. In our study, we found that the proposed filter produced the most favorable results in five of the six no-reference parameters (Blur Percent (BP), Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE), Naturalness Image Quality Evaluator (NIQE), Wavelet Variance (WAVV), Wavelet Variance Radial (WAVR)) used to assess the effectiveness of the proposed image enhancement technique. The OCT dataset utilized in the study was compiled by the University of California San Diego. The proposed adaptive convolution layer and its accompanying activation function were tested using seven OCT image classification CNN architectures. The test architectures comprise OctNET, NT-CNN, AOCT-NET, M-CNN, LightOCT, RetiNet, and DeepOCT. Experiments were conducted to assess the impact of the new preprocessing algorithm and the placement of the adaptive convolution layer as a substitute for the conventional convolution layer. Implementing the proposed approaches resulted in accuracy improvements ranging from 0.44% to 2.44% across architectures. Our findings highlight the efficacy of the proposed indirect noise reduction technique and a texture-sensitive adaptive convolution layer.

Discrimination of Internal Solitary Waves from Coarse Time Resolution Field Observational Data by Using Wavelet Analysis

Internal solitary waves (ISWs) are large-amplitude internal waves which would destroy underwater engineering. Finding an easy way to discriminate ISWs from field observational data is crucial. Two time--series datasets, one contained ISWs and another only containing internal tides, were obtained from filed observations. Based on single-layer velocity data, wavelet spectrum shows significant high value in short time-scale domain when ISWs pass, whilst having no signal in that domain when only internal tides exist, indicating the capability of wavelet analysis on ISWs detection. Wavelet variances of the dataset with ISWs has a bimodal distribution versus periods with two peaks around 40 min and 110 min, which can also be reproduced by a numerical model, indicating that the energy within period band of 10–120 min is caused by ISWs. By using the conceived signal processing techne, data reconstruction can precisely obtain the arrival time of ISWs and retain about 91.4% of the original signal. It is found that, based on a field observational dataset with even a coarse sampling interval for up to 20 min, the existence of ISWs can be easily discriminated by using wavelet analysis, which provides us an economic method for the early warning of ISWs in ocean engineering.

A study on the correlation of cyclical fluctuations in vegetable commodity sales based on wavelet analysis modeling

As the sales volume and time of vegetable commodities tend to have a certain correlation, in order to explore the distribution law of the sales volume of each category and single product of vegetables, this paper firstly handles the data to get the monthly sales volume of each vegetable category and single product of time series data, then uses Matlab's Wavelet Toolbox to carry out wavelet analysis,drawing wavelet variance diagrams, the main cycle trend graph to judge the cyclical pattern of each vegetable category and single product,and then use Origin to make wavelet coefficients real part contour graph to verify the law, and finally get the distribution law. This study can help superstores better grasp the sales situation and development trend of each vegetable category and single product.

Fast white noise estimation in GNSS time series by wavelet variance

Fast white noise estimation in GNSS time series by wavelet variance

Fracture toughness evaluation of a nuclear graphite with non-linear elastic properties by 3D imaging and inverse finite element analysis

Effective small specimen tests are needed to obtain fracture toughness and elastic properties as the limited availability of irradiated graphite restricts the quantity and dimensions of test specimens. Both properties have evaluated simultaneously in a crack propagation test with the double cleavage drilled compression (DCDC) specimen geometry of a fine-grained graphite (SNG742) that has non-linear elastic properties in the unirradiated condition. Three-dimensional displacement fields were obtained by digital volume correlation of in situ laboratory X-ray computed tomographs, and the 3D crack geometry (crack tip position, crack opening displacements and angle) was determined objectively by a wavelet variance method. The tensile softening of the Young modulus was determined by inverse analysis of the strain field using the finite element model updating (FEMU) method. The strain energy release rate of the quasi-static propagating crack was calculated using the contour integral method in a finite element model with the derived non-linear elastic properties and the measured displacements as boundary conditions. The critical strain energy release rate was constant with crack length (118 ± 14 J m−2) and equivalent to a fracture toughness of 1.13 ± 0.07 MPa m1/2.

