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Wavelets transforms are effective mathematical tools useful in compression and denoising of n-D signals. Subjecting a signal to discrete wavelet transforms (DWT) generates approximation and detailed coefficients that are similar to the coefficients generated by passing the signal through lowpass and high pass filters respectively. Multilevel decomposition (filtering) can be carried out which can successively filter the signal at each bandpass. In this work, a normal sinus rhythm ECG signal noised with a sinewave was denoised by DWT using by members of mother wavelets like coiflet, symlet and biorthogonal families. The denoising performance of the wavelets were evaluated by comparing the signal characteristics of the original and the denoised signals. [ABSTRACT FROM AUTHOR]

The primary reason most people invest in stocks is the potential return compared to alternatives such as bank certificates of deposit, gold, and Treasury bonds. This requires accurate information about the stock market, price changes and predicting future trends. The main purpose of this study is to present a method based on wavelet denoising and dynamic time warping to identify the stock price pattern in the Tehran Stock Exchange. Instead of focusing and summarizing different and numerous methods to predict stock prices, this research concentrates on neural networks and wavelet denoising, and dynamic time warping to identify the stock price patterns. This methodology has been approved by researchers as a new effective technique. In this regard, first, using the wavelet denoising preprocessing step, noise is removed from the stock price time series, and then the extracted data was used as input to the dynamic time warping prediction model. MATLAB software version 9.11 was used to analyze the research data. The statistical population of the present study includes 3 shares among the shares of steel industry companies of Tehran Stock Exchange. The research was conducted in the period 2016 to 2020. The results show that the predictions obtained from the dynamic time warping method equipped with the wavelet denoising preprocessing step in comparison with the predictions obtainedfrom the dynamic time warping method without the wavelet denoising preprocessing step in the sample, have been associated with much less accuracy and error. [ABSTRACT FROM AUTHOR]

Purpose: The cutting tool wear is one of the major physical phenomena to be studied in order to optimize the production and to guarantee the quality of manufactured products. Indeed, the wear affects the quality of the machined surfaces, the durability of the cutting tool and the imposed geometric tolerances. Since uncontrolled wear can lead to premature tool breaking and therefore a drop in productivity, monitoring the machining process is a necessary important task. Methods: In this study, aims to combine experimental results from vibration signature and cutting forces with experimental and numerical methodology allowing the prediction of optimal lifetime of the tool's wear, and to detect the brutal damage of this last, based especially an optimized wavelet multi-resolution analysis (OWMRA), allowed the denoising of the measured signals. Results: The OWMRA revealed two peaks, which appear below and above the tool's resonance frequency. The amplitude evolution of these two peaks is directly related to the effect of the tool wear on the natural frequency band. The strategy adopted is based on a slight modification of a new spectral indicator and in particular the modified overall level (OLmod) calculated from the cutting forces and reconstructed signals. Conclusions: The modified overall level (OLmod) has also shown its effectiveness of providing the moment of transition of the wear of its normal phase to accelerated phase around the band of the cutting tool characteristic frequencies, corresponding to catastrophic wear leading to stopping machining at the appropriate time and which can alert the user as soon as the criterion of the transition to catastrophic wear is reached. [ABSTRACT FROM AUTHOR]

