Wavelet Shrinkage Research Articles

Advanced Ocular Artifact Removal In EEG For Enhanced Schizophrenia Diagnosis Using Wavelet Shrinkage And LSTM Deep Learning Techniques

Advanced Ocular Artifact Removal In EEG For Enhanced Schizophrenia Diagnosis Using Wavelet Shrinkage And LSTM Deep Learning Techniques

Adaptive dual-domain filtering for random seismic noise removal

Random noise significantly reduces the signal-to-noise ratio of seismic data and affects the accuracy of seismic interpretation. Traditional denoising methods typically require manual parameter tuning to increase robustness and accuracy across various random noise levels. In this study, based on the statistical definition of random noise, we use the variance of random noise as the level of random noise and develop an adaptive dual-domain filter (ADDF). The ADDF method estimates the random noise variance in the seismic data and uses this estimation to effectively denoise the seismic data. First, we use a difference operator in two directions to remove the useful structures from the seismic data. The processed data are then used to estimate the global random noise variance through iterative statistical processing. In the denoising process of the ADDF, the seismic data are masked by a bilateral filter in the spatial domain, followed by a short-time Fourier transform with wavelet shrinkage in the frequency domain, both controlled by the adaptively estimated random noise variance. The dual-domain filter is applied iteratively for the best performance. Synthetic experiments demonstrate the robustness of the ADDF in accurately estimating the noise variance without tuning parameters, and its superior denoising performance is evident in synthetic examples and field data when compared with two typical denoising methods: f- x deconvolution and curvelet domain thresholding. As an adaptive random noise estimation and removal method, ADDF relies only on seismic data, making denoising random noise more objective and accurate without manual adjustment.

A Recently Formulated Individual Control Chart Designed for Quality Control Applications within the Health-care Domain

Quality control charts are based on data that is also used for various statistical analyses, such as regression, time series analysis, and other types of analyses. This implies that the data used to create these charts may contain outliers, potentially compromising their accuracy. To eliminate any potential noise or pollution from the data, a researcher proposed using wavelet shrinkage with a threshold and comparing the resulting data with Shewart's individual chart. Based on this, a new quality control chart was proposed and built using a universal approach for assessing the level of thresholding, representing the individual chart for wavelet haar with soft and hard thresholding. Following that, a comparison was performed between them as well as with Shewart's individual chart. This letter's most significant conclusion is that, in addition to using two real data points—triglyceride, which was recorded by a laboratory blood analyzer in Al-Jumhuri and at the specialized Center for Cardiology Hospital in Erbil Governorate—it may be possible to use wavelet shrinkage with a threshold to address issues of noise or pollution when Shewart's individual chart was made and used. Moreover, the wavelet method effectively reduces deviation, as demonstrated in both sets of data.

A Wavelet Shrinkage Mixed with a Single-level 2D Discrete Wavelet Transform for Image Denoising

The single-level 2D discrete wavelet transform method is a powerful technique for effectively removing Gaussian noise from natural images. Its effectiveness is attributed to its ability to capture a signal's energy at low energy conversion values, allowing for efficient noise reduction while preserving essential image details. The wavelet noise reduction method mitigates the noise present in the waveform coefficients produced by the discrete wavelet transform. In this study, three different wavelet families—Daubechies (db7), Coiflets (coif5), and Fejér-Korovkin (fk4)—were evaluated for their noise removal capabilities using the Bayes shrink method. This approach was applied to a set of images, and the performance was analyzed using the Mean Squared Error (MSE) and Peak Signal-to-Noise Ratio (PSNR) metrics. Our results demonstrated that among the wavelet families tested, the Fejér-Korovkin (fk4) wavelet consistently outperformed the others. The fk4 wavelet family yielded the lowest MSE values, indicating minimal reconstruction error, and the highest PSNR values, reflecting superior noise suppression and better image quality across all tested images. These findings suggest that the fk4 wavelet family, when combined with the Bayes shrink method, provides a robust framework for Gaussian noise reduction in natural images. The comparative analysis highlights the importance of selecting appropriate wavelet families to optimize noise reduction performance, paving the way for further research and potential improvements in image denoising techniques.