Spatiotemporal characterization and prediction of the subsurface temperature front of the Kuroshio extension

The Kuroshio Extension Front (KEF) is one of the most representative mesoscale dynamic processes in the Northwest Pacific, particularly the subsurface KEF that has a substantial influence on the marine environment. Based on the JCOPE2M reanalysis data and WOA23 climatological mean data, this study proposed the Ocean Front Fit Degree (OFFD) as an evaluation criterion for extracting the front lines. For the extraction of the KEF front line, an approach combining isotherms and meridians with the highest temperature gradient was employed. The absolute gradient method and wavelet variance were used for analyzing the spatiotemporal characteristics of the subsurface KEF strength and position. Considering the variations in the KEF characteristics at different time scales, a KEF prediction model based on VMD-LSTM was constructed. The results demonstrated that: (1) The front-line recognition and optimization method proposed in this study is applicable across all water depths and areas with interference and weak fronts, yielding accurate KEF prediction results; (2) The KEF strength and position can be decomposed into trend changes, periodic changes, and irregular wave changes. The factors that may contribute to the low-frequency variations in subsurface KEF include the meridional movement of the Aleutian Low and the Pacific Decadal Oscillation (PDO); (3) The combined VMD-LSTM model predicts the KEF strength with high accuracy, indicating excellent prediction performance and high potential application value compared to individual LSTM model.

Statistical Characterization of Bubble Breakup Flow Structures in Swirl-Type Bubble Generator Systems

The bubble breakup pattern on a swirl-type bubble generator (MBG) with water and air fluids was experimentally studied. The bubble breakup pattern was analyzed visually and characterized using several parameters such as Pressure Drop (∆P), Kolmogorov Entropy, Standard Deviation, and DWT (Discrete Wavelet Transform), which were taken from the extraction of pressure signals at the water inlet and outlet of the bubble generator. The wavelet spectrum of the measured signal was shown to identify the overall bubble breakup pattern, and the wavelet variance vector is proposed as a character vector to identify the bubble breakup pattern. The results show that there were three types of different flow breakup patterns: (1) static breakup, (2) dynamic breakup, and (3) tensile breakup. The observed bubble breakup sub-patterns can be categorized into tensile, moderate tensile, high tensile, dynamic, low dynamic, static, and high static sub-patterns. The static clustered breakup pattern has the highest wavelet energy compared to the tensile and dynamic clustered breakup.

Serotonergic modulation of normal and abnormal brain dynamics: The genetic influence of the TPH2 G-703T genotype and DNA methylation on wavelet variance in children and adolescents with and without ADHD.

Attention-deficit/hyperactivity disorder (ADHD) is a neurodevelopmental disorder that often persists into adulthood. Core symptoms of ADHD, such as impulsivity, are caused by an interaction of genetic and environmental factors. Epigenetic modifications of DNA, such as DNA methylation, are thought to mediate the interplay of these factors. Tryptophan hydroxylase 2 (TPH2) is the rate-limiting enzyme in brain serotonin synthesis. The TPH2 gene has frequently been investigated in relation to ADHD, e.g., showing that TPH2 G-703T (rs4570625) polymorphism influences response control and prefrontal signaling in ADHD patients. In this (epi)genetic imaging study we examined 144 children and adolescents (74 patients, 14 females) using fMRI at rest and during performing a waiting impulsivity (WI) paradigm. Both, TPH2 G-703T (rs4570625) genotype and DNA methylation in the 5' untranslated region (5'UTR) of TPH2 were associated with wavelet variance in fronto-parietal regions and behavioral performance, taking TPH2 genotype into account. In detail, comparisons between genotypes of patients and controls revealed highest wavelet variance and longest reaction times in patients carrying the T allele [indicative for a gene-dosage effect, i.e., the WI phenotype is a direct result of the cumulative effect of ADHD and TPH2 variation]. Regressions revealed a significant effect on one specific DNA methylation site in ADHD patients but not controls, in terms of a significant prediction of wavelet variance in fronto-parietal regions as well as premature responses. By the example of the TPH2 G-703T (rs4570625) polymorphism, we provide insight into how interactive genetic and DNA methylation affect the ADHD and/or impulsive endophenotype.