Convolutional neural networks are widely used for feature extraction in signal recognition. A critical issue in convolutional neural networks is the loss of information which increases with the depth of the network. To reduce information loss, this paper proposes a downsampling operator based on wavelet transforms, in which all wavelet components are fused as an output. The corresponding weights of the components are computed via signal back-propagation of the neural network. Meanwhile, a denoising rule of soft-threshold is devised for all wavelet components to achieve multi-channel adaptive denoising of the signal in the frequency domain. More precisely, the thresholds in each frequency band are optimised using a gradient descent algorithm so that the reconstructed signal carries information from each frequency band of the original signal while the noise is filtered out. Based on this, a 1-level wavelet feature extraction structure consisting of 1-stride convolution and full-component wavelet downsampling operation is designed. Finally, with a number of experiments on signal recognition, the proposed algorithm achieves favourable performance compared with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In many practical communication environments, the presence of uncertain and hard-to-estimate noise poses significant challenges to cognitive radio spectrum sensing systems, especially when the noise distribution deviates from the Gaussian distribution. This paper introduces a cutting-edge multi-antenna spectrum sensing methodology that synergistically integrates complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), wavelet packet analysis, and differential entropy. Signal feature extraction commences by employing CEEMDAN decomposition and wavelet packet analysis to denoise signals collected by secondary antenna users. Subsequently, the differential entropy of the preprocessed signal observations serves as the feature vector for spectrum sensing. The spectrum sensing module utilizes the SVM classification algorithm for training, while incorporating elite opposition-based learning and the sparrow search algorithm with genetic variation to determine optimal kernel function parameters. Following successful training, a decision function is derived, which can obviate the need for threshold derivation present in conventional spectrum sensing methods. Experimental validation of the proposed methodology is conducted and comprehensively analyzed, conclusively demonstrating its remarkable efficacy in enhancing spectrum sensing performance. [ABSTRACT FROM AUTHOR]

In order to meet the requirements of mobile marine seismometers to observe and record seismic signals, a study of fast and accurate seismic signal recognition was carried out. This paper introduces the use of the wavelet analysis method for seismic signal processing and recognition, and compares and analyzes the abilities of different wavelet basis functions to detect the seismic signal. By denoising and reconstructing the signal, the distribution law of the wavelet coefficients of seismic signal at different scales was obtained. On this basis, this paper proposes an identification model of seismic signals based on wavelet analysis and thereby solves the conflict between high speed and high accuracy of seismic signal recognition methods. In this study, the simulation was carried out in the Matlab2020b environment, and the feasibility of wavelet recognition algorithm was proven by applying this algorithm to the seismic signal database for experimental verification. [ABSTRACT FROM AUTHOR]

To further improve the separation accuracy of the denoising source separation algorithm under the noisy model X = AS + N, this paper replaces the original nonlinear function with a new nonlinear function (sin) for non-Gaussian signals and the separated signal is denoised by the maximum overlap discrete wavelet transform (MODWT). The simulation results based on communication signals and image signals show that the improved algorithm achieves better performance in blind source separation (BSS) under the universal noisy model X = A(S + n) + N. [ABSTRACT FROM AUTHOR]

Guided wave technology shows excellent capacity in the damage identification of the pipeline. In practical inspection, the detection ability is greatly reduced due to the interference echo signal from the feature structure in the pipeline. In this paper, the propagation models of guided wave in straight pipe and pipe with feature structures are established, and the effect of feature structure on the guided wave echo signal is analyzed, including pipe with an elbow, ring joint, and accessory structure, and the corresponding damage identification strategies for pipe with different forms of features are proposed. The damage index of the echo signal difference and radial displacement signal is proposed to extract the signal from damage. Besides, to eliminate the noise effect caused by the actual detection situation, a novel guided wave denoising method based on the wavelet analysis is studied, and the analysis results indicate that the damage detection strategy based on the guided wave can accurately locate the damage region in both straight pipe and pipe with features and that the proposed denoising method can effectively eliminate the noise in the echo signal. [ABSTRACT FROM AUTHOR]

In view of the shortcomings of current wire rope magnetic flux leakage (MFL) detection devices such as large size and low sensitivity, as well as the poor noise reduction effect of MFL data and the low recognition rate of defects, this paper designs a wire rope three-dimensional MFL detection device based on unsaturated magnetic excitation (UME) and proposes a multilevel filtering algorithm. Six types of small gap broken wire defects can be effectively detected by the three-dimensional tunnel magnetoresistive sensor array. The multilevel filtering method based on EEMD and optimal wavelet is applied to three-dimensional UME signal processing, effectively suppressing noise interference. And color processing technology is applied to enhance the characterization of the defect images. A support vector machine recognition network based on the color moment feature vector as input is designed to classify broken wire defects, and the quantitative recognition rate of 98.572% is achieved when the limit error is 0.901%. The experimental results show that the detection device has the advantages of high sensitivity and simple structure and can collect MFL information in three directions, and the filtering algorithm effectively improves the signal-to-noise ratio and can realize the preliminary quantification of broken wire defects. [ABSTRACT FROM AUTHOR]