A Bayesian wavelet shrinkage rule under LINEX loss function

A Bayesian wavelet shrinkage rule under LINEX loss function

Long-term software fault prediction with wavelet shrinkage estimation

Wavelet shrinkage estimation received considerable attentions to estimate stochastic processes such as a non-homogeneous Poisson process in a non-parametric way, and was applied to software reliability estimation/prediction. However, it lacks the prediction ability for unknown future patterns in long term and penalizes assessing the software reliability in practice. In this paper, we focus on the long-term prediction of the number of software faults detected in the testing phase and propose many novel long-term prediction methods based on the wavelet shrinkage estimation. The fundamental idea is to adopt both the denoised fault-count data and prediction values, and to minimize several kinds of loss functions to make effective predictions. We also develop an automated wavelet-based software reliability assessment tool, W-SRAT2, which is a drastic extension of the existing tool, W-SRAT, by adding those prediction algorithms. In numerical experiments with 6 actual software development project data, we investigate the predictive performance of our long-term prediction approaches, which consist of 2,640 combinations, and compare them with the common software reliability growth models with the maximum likelihood estimation. It is shown that our wavelet shrinkage estimation/prediction methods outperform the existing software reliability growth models.

Denoising of Digital Images Using Spatial Domain Edge Detection Approach

Better results can be produced by the Hybridization of the Wavelet-based image denoising technique and sparse representation of edges. A novel method for spatial domain edge identification that produces a denoised image that has been tainted by additive white Gaussian noise without sacrificing the image's detail information. By combining bivariate shrinkage and local profile edge detection, a denoised image is produced. In this paper, the hybridization method is proposed by modifying the existing Wavelet Transform for image denoising leading to an increase in the PSNR and SSIM as compared to that given by existing Wavelet denoising techniques, maintaining the visual quality of an image. To modify the wavelet coefficients Bivariate Wavelet Shrinkage is used. The quality assessment is evaluated in terms of SSIM value and PSNR value.

Wavelet Shrinkage Estimation for Mean Matrix of Matrix-Variate Elliptically Contoured Distributions

Wavelet Shrinkage Estimation for Mean Matrix of Matrix-Variate Elliptically Contoured Distributions

AN ENHANCED SHRINKAGE FUNCTION FOR DENOISING ECONOMIC TIME SERIES DATA USING WAVELET ANALYSIS

In the realm of economic (financial) time series analysis, accurate prediction holds paramount importance. However, these data often suffer from the presence of noise, particularly in highly random and non-stationary datasets like stock market data. Dealing with noisy data makes predicting noise-free economic models exceedingly challenging. This research paper introduces an innovative shrinkage (thresholding) function designed to improve the efficiency of wavelet shrinkage denoising in the context of financial time series data. The proposed function is constructed based on an arctangent model with adjustable parameters meticulously chosen to ensure the function maintains continuous differentiability. The application of this novel shrinkage function effectively reduces noise in stock data. Employing R program for data analysis and figure plotting, the performance of this approach is rigorously validated using closing price data from the Shanghai Composite Index, spanning the period from January 4, 2000 to August 28, 2023. The experimental results demonstrate that the proposed thresholding function outperforms classical shrinkage functions (hard, soft, and nonnegative garrote) in both continuous derivative property and denoising efficacy.

Low and high dimensional wavelet thresholds for matrix-variate normal distribution

The matrix-variate normal distribution is a probability distribution that is a generalization of the multivariate normal distribution to matrix-valued random variables. In this paper, we introduce a wavelet shrinkage estimator based on Stein’s unbiased risk estimate (SURE) threshold for matrix-variate normal distribution. We find a new SURE threshold for soft thresholding wavelet shrinkage estimator under the reflected normal balanced loss function in low and high dimensional cases. Also, we obtain the restricted wavelet shrinkage estimator based on non-negative sub matrix of the mean matrix. Finally, we present a simulation study to test the validity of the wavelet shrinkage estimator and two real examples for low and high dimensional data sets.

