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A major key success factor regarding proficient Bayes threshold denoising refers to noise variance estimation. This paper focuses on assessing different noise variance estimations in three Bayes threshold models on two different characteristic brain lesions/tumor magnetic resonance imaging (MRIs).

Here, three Bayes threshold denoising models based on different noise variance estimations under the stationary wavelet transforms (SWT) domain are mainly assessed, compared to state-of-the-art non-local means (NLMs). Each of those three models, namely D1, GB and DR models, respectively, depends on the most detail wavelet subband at the first resolution level, on the entirely global detail subbands and on the detail subband in each direction/resolution. Explicit and implicit denoising performance are consecutively assessed by threshold denoising and segmentation identification results.

Implicit performance assessment points the first–second best accuracy, 0.9181 and 0.9048 Dice similarity coefficient (Dice), sequentially yielded by GB and DR; reliability is indicated by 45.66% Dice dropping of DR, compared against 53.38, 61.03 and 35.48% of D1 GB and NLMs, when increasing 0.2 to 0.9 noise level on brain lesions MRI. For brain tumor MRI under 0.2 noise level, it denotes the best accuracy of 0.9592 Dice, resulted by DR; however, 8.09% Dice dropping of DR, relative to 6.72%, 8.85 and 39.36% of D1, GB and NLMs is denoted. The lowest explicit and implicit denoising performances of NLMs are obviously pointed.

A future improvement of denoising performance possibly refers to creating a semi-supervised denoising conjunction model. Such model utilizes the denoised MRIs, resulted by DR and D1 thresholding model as uncorrupted image version along with the noisy MRIs, representing corrupted version ones during autoencoder training phase, to reconstruct the original clean image.

This paper should be of interest to readers in the areas of technologies of computing and information science, including data science and applications, computational health informatics, especially applied as a decision support tool for medical image processing.

In most cases, DR and D1 provide the first–second best implicit performances in terms of accuracy and reliability on both simulated, low-detail small-size region-of-interest (ROI) brain lesions and realistic, high-detail large-size ROI brain tumor MRIs.

The purpose of this paper is to investigate the condition of insulation in high-voltage equipments using partial discharge (PD) measurements. It proposes the methods to eliminate several noises like white noise, random noise and discrete spectral interferences which severely pollutes the PD signals. The study aims to remove these noises from the PD signal effectively by preserving the signal features.

This paper employs fast Fourier transform, discrete wavelet transform and translational invariant wavelet transform (TIWT) for denoising the PD signals. The simulated damped exponential pulse and damped oscillatory pulse with low- and high-level noises and a measured PD signal are considered for this analysis. The conventional wavelet denoising approach is also improved by estimating the automated global optimum threshold value using genetic algorithm (GA). The statistical parameters are evaluated and compared. Among these methods, GA-based TIWT approach provides robustness and reduces computational complexity.

This paper provides effective condition monitoring of power apparatus using GA-based TIWT approach. This method provides the low value of mean square error, pulse amplitude distortion and also high reduction in noise level due to its robustness and reduced computational complexity. It suggests that this approach works well for both signals immersed in noise as well as for noise immersed in signals.

Because of the chosen PD signals, the research results may lack for multiple discharges. Therefore, researchers are encouraged to test the proposed propositions further.

The paper includes implication for the development of online testing for equipment analysis and diagnostics during normal operating condition. Corrective actions can be planned and implemented, resulting in reduced unscheduled downtime.

This PD-based analysis often present well in advance of insulation failure, asset managers can monitor it over time and make informed strategic decisions regarding the repair or replacement of the equipment. These predictive diagnostics help society to prioritize investments before an unexpected outage occurs.

This paper provides an enhanced study of condition monitoring of HV power apparatus by which life time of insulation can be increased by taking preventive measures.

Ciliated microelectromechanical system (MEMS) vector hydrophones pick up sound signals through Wheatstone bridge in cross beam-ciliated microstructures to achieve information transmission. This paper aims to overcome the complexity and variability of the marine environment and achieve accurate location of targets. In this paper, a new method for ocean noise denoising based on improved complete ensemble empirical mode decomposition with adaptive noise combined with wavelet threshold processing method (CEEMDAN-WT) is proposed.

Based on the CEEMDAN-WT method, the signal is decomposed into different intrinsic mode functions (IMFs), and relevant parameters are selected to obtain IMF denoised signals through WT method for the noisy mode components with low sample entropy. The final pure signal is obtained by reconstructing the unprocessed mode components and the denoising component, effectively separating the signal from the wave interference.

The three methods of empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD) and CEEMDAN are compared and analyzed by simulation. The simulation results show that the CEEMDAN method has higher signal-to-noise ratio and smaller reconstruction error than EMD and EEMD. The feasibility and practicability of the combined denoising method are verified by indoor and outdoor experiments, and the underwater acoustic experiment data after processing are combined beams. The problem of blurry left and right sides is solved, and the high precision orientation of the target is realized.

This algorithm provides a theoretical basis for MEMS hydrophones to achieve accurate target positioning in the ocean, and can be applied to the hardware design of sonobuoys, which is widely used in various underwater acoustic work.

The traditional total variation (TV) models in wavelet domain use thresholding directly in coefficients selection and show that Gibbs' phenomenon exists. However, the nonzero coefficient index set selected by hard thresholding techniques may not be the best choice to obtain the least oscillatory reconstructions near edges. This paper aims to propose an image denoising method based on TV and grey theory in the wavelet domain to solve the defect of traditional methods.

In this paper, the authors divide wavelet into two parts: low frequency area and high frequency area; in different areas different methods are used. They apply grey theory in wavelet coefficient selection. The new algorithm gives a new method of wavelet coefficient selection, solves the nonzero coefficients sort, and achieves a good image denoising result while reducing the phenomenon of “Gibbs.”