Cylindrical shell is a fundamental structure in the area of mechanical and architectural engineering. In the predesign stage, accurate analysis is a key step to guarantee the performance in application. Finite element method is a commonly used method in structural analysis. However, due to the limitations of interpolation functions, accuracy and efficiency are restricted. Wavelet finite element method is an advanced numerical method which uses wavelet functions to replace the traditional polynomial function to discrete the solving variables. Daubechies, B-spline wavelet on the interval (BSWI) etc. have been used to construct the elements. However, they are mainly focused on the elements with one kind of variable. That is, only the displacement variable is interpolated directly and the generalized stress and strain are calculated second. Multivariable wavelet finite element can deal with this problem, in which the three kinds of variables can be interpolated and solved directly, thus the calculation error can be avoiding. In this paper, the BSWI scaling functions are used to construct the wavelet finite elements for cylindrical shell, including BSWI element with one kind of variables (BSWI-WFE), BSWI element with two kinds of variables (BSWI-TwWFE) and BSWI element with three kinds of variables (BSWI-ThWFE). Several numerical examples for cylindrical shell are provided to analyze the performance of the constructed elements and compared with each other to indicate superiority and efficiency. [ABSTRACT FROM AUTHOR]

In this study, a wavelet denoising method is first used to eliminate the influence of noise. Then, an overlapping smooth window technique is introduced into the asymmetric multifractal detrended cross-correlation analysis method, which was combined with the multiscale multifractal analysis method, resulting in the proposed asymmetric multiscale multifractal detrended cross-correlation analysis method. This method not only remedies the pseudo-fluctuation defect of the traditional method, but also explores the asymmetric multifractal cross-correlation between China's rebar futures and spot markets at different scales. The results show the existence of an asymmetric multifractal cross-correlation between rebar futures and spot markets with upward and downward trends at different scales. This cross-correlation is highly complex at the small-scale, and more pronounced when the futures market is in an uptrend. [ABSTRACT FROM AUTHOR]

Stripe non-uniformity severely affects the quality of infrared images. It is challenging to remove stripe noise in low-texture images without blurring the details. We propose a single-frame image stripe correction algorithm that removes infrared noise while preserving image details. Firstly, wavelet transform is used for multi-scale analysis of the image. At the same time, Total variation model is used for small window to smooth the original image. The small-scale total variation model can well preserve the edge information of the image, but it will leave stripe noise. Therefore, according to the prior knowledge of the vertical component of the stripe noise, the spatial filtering is finally performed: the smoothed image is used as the guide image for the stripe noise denoising. It is possible to prevent the lead filter from mistaking the strong stripe noise as edge detail, resulting in corrected image residual streak noise. The algorithm is systematically evaluated by experiments on simulated images and original infrared images, as well as compared with the current advanced infrared stripe non-uniformity correction algorithms. It is proved that our algorithm can better eliminate stripe noise and preserve edge details. [ABSTRACT FROM AUTHOR]

With the electromagnetic environment becoming more and more complex and the analysis demand of the radar emitter intropulse signal presenting more and more urgent, a modified method of the radar emitter intrapulse signal blind sorting under wavelet denoising is proposed. This study aims to improve the weak adaptability to the noise of the fast independent component analysis (FastICA) algorithm and its blind source separating performance. In this method, a pre-processing of noise based on the modified wavelet denoising is added. Then the FastICA algorithm is used to sort the unknown radar emitter intrapulse signal for the next intrapulse signal analysis. Simulations and analysis indicate that the modified method improves the signal to noise ratio of the received intermediate signals and the blind sorting performance. [ABSTRACT FROM AUTHOR]