Implementation of Adaptive-Bayesian DStoch technique for obtaining winds from MST radar covering higher altitudes

It is challenging to estimate winds accurately from higher altitudes using VHF-MST radar. The current study introduces the Adaptive-Bayesian Deterministic Stochastics Technique (ADStoch), which implements an Empirical Bayesian 1D prediction method using stochastics to analyze radar signals. A new and robust estimator for empirical wavelet shrinkage with Gaussian prior of the nonzero mean for wavelet coefficients is presented, which makes the current prior different from other priors. The mean parameters and the prior covariance hyperparameters follow a pseudo maximum likelihood method for computation. Details on the implemented algorithm developed from scratch using C# are also presented. This technique outperforms contemporary techniques discussed in this context that can recover signals buried in noise established based on the analysis of moment and quality. The estimated Wind is cross-validated for accuracy with the observed wind from the GPS radiosonde operated simultaneously. This technique can consistently extract 3D wind that can reach the range of 25.5 km–28.2 km, improving the conventional maximum altitude of 21.2 km in real time for the MST radar. It is concluded that the ADStoch analysis technique can effectively obtain VHF-MST radar signals at significantly higher altitudes, which is helpful in various scientific investigations.

Using Wavelet Shrinkage to Deal with Contamination Problem in Survival Function for Weibull Distribution

Using Wavelet Shrinkage to Deal with Contamination Problem in Survival Function for Weibull Distribution

A new wavelet-based estimation of conditional density via block threshold method

A new wavelet-based estimator of the conditional density is investigated. The estimator is constructed by combining a special ratio technique and applying a non negative estimator to the density function in the denominator. We used a wavelet shrinkage technique to find an adaptive estimator for this problem. In particular, a block thresholding estimator is proposed, and we prove that it enjoys powerful mean integrated squared error properties over Besov balls. Moreover, it is shown that convergence rates for the mean integrated squared error (MISE) of the adaptive estimator are optimal under some mild assumptions. Finally, a numerical example has been considered to illustrate the performance of the estimator.

A wavelet-based method in aggregated functional data analysis

Abstract In this paper, we consider aggregated functional data composed by a linear combination of component curves and the problem of estimating these component curves. We propose the application of a bayesian wavelet shrinkage rule based on a mixture of a point mass function at zero and the logistic distribution as prior to wavelet coefficients to estimate mean curves of components. This procedure has the advantage of estimating component functions with important local characteristics such as discontinuities, spikes and oscillations for example, due the features of wavelet basis expansion of functions. Simulation studies were done to evaluate the performance of the proposed method, and its results are compared with a spline-based method. An application on the so-called Tecator dataset is also provided.

Simulation studies to compare bayesian wavelet shrinkage methods in aggregated functional data

Simulation studies to compare bayesian wavelet shrinkage methods in aggregated functional data

Wavelet shrinkage in nonparametric regression models with positive noise

ABSTRACT Wavelet shrinkage estimators are widely applied to analyse datasets in wavelet domain from several fields of science. They typically act by reducing magnitudes of empirical coefficients in a discrete wavelet transformation to estimate wavelet coefficients. In nonparametric regression problems, most of the shrinkage rules are derived from models composed of an unknown function with additive Gaussian noise. Although Gaussian noise assumption is reasonable in several real data analysis, mainly for large sample sizes, it is not general. Contaminated data with positive noise can occur in practice and nonparametric regression models with positive noise bring challenges in wavelet shrinkage point of view. In this sense, this work proposes bayesian shrinkage rules to estimate wavelet coefficients from a nonparametric regression framework with additive and strictly positive noise under exponential and lognormal distributions. Computational aspects are discussed and simulation studies to analyse the performances of the proposed shrinkage rules and compare them with standard techniques are done. An application for winning times Boston Marathon dataset is also provided.