Hourly and Sub-Hourly Rainfall under Synoptic Patterns during the Anomalous Meiyu Season 2020

The 2020 Meiyu season has received extensive attention due to its record-breaking rainfall in the Yangtze–River Huai Basin (YHRB) region of China. Although its rainfall features have been well studied on various time scales, the sub-hourly/hourly rainfall features are unknown. In this study, a wavelet analysis was applied to 1 min rainfall data from 480 national rain gauges across the YHRB, and hourly synoptic patterns during the Meiyu season were grouped using an obliquely rotated principal component analysis in T-mode (PCT). The results suggest that variances on the sub-hourly and hourly scales contributed 63.4% of the 2020 Meiyu rainfall. The hourly synoptic variations in the Meiyu season can be categorized into three major patterns: weak synoptic forcing (P1), a convergence line (P2), and a vortex (P3). The rainfalls under P1 were spatially dispersed over the YHRB and on the shortest time scale, with a 70.4% variance from sub-hourly to hourly rainfalls. P2 had a peak wavelet variance around 30 min–1 h, with rainfalls concentrated to the south of the convergent line. The rainfalls under P3 were locally distributed with a longer duration of around 1–4 h. Compared with the climate mean, hourly rainfall frequencies are indispensable to understanding the 2020 accumulated Meiyu rainfall anomaly. This research highlights the dominant role of synoptic patterns on the temporal and spatial features of the Meiyu rainfall.

DETECTION OF AUTISM SPECTRUM DISORDER BY FEATURE EXTRACTION OF EEG SIGNALS AND MACHINE LEARNING CLASSIFIERS

Autism Spectrum Disorder (ASD), a neurodevelopmental disorder, impacts the subject’s social communication and interaction and the subjects exhibit restricted and repetitive behaviors. Subjects with ASD may need assistance throughout their life, depending on the severity. Early diagnosis of ASD is therefore critical for early intervention. ASD is diagnosed clinically based on behavioral assessments of the subjects, which results in delayed diagnosis, since the typical ASD traits due to aberrant brain development take time to develop. Neurological disorders associated with aberrant brain electrical activity have been detected by analyzing Electroencephalogram (EEG) signal patterns. In this study, we used features extracted from EEG brain waves to categorize ASD and normal subjects using Machine Learning (ML) classifiers. Autoregressive (AR) coefficients, Shannon entropy, Multifractal wavelet leader estimates, Multiscale wavelet variance and Discrete Fourier Transform (DFT) coefficients were extracted from EEG brain waves of ASD and normal subjects. Support Vector Machine (SVM), Decision Tree (DT), Logistic Regression (LR), k-Nearest Neighbor (k-NN) and Feed-forward Neural Network (FNN) were utilized as classification algorithms to categorize the ASD subjects and the control subjects. An accuracy of 90% was achieved by k-NN algorithm using AR features, Shannon entropy, Multifractal wavelet leader estimates and Multiscale wavelet variance estimates in ASD categorization. An accuracy of 93% was achieved by k-NN using the DFT features. The findings of this study indicate that features extracted from EEG are sufficient enough for categorization of ASD subjects and the control subjects.

Wavelet-based fuzzy clustering of interval time series

We investigate the fuzzy clustering of interval time series using wavelet variances and covariances; in particular, we use a fuzzy c-medoids clustering algorithm. Traditional hierarchical and non-hierarchical clustering methods lead to the identification of mutually exclusive clusters whereas fuzzy clustering methods enable the identification of overlapping clusters, implying that one or more series could belong to more than one cluster simultaneously. An interval time series (ITS) which arises when interval-valued observations are recorded over time is able to capture the variability of values within each interval at each time point. This is in contrast to single-point information available in a classical time series. Our main contribution is that by combining wavelet analysis, interval data analysis and fuzzy clustering, we are able to capture information which would otherwise have not been contemplated by the use of traditional crisp clustering methods on classical time series for which just a single value is recorded at each time point. Through simulation studies, we show that under some circumstances fuzzy c-medoids clustering performs better when applied to ITS than when it is applied to the corresponding traditional time series. Applications to exchange rates ITS and sea-level ITS show that the fuzzy clustering method reveals different and more meaningful results than when applied to associated single-point time series.

Machine learning-based classification of arterial spectral waveforms for the diagnosis of peripheral artery disease in the context of diabetes: A proof-of-concept study.

Point-of-care duplex ultrasound has emerged as a promising test for the diagnosis of peripheral artery disease (PAD). However, the interpretation of morphologically diverse Doppler arterial spectral waveforms is challenging and associated with wide inter-observer variation. The aim of this study is to evaluate the utility of machine learning techniques for the diagnosis of PAD from Doppler arterial spectral waveforms sampled at the level of the ankle in patients with diabetes. In two centres, 590 Doppler arterial spectral waveform images (PAD 369, no-PAD 221) from 305 patients were prospectively collected. Doppler arterial spectral waveform signals were reconstructed. Blinded full lower-limb reference duplex ultrasound results were used to label waveform according to PAD status (i.e., PAD, no-PAD). Statistical metrics and multiscale wavelet variance were extracted as discriminatory features. A long short-term memory (LSTM) network was used for the classification of raw signals, and logistic regression (LR) and support vector machines (SVM) were used for classification of extracted features. Signals and feature vectors were randomly divided into training (80%) and testing (20%) sets. The highest overall accuracy was achieved using a logistic regression model with a combination of statistical and multiscale wavelet variance features, with 88% accuracy, 92% sensitivity, and 82% specificity. The area under the receiver operating characteristics curve (AUC) was 0.93. We have constructed a machine learning algorithm with high discriminatory ability for the diagnosis of PAD using Doppler arterial spectral waveforms sampled at the ankle vessels.