• The trend component issues, like zero drift and low frequency response, are addressed by the least square method. • Optimal energy fraction of main frequency band of blast vibration signal is 75%. • Frequency-domain energy of blast vibration signals is concentrated mainly in the low frequency segment. As a key parameter in blasting safety criteria, accurately describing the frequency's characteristics is of practical significance. Due to the deficiency of Fourier transform in the analysis of non-periodic and non-stationary signals, this study defined a wavelet frequency domain parameter, referred to as a main frequency band. A computational method associated with the wavelet packet transform is also proposed. To verify the feasibility of main frequency band and the proposed computational method in describing blasting frequency characteristics, an application is exemplified with field blasting vibration signals monitored in a mine. The effects of explosive charge and distance on main frequency band distribution characteristics are also studied. Results show that the main frequency band based on the computational method is a sensitive, accurate and efficient frequency parameter; it can accurately describe the frequency characteristics of blasting signals and effectively overcome the drawbacks in Fourier transform. When the explosive charge is constant, the span of main frequency reduces as a whole as the distance increases, and the frequency domain energy of blast vibration signals are concentrated mainly in the low-frequency range. When the distance is constant, the peak energy of blast vibration signals increase with the increase of explosive charge, without obvious change in main frequency band. To avoid the effects of interferences on frequency characteristics, the least square method is employed to eliminate signal trend components, and the wavelet threshold method with a hard thresholding function and the Birge–Massart strategy is applied in denoising. [ABSTRACT FROM AUTHOR]

Aiming at the problems of selecting the adjustment parameters in threshold and threshold function, this paper proposed a signal denoising method based on artificial bee optimization algorithm and new threshold function. Firstly, it carried out the theoretical analysis of the new threshold function to verify its continuity, high-order differentiability and parameter adjustability. Secondly, according to the minimum mean square error (MSE) strategy, it used the artificial bee colony optimization algorithm to optimize the thresholds and adjustment parameters of each decomposition layer, and then obtained the optimal denoised signal. Finally, it carried out the simulation experiment to verify the denoising effect according to the signal-to-noise ratio (SNR) and MSE. The experimental result shows that the threshold parameters selected by artificial bee optimization algorithm and the new wavelet threshold function can effectively denoise a noisy signal. [ABSTRACT FROM AUTHOR]

For profit maximization, the model-based stock price prediction can give valuable guidance to the investors. However, due to the existence of the high noise in financial data, it is inevitable that the deep neural networks trained by the original data fail to accurately predict the stock price. To address the problem, the wavelet threshold-denoising method, which has been widely applied in signal denoising, is adopted to preprocess the training data. The data preprocessing with the soft/hard threshold method can obviously restrain noise, and a new multioptimal combination wavelet transform (MOCWT) method is proposed. In this method, a novel threshold-denoising function is presented to reduce the degree of distortion in signal reconstruction. The experimental results clearly showed that the proposed MOCWT outperforms the traditional methods in the term of prediction accuracy. [ABSTRACT FROM AUTHOR]

Noise interference, especially from human noise, seriously affects the quality of magnetotelluric (MT) data. Strong human noise distorts the apparent resistivity curve, known as the near-source effect, causing poor reliability of MT data inversion. Based on analyzing the frequency characteristics of human noise resulting from the surrounding environment, a new wavelet-based denoising method is proposed for both synthetic and real MT data in this paper. The new technique combines multi-resolution analysis with a wavelet threshold algorithm based on Bayes estimation and has a remarkable effect on denoising at all band frequencies. The multi-resolution analysis method was employed to reduce long-period noise, and a wavelet threshold algorithm was used to eliminate strong high-frequency noise. In this research, the improved algorithm was assessed via simulated experiments and field measurements with regard to the reduction in human noises. This study demonstrates that the new denoising technique can increase the signal-to-noise ratio by at least 112% and provides an extensive analysis method for mineral resource exploration. [ABSTRACT FROM AUTHOR]

Ultrasound (US) images are useful in medical diagnosis. US is preferred over other medical diagnosis technique because it is non-invasive in nature and has low cost. The presence of speckle noise in US images degrades its usefulness. A method that reduces the speckle noise in US images can help in correct diagnosis. This method also should preserve the important structural information in US images while removing the speckle noise. In this paper, a method for removing speckle noise using a combination of wavelet, total variation (TV) and morphological operations has been proposed. The proposed method achieves denoising by combining the advantages of the wavelet, TV and morphological operations along with the utilization of adaptive regularization parameter which controls the amount of smoothing during denoising. The work in this paper has the capability of reducing speckle noise while preserving the structural information in the denoised image. The proposed method demonstrates strong denoising for synthetic and real ultrasound images, which is also supported by the results of various quantitative measures and visual inspection. [ABSTRACT FROM AUTHOR]

