Wavelet Estimation Research Articles

Optimized early fusion of handcrafted and deep learning descriptors for voice pathology detection and classification

This study presents an automated noninvasive voice disorder detection and classification approach using an optimized fusion of modified glottal source estimation and deep transfer learning neural network descriptors. A new set of modified descriptors based on a glottal source estimator and pre-trained Inception-ResNet-v2 convolutional neural network-based features are proposed for the speech disorder detection and classification task. The modified feature set is obtained using mel-cepstral coefficients, harmonic model, phase discrimination means, distortion deviation descriptors, conventional wavelet, and glottal source estimation features. Early descriptor-level fusion is employed in this study for performance enhancement-however, the fusion results in higher feature vector dimensionality. A nature-inspired slime mould algorithm is utilized to remove redundant and select the best discriminating features. Finally, the classification is performed using the K-nearest neighbor (KNN) classifier. The proposed algorithm was evaluated using extensive experiments with different feature combinations, with and without feature selection, and with two popular datasets: the Arabic Voice Pathology Database (AVPD) and the Saarbrucken Voice Database (SVD). We show that the proposed optimized fusion method attained an enhanced voice pathology detection accuracy of 98.46%, encompassing a wide spectrum of voice disorders on the SVD database. Furthermore, compared to traditional handcrafted and deep neural network-based techniques, the proposed method demonstrates competitive performance with fewer features.

Integrating deep learning and discrete cosine transform for surface waves full waveform inversion

Summary Accurate estimations of near-surface S-wave velocity (Vs) models hold particular significance in geological and engineering investigations. On the one hand, the popular Multichannel Analysis of Surface Waves (MASW) is limited to the 1D and the plane wave assumptions. On the other hand, the more advanced and computationally expensive full-waveform inversion (FWI) approach is often solved within a deterministic framework that hampers an accurate uncertainty assessment and makes the final predictions heavily reliant on the starting model. Here we combine deep learning with Discrete Cosine Transforms (DCT) to solve the FWI of surface waves and to efficiently estimate the inversion uncertainties. Our neural network approach effectively learns the inverse non-linear mapping between DCT-compressed seismograms and DCT-compressed S-velocity models. The incorporation of DCT into the deep learning framework provides several advantages: it notably reduces parameter space dimensionality and alleviates the ill-conditioning of the problem. Additionally, it decreases the complexity of the network architecture and the computational cost for the training phase compared to training in the full domain. A Monte Carlo simulation is also used to propagate the uncertainties from the data to the model space. We first test the implemented inversion method on synthetic data to showcase the generalization capabilities of the trained network and to explore the implications of incorrect noise assumptions in the recorded seismograms and inaccurate wavelet estimations. Further, we demonstrate the applicability of the implemented method to field data. In this case, available borehole information is used to validate our predictions. In both the synthetic and field applications, the predictions provided by the proposed method are compared with those of a deterministic FWI and the outcomes of a network trained in the full data and model spaces. Our experiments confirm that the implemented deep-learning inversion efficiently and successfully solves the FWI problem and yields more accurate and stable results than a network trained without the DCT compression. This opens the possibility to efficiently train a neural network that provides accurate instantaneous predictions of Vs near-surface models and related uncertainties.

Asymptotic normality of wavelet estimators in heteroscedastic regression model with ANA errors

. In this article, we mainly study the asymptotic normality of wavelet estimators in the heteroscedastic regression model with asymptotically negatively associated (ANA or ρ −, for short) errors. Under some mild conditions, the asymptotic normality of the wavelet estimators of g(⋅) in the heteroscedastic regression model with ANA errors is obtained when f(⋅) is a known or unknown function, respectively. At the same time, we derive a Berry-Esseen-type bound for the estimators of g(⋅). As a corollary, by making a certain choice of the weights, the Berry-Esseen-type bound of the estimator can reach nearly O ( n − 1 / 12 ) , which in some sense generalizes or improves the corresponding ones for negatively associated (NA, for short) random variables and φ−mixing sequence. Finally, the finite sample simulation study presented in this article shows the validity of our theoretical results.