Graph neural network approach for anomaly detection

To ensure the stable long-time operation of satellites, evaluate the satellite status, and improve satellite maintenance efficiency, we propose an anomaly detection method based on graph neural network and dynamic threshold (GNN-DTAN). Firstly, we build the graph neural network model for telemetry data. The graph construction module in the model extracts the relationship between features, and the spatial dependency extraction module and the temporal dependency extraction module extract the spatial and temporal dependencies of the data, respectively. The trained model is then used to predict the data, and the anomaly score between the predicted and actual values is calculated. Finally, the wavelet variance is used to analyze the data period. A dynamic threshold method based on the period time window is used to detect anomalies in the data set. Experimental results of satellite power system telemetry data show that the proposed algorithm's accuracy reaches more than 98%, with good effectiveness and robustness.

Robust Two-Step Wavelet-Based Inference for Time Series Models

Latent time series models such as (the independent sum of) ARMA(p, q) models with additional stochastic processes are increasingly used for data analysis in biology, ecology, engineering, and economics. Inference on and/or prediction from these models can be highly challenging: (i) the data may contain outliers that can adversely affect the estimation procedure; (ii) the computational complexity can become prohibitive when the time series are extremely large; (iii) model selection adds another layer of (computational) complexity; and (iv) solutions that address (i), (ii), and (iii) simultaneously do not exist in practice. This paper aims at jointly addressing these challenges by proposing a general framework for robust two-step estimation based on a bounded influence M-estimator of the wavelet variance. We first develop the conditions for the joint asymptotic normality of the latter estimator thereby providing the necessary tools to perform (direct) inference for scale-based analysis of signals. Taking advantage of the model-independent weights of this first-step estimator, we then develop the asymptotic properties of two-step robust estimators using the framework of the generalized method of wavelet moments (GMWM). Simulation studies illustrate the good finite sample performance of the robust GMWM estimator and applied examples highlight the practical relevance of the proposed approach.

Application of remote sensing technology in the analysis of periodic precipitation change in China’s Northern semi-arid area

The remote sensing technology is used to analyze the periodic changes of precipitation in the semi-arid areas of northern China and provide a reference basis for precipitation prediction. Authors were based on GPS observation data and corresponding ground meteorological parameters to obtain the study area’s comprehensive water vapor content value and use precipitation and time to establish a linear regression equation based on the content value to express the precipitation trend change. The periodic structure and abnormal changes of the periodic precipitation series on different time scales were obtained through wavelet analysis, combined with anomaly calculations to analyze the increase and decrease precipitation characteristics. The Morlet continuous wavelet transform map was also used to reflect the periodic oscillations of precipitation on different time scales. The wavelet variance map was used to reflect the distribution of regional precipitation with scale years. The authors analyzed the cycle change characteristics of the comprehensive precipitation series in Harbin, Changchun, Shenyang, and Dalian. They concluded that the annual precipitation in the four regions showed a decreasing trend in 50 years. And through the wavelet cycle frequency-domain relationship change law, the change characteristics of precipitation in the northern semi-arid area in the entire time domain were obtained.

Method of Translation Transfer for Estimation of Stability of a Nonstationary Quantum Frequency Standard

A continuous wavelet transform is used to analyze operation of a nonstationary signal of a quantum frequency standard. A method of translation transfer is proposed for elimination of the boundary effects in such a transform. Spectral integrals of the signal of the quantum frequency standard are calculated in several frequency intervals. A wavelet variance is introduced to determine time moments of the strongest fluctuations of the signal. The wavelet variance is compared with conventional and Allan variances.