When applying the foreground removal methods to uncover the faint cosmological signal from the epoch of reionization (EoR), the foreground spectra are assumed to be smooth. However, this assumption can be seriously violated in practice since the unresolved or mis-subtracted foreground sources, which are further complicated by the frequency-dependent beam effects of interferometers, will generate significant fluctuations along the frequency dimension. To address this issue, we propose a novel deep-learning-based method that uses a nine-layer convolutional denoising autoencoder (CDAE) to separate the EoR signal. After being trained on the SKA images simulated with realistic beam effects, the CDAE achieves excellent performance as the mean correlation coefficient (⁠|$\bar{\rho }$|⁠) between the reconstructed and input EoR signals reaches 0.929 ± 0.045. In comparison, the two representative traditional methods, namely the polynomial fitting method and the continuous wavelet transform method, both have difficulties in modelling and removing the foreground emission complicated with the beam effects, yielding only |$\bar{\rho }_{\mathrm{poly}} = {0.296 \pm 0.121}$| and |$\bar{\rho }_{\mathrm{cwt}} = {0.198 \pm 0.160}$|⁠, respectively. We conclude that, by hierarchically learning sophisticated features through multiple convolutional layers, the CDAE is a powerful tool that can be used to overcome the complicated beam effects and accurately separate the EoR signal. Our results also exhibit the great potential of deep-learning-based methods in future EoR experiments. [ABSTRACT FROM AUTHOR]

Due to the influence of the external environment and the performance of measuring equipment, the on-line oil chromatography data contains obvious noise which makes the signal to oscillate. The monitoring data is difficult to be directly applied to the equipment state analysis. A novel wavelet-based de-noising method is proposed for pre-processing the on-line oil chromatography data. By analysing the characteristics of on-line oil chromatography data, the method of determining the decomposition layer number based on the probability distribution of wavelet coefficients and the method of determining the threshold value based on outliers conservation are proposed. The improved wavelet de-noising method is applied to analysing the on-line oil chromatography data of a defective ultra-high voltage (UHV) reactor. The results show that the proposed method is feasible and effective. [ABSTRACT FROM AUTHOR]

Ground penetrating radar (GPR) weak signals have the characteristics of low signal-to-noise ratio (SNR) and high frequency, which is a major challenge to noise attenuation. In this paper, we propose a GPR denoising approach based on empirical wavelet transform (EWT) combined with semi-soft thresholding. According to the frequency characteristics of signal, a spectrum segmentation strategy is designed. It can adaptively decompose signal and noise into different modes. The mode which contains more valid signals is processed by hard thresholding to reserve amplitude; the other modes which contain useless signals are processed by soft threshold functions to maintain the continuity of the signal. After weak signal denoising by our proposed method, we compared its performance on synthetic and field data using complete ensemble empirical mode decomposition (CEEMD) and synchro squeezed wavelet transform (SWT). The proposed method denoising performance is better than other two methods. [ABSTRACT FROM AUTHOR]

Highlights • A new method (PPIs-WDSVM) for prediction protein–protein interactions. • The protein sequence features are extracted by fusing the PseAAC, AC and EBGW methods. • 2-D wavelet denoising can effectively remove the redundant information in the protein sequences. • We compared the effect of the five different classifiers on the results. • The proposed method increases the prediction performance over several methods. Abstract Research on protein–protein interactions (PPIs) not only helps to reveal the nature of life activities but also plays a driving role in understanding the mechanisms of disease activity and the development of effective drugs. The rapid development of machine learning provides new opportunities and challenges for understanding the mechanism of PPIs. It plays an important role in the field of proteomics research. In recent years, an increasing number of computational methods for predicting PPIs have been developed. This paper proposes a new method for predicting PPIs based on multi-information fusion. First, the pseudo-amino acid composition (PseAAC), auto-covariance (AC) and encoding based on grouped weight (EBGW) methods are used to extract the features of protein sequences, and the extracted three groups of feature vectors were fused. Secondly, the fused feature vectors are denoised by two-dimensional (2-D) wavelet denoising. Finally, the denoised feature vectors are input to the support vector machine (SVM) classifier to predict the PPIs. The ACC of PPIs of Helicobacter pylori (H. pylori) and Saccharomyces cerevisiae (S. cerevisiae) datasets were 95.97% and 95.55% by 5-fold cross-validation test and compared with other prediction methods. The experimental results show that the proposed multi-information fusion prediction method can effectively improve the prediction performance of PPIs. The source code and all datasets are available at https://github.com/QUST-AIBBDRC/PPIs-WDSVM/. [ABSTRACT FROM AUTHOR]