Wavelet estimation of a regression model with mixed noises

Wavelet estimation of a regression model with mixed noises

Estimation of the depth-variant seismic wavelet based on the modified unscaled S-transform

Seismic inversion is one of the key techniques used for reservoir characterization. Depth-domain seismic inversion eliminates the cumulative errors associated with depth-to-time and time-to-depth conversions, thus providing geologists and reservoir engineers with an intuitive basis for geological interpretation. The method has received increasing attention in the field of reservoir characterization. Extracting accurate depth-domain seismic wavelets is a prerequisite for successful depth-domain seismic inversion. However, the depth-domain wavelet is velocity-dependent and exhibits significant non-stationarity, which leads to the failure of seismic wavelet estimation methods based on the stationary convolutional model. To this end, we propose a modified wavenumber-domain unscaled S-transform (MWUST) method to accomplish accurate estimation of depth-domain seismic wavelets. The proposed method enhances the accuracy of wavenumber components by removing the linear wavenumber-dependent term from the S-transform. Furthermore, it introduces slope and intercept parameters to improve the depth resolution at low wavenumbers, thereby yielding a more reliable depth–wavenumber spectrum. Subsequently, the relationship between the non-stationary depth-domain seismic wavelet and the depth–wavenumber spectrum is established, allowing for the accurate extraction of non-stationary wavelets under the assumption that the depth-domain reflectivity is a random sequence. Synthetic and real data applications have been used to verify the effectiveness of the proposed method.

Bayesian estimation for mean vector of multivariate normal distribution on the linear and nonlinear exponential balanced loss based on wavelet decomposition

This paper addresses the problem of Bayesian wavelet estimating the mean vector of multivariate normal distribution under a multivariate normal prior distribution based on linear and nonlinear exponential balanced loss functions. The covariance matrix of multivariate normal distribution is considered known. Bayes estimators of mean vector parameter of multivariate normal distribution are achieved. Then two soft shrinkage wavelet threshold estimators based on Stein’s unbiased risk estimate (SURE) and Bayes estimators are provided. Finally, the performance of the soft shrinkage wavelet estimators was checked through simulation study and Electrical Grid Stability Simulated data set. Simulation and real data results showed the better performance of SURE thresholds based on linear and nonlinear exponential balanced loss functions compared to other classical wavelet methods. Also, they showed better performance for SURE threshold based on nonlinear exponential balanced loss function in multivariate normal distribution with small dimensions.

Strong Consistency of Wavelet Estimator for Biased Nonparametric Regression Function Under Strong Mixing

Strong Consistency of Wavelet Estimator for Biased Nonparametric Regression Function Under Strong Mixing

The Berry-Esseen bounds of wavelet estimator for nonparametric regression models whose errors form a linear process based on ANA sequences

In this paper, we consider the nonparametric regression model Y ni = g ( t ni ) + ϵ i ( 1 ≤ i ≤ n ), where ϵ i = ∑ j = − ∞ ∞ a j e i − j and e i are identically distributed and asymptotically negatively associated (ANA or ρ − , for short) sequences. This paper obtains the Berry-Esseen bounds of the wavelet estimator of g ( ⋅ ) , and the rate of the normal approximation is shown as O ( n − 1 / 4 ) under certain conditions. Finally, the simulation study is provided to verify the validity of the theoretical results.

Design of Multidomain Feature Analysis Model for Estimation of Anemic Conditions via Deep Transfer Learning

The detection of anemia from anemic retinopathy involves the identification and analysis of specific retinal changes that occur as a result of severe anemia which requires analysis of multimodal sources. Existing models for identification of these conditions either showcase high complexity, or have lower efficiency when evaluated on clinical scans. Moreover, most of these models cannot be scaled for multi-disease images, which limits their applicability under real-time use cases. To overcome these issues, this research article proposes the design of an efficient and novel multidomain feature analysis model for the estimation of anemic conditions with the help of deep transfer learning process. The proposed model initially represents retinal image scans into multiple domains via estimation of Frequency, Gabor, Convolution, Wavelet and Entropy features. These features are selected via Bacterial Foraging Optimizer (BFO), which assists in retaining high variance feature sets. Due to this, the model is able to reduce redundancies, that assists in improving the speed and accuracy of classification operations. To perform this task, the model uses a set of customized 1-D Cascaded Binary CNN, that assist in categorizing input images into 4 different classes. These include, “Anemic due to Glaucoma”, “Glaucoma”, “Anemic”, and “Normal”, with 98.3% accuracy which is 4.5% higher than existing methods. The model is also able to improve the precision by 2.9%, recall by 3.5%, while reducing the delay needed for classification by 5.9% when compared with existing techniques. Due to which, the model is highly useful for clinical deployments.