The results show that the method proposed in this paper can distinguish between the information of image and noise accurately and also reduce the Gibbs artifacts. From the comparisons, the model proposed preserves the important information of the image very well and shows very good performance.

The proposed image denoising model introducing grey relation analysis in the wavelet coefficients selecting and modifying is original. The proposed model provides a viable tool to engineers for processing the image.

The paper aims to do some further research on grey relational analysis applied in wavelet transform, and proposed a grey relational threshold algorithm for image denoising. This study tries to suppress the noise while retaining the edges and important structures as much as possible.

The paper analyzed the characters of noises and edges distribution in different subbands; then used the grey relational value to calculate the relationship of scale, direction and noise deviation. This paper used the grey relational value of scale, direction and noise deviation as influenced factors, and proposed a grey relational threshold algorithm.

Grey relational analysis used in threshold setting has the superiority in image denoising. The simulation results have already certified both in visual effect and peak signal to noise ratio (PSNR).

This paper applied grey relation theory into image denoising, and proposed a grey relational threshold algorithm. It provides a novel method for image denoising.

Multiresolution representations of data are classical tools in image processing applications. The purpose of this paper is to discuss a particular problem, obtaining good reconstructions of noise images.

A nonlinear multiresolution scheme within Harten's framework corresponding to a nonlinear cell‐average technique is used for color image denoising.

This paper finds it is possible, for example, to apply the theoretical framework to case studies in internationally operating companies delivering a mix of goods and services.

The present study provides a starting point for further research in the denoising problems using nonlinear techniques.

Moreover, the proposed framework has proven to be useful in improving the classical linear multiresolution approaches.

The purpose of this paper is to construct a novel grey filter model for image denoising and to solve the problems which exist in the image denoising filter method, in which the true intensity value of each noisy pixel cannot be predicted better.

Based on the definition of stepwise, the defects of traditional grey prediction models are found. A new grey filter model, named grey stepwise prediction model, is proposed. The new filter model for the image denoising is based on each noisy pixel's neighborhoods stepwise, which is the eight pixels around the noisy pixel, to predict its intensity value and to solve the problems which exist in the image denoising filter method.

The experiment results show that the improved filter model can effectively eliminate image noise, preserve the image's details and edges, increase SNR (signal‐to‐noise ratio) as well as PSNR (peak signal‐to‐noise ratio), reduce MSE (mean square error) and MAE (mean absolute error), and significantly improve the image's visual effect.

The new filter method exposed in the paper can be used to 8‐bit gray‐scale image denoising. The method can also be used to binary image denoising.

The paper succeeds in constructing a novel filter method for image denoding, and it is undoubtedly a new development in image recovery algorithm and grey systems theory.

This paper aims to solve the problem that strong noise interference seriously affects the direction of arrival (DOA) estimation in complex underwater acoustic environment. In this paper, a combined noise reduction algorithm and micro-electro-mechanical system (MEMS) vector hydrophone DOA estimation algorithm based on singular value decomposition (SVD), variational mode decomposition (VMD) and wavelet threshold denoising (WTD) is proposed.

Firstly, the parameters of VMD are determined by SVD, and the VMD method can decompose the signal into multiple intrinsic mode functions (IMFs). Secondly, the effective IMF component is determined according to the correlation coefficient criterion and the IMF less than the threshold is processed by WTD. Then, reconstruction is carried out to achieve the purpose of denoising and calibration baseline drift. Finally, DOA estimation is achieved by the combined directional algorithm of preprocessed signal.

Simulation and field experiments results show that the algorithm has good noise reduction and baseline drift correction effects for nonstationary underwater signals, and high-precision azimuth estimation is realized.

This research provides the basis for MEMS hydrophone detection and positioning and has great engineering significance in underwater detection system.

In this paper, it is set out a hybrid data analysis method based on the combination of wavelet techniques and principal‐components regression (PCR). The purpose of this paper is to study the dynamics of the stock returns within the French stock market.

Wavelet‐based thresholding techniques are applied to the stock price series in order to obtain a set of explanatory variables that are practically noise‐free. The PCR is then carried out on the new set of regressors.

The empirical results show that the suggested method allows extraction and interpretation of the factors that influence the stock price changes. Moreover, the wavelet‐PCR improves the explanatory power of the regression model as well as its forecasting quality.

The proposed technique offers investors a better understanding of the mechanisms that explain the stock return dynamics as it removes the noise that affects financial time series.

The paper uses a new denoising framework for financial assets. The paper thinks that this framework might be of great value for academics as well as for financial investors.

This paper aims to propose a hybrid method based on polynomial fitting bias self-compensation, grey forward-backward linear prediction (GFBLP) and moving average filter (MAF) for error compensation in micro-electromechanical system gyroscope signal especially under motion state.

The error compensation can be divided into two processes: bias correction and noise reduction. A polynomial drift angle fitting algorithm is used to correct bias before denoising processing. For noise reduction, operation can be taken in two stages: detection and processing. First, sample variances are used to judge motion state. According to the detection results, algorithmic system switches between grey GFBLP and MAF to ensure fast convergence rate and small steady-state error.

Experimental results show that the proposed method can correct bias effectively for practical gyroscope signal, and can eliminate noise effectively for both practical gyroscope signal and synthetic signal, which indicates the effectiveness of the proposed method.

Bias correction and noise reduction are considerations. Noise contained in practical or synthetic signal can be reduced rapidly and effectively, which benefits from the new idea of combination grey GFBLP, MAF and sample variances. And most importantly, it is applicable for signal denoising under arbitrary motion state condition, which is different from other methods where the convergence performance is seldom analyzed.