Wavelet families have different statistical characteristics and specifications which give them a different response against the same signal or image when they are used for a certain task such as signal denoising. Therefore, a comparison evaluation study using new proposed procedure is required to obtain the optimal results when wavelet analysis tool is used to remove the noise from a synthetic signal. In this work, a sawtooth wavelet thresholding method is proposed and evaluated as compared to the other wavelet thresholding methods such as (soft and hard). The main goal of this work is to design and implement a new wavelet thresholding method and evaluate it against other classical wavelet thresholding methods and hence search for the optimal wavelet mother function among the above mentioned families with a suitable level of decomposition followed by a novel thresholding method among the existing methods. This optimal method will be used to shrink the wavelet coefficients and yield an adequate denoised pressure signal prior the transmission. There are different performance indices to establish the comparison and evaluation process for signal denoising; but the most well-known measuring scores are: NMSE (normalized mean square error), ESNR (enhancement of signal to noise ratio), and PDR (percentage root mean squared difference). The obtained results shown the outperformance of the sawtooth wavelet thresholding method against other methods using different measuring scores and hence the conclusion is to suggest the adopting of this proposed wavelet thresholding for 1D signal denoising in future researches. [ABSTRACT FROM AUTHOR]

Highlights • A novel threshold function with adaptive threshold of wavelet analysis. • Improves speech quality of optical fiber acoustic sensor. • More suitable for optical fiber acoustic sensor to extract speech signal. Abstract In this paper, we demonstrate a novel speech enhancement method for improving detection performance of optical fiber acoustic sensor. The proposed method is based on a novel threshold function with adaptive threshold for wavelet analysis. For a certain speech signal, the adaptive threshold in the function is set lower in speech presence region and higher in speech absence region, which ensures more speech details preserved as well as noise reduced. At the same time, the new threshold function guarantees the continuity and no deviation of speech signal. Experimental results show that the proposed method is more suitable for optical fiber acoustic sensor to extract speech signal compared with universal wavelet packet method, and it improves speech quality significantly. The clear speech can be obtained via the optical fiber acoustic sensor even if work surroundings of sensing unit is noisy. [ABSTRACT FROM AUTHOR]

Wavelet based image processing techniques do not strictly follow the conventional probabilistic models that are unrealistic for real world images. However, the key features of joint probability distributions of wavelet coefficients are well captured by HMT (Hidden Markov Tree) model. This paper presents the HMT model based technique consisting of Wavelet based Multiresolution analysis to enhance the results in image processing applications such as compression, classification and denoising. The proposed technique is applied to colored video sequences by implementing the algorithm on each video frame independently. A 2D (Two Dimensional) DWT (Discrete Wavelet Transform) is used which is implemented on popular HMT model used in the framework of Expectation-Maximization algorithm. The proposed technique can properly exploit the temporal dependencies of wavelet coefficients and their non-Gaussian performance as opposed to existing wavelet based denoising techniques which consider the wavelet coefficients to be jointly Gaussian or independent. Denoised frames are obtained by processing the wavelet coefficients inversely. Comparison of proposed method with the existing techniques based on CPSNR (Coloured Peak Signal to Noise Ratio), PCC (Pearson's Correlation Coefficient) and MSSIM (Mean Structural Similarity Index) has been carried out in detail. The proposed denoising method reveals improved results in terms of quantitative and qualitative analysis for both additive and multiplicative noise and retains nearly all the structural contents of a video frame. [ABSTRACT FROM AUTHOR]