On consistency for wavelet estimator of regression function based on biased samples under extended negatively dependence

ABSTRACT For a nonparametric regression model with biased samples under extended negatively dependence, we concern with the estimation problem of the regression function over Sobolev space. On the basis of the wavelet kernel, we propose a wavelet estimator and investigate its consistency properties under mild conditions. For the proposed wavelet estimator, we establish the pth mean consistency based on moment inequality and get the complete consistency by virtue of exponential inequality and truncation technique. It should be pointed out that the complete consistency of wavelet estimator is a novel theoretical result in the nonparametric regression model with biased samples. In addition, the effectiveness of the proposed wavelet estimator is demonstrated on some numerical experiments.

Nonparametric statistical inference for stochastic optimal control problems and its applications for financial investment

Against a backdrop of financial decision-making, this study examines nonparametric statistical inference problems in stochastic optimal control problems. First, we construct a nonparametric estimation model using the wavelet estimation method for drift and diffusion coefficients. In this study, we focus on stochastic linear–quadratic (SLQ) problems, solved using Riccati equations, and apply this to a cash management problem within the linear–quadratic framework. The results show the effectiveness of the wavelet method using a numerical case.

Partial Derivatives Estimation of Multivariate Variance Function in Heteroscedastic Model via Wavelet Method

For derivative function estimation, conventional research only focuses on the derivative estimation of one-dimensional functions. This paper considers partial derivatives estimation of a multivariate variance function in a heteroscedastic model. A wavelet estimator of partial derivatives of a multivariate variance function is proposed. The convergence rates of a wavelet estimator under different estimation errors are discussed. It turns out that the strong convergence rate of the wavelet estimator is the same as the optimal uniform almost sure convergence rate of nonparametric function problems.

Statistical inference for wavelet curve estimators of symmetric positive definite matrices

In this paper we treat statistical inference for a wavelet estimator of curves of symmetric positive definite (SPD) using the log-Euclidean distance. This estimator preserves positive-definiteness and enjoys permutation-equivariance, which is particularly relevant for covariance matrices. Our second-generation wavelet estimator is based on average-interpolation (AI) and allows the same powerful properties, including fast algorithms, known from nonparametric curve estimation with wavelets in standard Euclidean set-ups. The core of our work is the proposition of confidence sets for our AI wavelet estimator in a non-Euclidean geometry. We derive asymptotic normality of this estimator, including explicit expressions of its asymptotic variance. This opens the door for constructing asymptotic confidence regions which we compare with our proposed bootstrap scheme for inference. Detailed numerical simulations confirm the appropriateness of our suggested inference schemes.

Wavelet estimations of a density function in two-class mixture model

This paper considers nonparametric estimations of a density function in a two-class mixture model. A linear wavelet estimator and an adaptive wavelet estimator are constructed. Upper bound estimations over $ L^{p}\; (1\leq p < +\infty) $ risk of those wavelet estimators are proved in Besov spaces. When $ \tilde{p}\geq p\geq1 $, the convergence rate of adaptive wavelet estimator is the same as the linear estimator up to a $ \ln n $ factor. The adaptive wavelet estimator can get better than the linear estimator in the case of $ 1\leq \tilde{p} < p $. Finally, some numerical experiments are presented to validate the theoretical results.