Response and Uncertainty of the Parabolic Variance PVAR to Noninteger Exponents of Power Law

The oscillator fluctuations are described as the phase or frequency-noise spectrum or in terms of a wavelet variance as a function of the measurement time. The spectrum is generally approximated with the “power law,” i.e., a Laurent polynomial with integer exponents of the frequency. This article provides: 1) the analytical expression of the response of the wavelet variance parabolic variance (PVAR) to the frequency-noise spectrum in the general case of noninteger exponents of the frequency and 2) a useful approximate expression of the statistical uncertainty. In turn, PVAR is relevant in that it replaces the widely used modified Allan variance (MVAR), featuring the identification of noise processes with fewer data.

Wavelet Variance Maximization: A contactless respiration rate estimation method based on remote photoplethysmography

Respiration is an important parameter in critical and pediatric care since its monitoring allows medical staff to detect many life-threatening diseases. One of the existing monitoring methods is based on remote photoplethysmography (rPPG). This technique consists of extracting a signal related to blood volume variations using a camera. This signal carries useful physiological information such as cardiac and respiratory rates. However, the quality of the signal is lower than regular contact-based methods and represents a major weakness of the rPPG method. In this paper, we propose an algorithm to explicitly maximize the respiratory signal quality by maximizing the Signal-to-Noise Ratio (SNR). Instead of using the regular Fast-Fourier-based energy ratio for the signal-to-noise-ratio estimation, we propose to use the continuous wavelet transform to deal with non-stationarities of the respiratory signal. The method, named Wavelet Variance Maximization (WVM), is based on the Generalized Eigen Value Decomposition (GEVD) algorithm and estimates the optimal combination of the temporal color traces to obtain a high-quality rPPG signal. Our method was tested on 12 healthy adult volunteers and the results confirm that the estimated signal has better quality than existing methods, with approximately 20% reduction of error compared to the best tested state-of-the-art method.

Wavelet periodic and compositional characteristics of atmospheric PM2.5 in a typical air pollution event at Jinzhong city, China

To investigate the contributions of atmospheric particulate matter less than 2.5 μm in aerodynamic diameter (PM2.5) to heavy air pollution events in Fen-Wei Plain, China and identify their sources, a combination of wavelet analysis and low-atomic number (Z) particle electron probe X-ray microanalysis (EPMA) was utilized in a typical haze episode lasting 10 days (from Nov. 11 to 20, 2016) at Jinzhong, an inland city adjacent to Taiyuan, the capital of Shanxi Province. A 3-layer wavelet decomposition filtration was performed using the daubechies wavelet functions (db6) and the distribution of the real wavelet transformation coefficients and variance of wavelet series for various pollutants within 240 h was plotted. Five dominant periods of PM2.5 in mass concentration were observed, peaking at 101 h, 144 h, 50–51 h, 27–28 h, and 18 h in sequence from high to low in the wavelet variance chart. They were similar to those of PM10, SO2, and CO and partially overlapped with those of NO2, but different from those of O3, implying that PM2.5 have the same sources as PM10, SO2, and CO and have complicated relations with O3 and NO2. It was further found that the chemical compositions of PM2.5 in the dominant periods made great changes compared to the non-dominant periods. The relative number abundance of elemental carbon (EC) and droplets rich in CNOS (likely the mixture of carbonaceous matter with secondary aerosols such as NH4NO3 and (NH4)2SO4/NH4HSO4) in the first and second dominant period were significantly higher than that in other periods. It is concluded that coal and biomass combustion and secondary particles are still the main contributors to the wintertime heavy air pollution events in Fen-Wei Plain, suggesting that the wavelet analysis combined with low-Z particle EPMA is useful in examination of atmospheric particulate matter's origin, evolution, and roles played in haze events.

Variability analysis of epileptic EEG using the maximal overlap discrete wavelet transform.

To determine if there is a difference in the wavelet variances of seizure and non-seizure channels in the EEG of an epileptic subject. A six-level decomposition was applied using the Maximal Overlap Discrete Wavelet Transform (MODWT). The wavelet variance and 95% CIs were calculated for each level of the decomposition. The number of changes in variance for each level were found using a change-point detection method of Whitcher. The Kruskal-Wallis test was used to determine if there were differences in the median number of change points within channels and across frequency bands (levels). No distinctive pattern was found for the wavelet variances to differentiate the seizure and non-seizure channels. The seizure channels tended to have lower variances for each level and overall, but this pattern only held for one of the three seizure channels (RAST4). The median number of change points did not differ between the seizure and non-seizure channels either within each channel or across the frequency bands. The use of the MODWT in examining the variances and changes in variance did not show specific patterns which differentiate between seizure and non-seizure channels.