Noise and fluorescent background are two major problems for acquiring Raman spectra from samples, which blur Raman spectra and make Raman detection or imaging difficult. In this paper, a novel algorithm based on wavelet transform that contains denoising and baseline correction is presented to automatically extract Raman signals. For the denoising section, the improved conventional-scale correlation denoising method is proposed. The baseline correction section, which is performed after denoising, basically consists of five aspects: (1) detection of the peak position; (2) approximate second derivative calculation based on continuous wavelet transform is performed using the Haar wavelet function to find peaks and background areas; (3) the threshold is estimated from the peak intensive area for identification of peaks; (4) correction of endpoints, spectral peaks, and peak position; and (5) determine the endpoints of the peak after subtracting the background. We tested this algorithm for simulated and experimental Raman spectra, and a satisfactory denoising effect and a good capability to correct background are observed. It is noteworthy that this algorithm requires few human interventions, which enables automatic denoising and background removal. [ABSTRACT FROM AUTHOR]

Purpose The real challenges in online crack detection testing based on guided waves are random noise as well as narrow-band coherent noise; and to achieve efficient structural health assessment methodology, magnificent extraction of noise and analysis of the signals are essential. The purpose of this paper is to provide optimal noise filtering technique for Lamb waves in the diagnosis of structural singularities.Design/methodology/approach Filtration of time-frequency information of guided elastic waves through the noisy signal is investigated in the present analysis using matched filtering technique which “sniffs” the signal buried in noise and most favorable mother wavelet based denoising methods. The optimal wavelet function is selected using Shannon’s entropy criterion and verified by the analysis of root mean square error of the filtered signal.Findings Wavelet matched filter method, a newly developed filtering technique in this work and which is a combination of the wavelet transform and matched filtering method, significantly improves the accuracy of the filtered signal and identifies relatively small damage, especially in enormously noisy data. A comparative study is also performed using the statistical tool to know acceptability and practicability of filtered signals for guided wave application.Practical implications The proposed filtering techniques can be utilized in online monitoring of civil and mechanical structures. The algorithm of the method is easy to implement and found to be successful in accurately detecting damage.Originality/value Although many techniques have been developed over the past several years to suppress random noise in Lamb wave signal but filtration of interferences of wave modes and boundary reflection is not in a much matured stage and thus needs further investigation. The present study contains detailed information about various noise filtering methods, newly developed filtration technique and their efficacy in handling the above mentioned issues. [ABSTRACT FROM AUTHOR]

Zhu, W.; Wang, E.; Hou, Y.; Xian, L., and Ashraf, M.A., 2018. Hybrid filtering optimization method for denoising contaminated spot images at near-sea-surface intervals. In: Ashraf, M.A., and Chowdhury, A.J.K. (eds.), Coastal Ecosystem Responses to Human and Climatic Changes throughout Asia. The presence of noise affects the visual effect of images near the sea surface and reduces the quality of the images. Thus, denoising of the contaminated spot image near the sea surface is required. The current filtering method uses a noise image as mixed model, and uses wavelet transform to denoise a spot image. However, there is a problem of missing details of images near the sea surface. Therefore, a hybrid filtering optimization method of contaminated spot image denoising is proposed. First, the feature extraction of the spot image near the sea surface is carried out, and the contaminated spot image is detected by hybrid filtering. Then the denoising of the contaminated spot image is completed according to the image detection result. Experiments show that the proposed method is practical. [ABSTRACT FROM AUTHOR]

We present the nanoparticle-enabled experimentally trained wavelet-domain denoising method for optical coherence tomography (OCT). It employs an experimental training algorithm based on imaging of a test-object, made of the colloidal suspension of the monodisperse nanoparticles and contains the microscale inclusions. The geometry and the scattering properties of the test-object are known a priori allowing us to set the criteria for the training algorithm. Using a wide set of the wavelet kernels and the wavelet-domain filtration approaches, the appropriate filter is constructed based on the test-object imaging. We apply the proposed approach and chose an efficient wavelet denoising procedure by considering the combinations of the decomposition basis from five wavelet families with eight types of the filtration threshold. We demonstrate applicability of the wavelet-filtering for the in vitro OCT image of human brain meningioma. The observed results prove high efficiency of the proposed OCT image denoising technique. [ABSTRACT FROM AUTHOR]