Data-driven wavelet estimations in the convolution structure density model

<abstract><p>Based on a data-driven kernel estimator, Lepski and Willer considered the problem of adaptive $ L^{p} $ risk estimations in the convolution structure density model in 2017 and 2019. This current paper studies the same problem with a data-driven wavelet estimator on Besov spaces, as wavelet estimations offer fast algorithm and provide more local information. Our results can reduce to the traditional adaptive wavelet estimations in the classical density model with no errors, as well as deconvolutional model.</p></abstract>

Regularized Bi-Directional Deconvolution for Wavelet Estimation and Its Field Application in CO₂ Storage Characterization

Regularized Bi-Directional Deconvolution for Wavelet Estimation and Its Field Application in CO₂ Storage Characterization

Pointwise Estimation of Anisotropic Regression Functions Using Wavelets with Data-Driven Selection Rule

For nonparametric regression estimation, conventional research all focus on isotropic regression function. In this paper, a linear wavelet estimator of anisotropic regression function is constructed, the rate of convergence of this estimator is discussed in anisotropic Besov spaces. More importantly, in order to obtain an adaptive estimator, a regression estimator is proposed with scaling parameter data-driven selection rule. It turns out that our results attain the optimal convergence rate of nonparametric pointwise estimation.

Wavelet estimation for the nonparametric additive model in random design and long-memory dependent errors

We investigate the nonparametric additive regression estimation in random design and long-memory errors and construct adaptive thresholding estimators based on wavelet series. The proposed approach achieves asymptotically near-optimal convergence rates when the unknown function and its univariate additive components belong to Besov space. We consider the problem under two noise structures; (1) homoskedastic Gaussian long memory errors and (2) heteroskedastic Gaussian long memory errors. In the homoskedastic long-memory error case, the estimator is completely adaptive with respect to the long-memory parameter. In the heteroskedastic long-memory case, the estimator may not be adaptive with respect to the long-memory parameter unless the heteroskedasticity is of polynomial form. In either case, the convergence rates depend on the long-memory parameter only when long-memory is strong enough, otherwise, the rates are identical to those under i.i.d. errors. In addition, convergence rates are free from the curse of dimensionality.

Robust Elastic Full-Waveform Inversion Based on Normalized Cross-Correlation Source Wavelet Inversion

The elastic full-waveform inversion (EFWI) method efficiently utilizes the amplitude, phase, and travel time information present in multi-component seismic recordings to create detailed parameter models of subsurface structures. Within full-waveform inversion (FWI), accurate source wavelet estimation significantly impacts both the convergence and final result quality. The source wavelet, serving as the initial condition for the wave equation’s forward modeling algorithm, directly influences the matching degree between observed and synthetic data. This study introduces a novel method for estimating the source wavelet utilizing cross-correlation norm elastic waveform inversion (CNEWI) and outlines the EFWI algorithm flow based on this CNEWI source wavelet inversion. The CNEWI method estimates the source wavelet by employing normalized cross-correlation processing on near-offset direct waves, thereby reducing the susceptibility to strong amplitude interference such as bad traces and surface wave residuals. The proposed CNEWI method exhibits a superior computational efficiency compared to conventional L2-norm waveform inversion for source wavelet estimation. Numerical experiments, including in ideal scenarios, with seismic data with bad traces, and with multi-component data, validate the advantages of the proposed method in both source wavelet estimation and EFWI compared to the traditional inversion method.

Quantification of Long-Range Dependence in Hydroclimatic Time Series: A Method-Comparison Study

Abstract Accurate evaluation of the long-range dependence in hydroclimatic time series is important for understanding its inherent characteristics. However, the reliability of its evaluation may be questioned, since different methods may yield various outcomes. In this study, we evaluate the performances of seven widely used methods for estimating long-range dependence: absolute moment estimation, difference variance estimation, residuals variance estimation, rescaled range estimation, periodogram estimation, wavelet estimation (WLE), and discrete second derivative estimation (DSDE). We examine the influences of six major factors: data length, mean value, three nonstationary components (trend, jump, and periodicity), and one stationary component (short-range dependence). Results from the Monte Carlo experiments show that WLE and DSDE have greater credibility than the other five methods. They also reveal that data length, as well as stationary and nonstationary components, have notable influences on the evaluation of long-range dependence. Following it, we use the WLE and DSDE methods to evaluate the long-range dependence of precipitation during 1961–2015 on the Tibetan Plateau. The results indicate that the precipitation variability mirrors the long-range dependence of the Indian summer monsoon but with obvious spatial difference. This result is consistent with the observations made by previous studies, further confirming the superiority of the WLE and DSDE methods. The outcomes from this study have important implications for modeling and prediction of hydroclimatic time series.