Smart fabric inspection using Mimosa pudica plant

Fabric quality governing and defect detection are playing a crucial role in the textile industry with the development of high customer demand in the fashion market. This work presents fabric defect detection using the sensitive plant segmentation algorithm (SPSA) which, is developed with the sensitive behaviour of the plant biologically named “Mimosa pudica”i. This method consists of two stages. The first stage enhances the contrast of the defective fabric image and the second stage segments the fabric defects with aid of SPSA. The proposed work SPSA is developed for defective pixels identification in both uniform and non-uniform patterns of fabrics. In this work, SPSA has been done by checking with devised condition, correlation and error probability. Every pixel will be checked with the developed algorithm, to get marked either defective or non-defective pixels. The proposed SPSA has been tested on the different types of fabric defect databases and shows a prodigious performance over existing methods like the Differential evolution based optimal Gabor filter model (DEOGF), Gabor filter bank (GFB), Adaptive sparse representation-based detection model (ASR) and Fourier and wavelet shrinkage (FWR).

Research on Improved Wavelet Threshold Denoising Method for Non-Contact Force and Magnetic Signals

In order to solve the problem of noise interference in the collected magneto mechanical signals, a new wavelet shrinkage threshold based on adaptive estimation is proposed. Based on the shortcomings of the traditional threshold function, an improved threshold function is proposed, and the parameters of the threshold function are solved by the improved genetic algorithm, and the optimal denoising effect is finally obtained. The new threshold function can not only make up the defects of each threshold function, ensure the continuity of threshold function, but also flexibly adjust the threshold to adapt to different noise conditions, and solve the deviation caused by inherent threshold function, and protect the useful information with noise signals.

Denoising Of Digital Images Using Cyclespinning Algorithm With Shifted DWT

Noise determination and estimating a signal along with all its details proves a challenging task in signal processing. This issue has been addressed in the past using various discrete wavelet transform (DWT) based techniques. The signal is estimated as linear average of individual estimates derived from translated and wavelet-thresholded versions of a noisy signal by cycle spinning technique. In this paper, we propose a modified cycle zpinning algorithm with a new scaled down threshold of wavelet shrinkage for denoising images containing zero mean Gaussian noise using linear average of reconstructions obtained from shifted sequences’ DWT. This considerably improves the denoising performance of the conventional recursive cycle spinning algorithm and requires drasticallyless computations. Denoising performance of the proposed algorithm is benchmarked with published Recursive Cycle spinning, Buades NL means and Dual tree Complex Wavelet algorithms visually and quantitatively.

Terahertz Spectroscopic Characterization and Thickness Evaluation of Internal Delamination Defects in GFRP Composites

The use of terahertz time-domain spectroscopy (THz-TDS) for the nondestructive testing and evaluation (NDT&E) of materials and structural systems has attracted significant attention over the past two decades due to its superior spatial resolution and capabilities of detecting and characterizing defects and structural damage in non-conducting materials. In this study, the THz-TDS system is used to detect, localize and evaluate hidden multi-delamination defects (i.e., a three-level multi-delamination system) in multilayered GFRP composite laminates. To obtain accurate results, a wavelet shrinkage de-noising algorithm is used to remove the noise from the measured time-of-flight (TOF) signals. The thickness and location of each delamination defect in the z-direction (i.e., through-the-thickness direction) are calculated from the de-noised TOF signals considering the interaction between the pulsed THz waves and the different interfaces in the GFRP composite laminates. A comparison between the actual and the measured thickness values of the delamination defects before and after the wavelet shrinkage denoising process indicates that the latter provides better results with less than 3.712% relative error, while the relative error of the non-de-noised signals reaches 16.388%. Also, the power and absorbance levels of the THz waves at every interface with different refractive indices in the GFRP composite laminates are evaluated based on analytical and experimental approaches. The present study provides an adequate theoretical analysis that could help NDT&E specialists to estimate the maximum thickness of GFRP composite materials and/or structures with different interfaces that can be evaluated by the THz-TDS. Also, the accuracy of the obtained results highlights the capabilities of the THz-TDS for the NDT&E of multilayered GFRP composite laminates.