Spectral noise has direct influences on the optical electronic nose (e-nose) to predicted effect and the detection accuracy of the test gas. In this paper, a spectral denoising method based on least squares support vector machine (LSSVM) was proposed after comprehensive analysis of spectral characteristics including small sample, non-linear, local extreme points and so on. The optical e-nose sensing data of NO 2 , SO 2 , C 6 H 6 and C 7 H 8 collected by the system were denoised by LSSVM. The normalized correlation coefficient (NCC) between the deniosed spectrum and the standard spectrum in HITRAN database is over 98%. Compared with the results of moving window average filtering (MWA), Savitzky-Golay filtering (SG) and wavelet threshold filtering, it is found that the waveform obtained by LSSVM can retain the information such as relative extreme value and width of the spectrum peak. The validity and superiority of LSSVM were verified by the experiment. [ABSTRACT FROM AUTHOR]

Cryo-electron microscopy (Cryo-EM) imaging has the unique potential to bridge the gap between cellular and molecular biology by revealing the structures of large macromolecular assemblies and cellular complexes. Therefore, cryo-EM three-dimensional (3D) reconstruction has been rapidly developed in recent several years and applied widely in life science research; however, it suffers from reduced contrast and low signal-to-noise ratios with a high degree of noise under low electron dose conditions, resulting in failures of many conventional filters. In this article, we explored a modified wavelet shrinkage filter (with optimal wavelet parameters: three-level decomposition, level-1 zeroed out, subband-dependent threshold, soft thresholding, and spline-based discrete dyadic wavelet transform) and extended its application in the cryo-EM field in two aspects: single-particle analysis and cryo-electron tomography. Its performance was assessed with simulation data and real cryo-EM experimental data. Compared with the undenoised results and conventional denoising techniques (e.g., Gaussian, median, and bilateral filters), the modified wavelet shrinkage filter maintained the resolution and contrast but reduced the noise, leading to higher quality images and more accurate measures of the biological structure. We expect that our study can provide benefits to cryo-EM applications: 3D reconstruction, visualization, structural analysis, and interpretation. All these data and programs are available. [ABSTRACT FROM AUTHOR]

To address the problem that wavelet packet denoising is unable to process signals with strong white noise, an optimized VMD-wavelet packet threshold denoising method based on cross-correlation analysis is proposed. This method combines the advantages of VMD and wavelet packet denoising. By decomposing the noisy signal into several modal components using VMD, the excellent modal components are selected from all modal components according to the cross-correlation analysis based critical correlation coefficient. After that, these excellent modal components are processed using the wavelet packet threshold denoising method. Experimental results show that the proposed method has the advantage of denoising signal with strong white noise, which preserves the effective components of signal, overcomes the blindness of traditional VMD denoising methods and ensures the authenticity of the denoised signal. [ABSTRACT FROM AUTHOR]

By analyzing the error models of the measured vectors of the gravitational apparent motion, an in-motion filter-QUEST alignment method only with the inertial measurement unit is presented in this paper. The contribution of the proposed method lies in constructing the in-motion model of the measured vectors of the gravitational apparent motion and developing the extracted method to reconstruct the measured vectors. Furthermore, the relationship between the noise characteristic and the moving state of the vehicle is analyzed in detail. Different from the several current techniques, the presented method can be carried out without any other external additional equipment, when the vehicle is in-motion. With the designed real-time wavelet denoising (RWD) method, the high-frequency noises of the measured vectors are filtered. Based on the constructed parameter recognition model of the measured vectors, a robust adaptive Kalman filter is devised to estimate the optimal parameters, which are used to calculate the reconstructed observation vectors. Moreover, the gross outliers, which are contained in the filtered vectors of the RWD, are eliminated effectively. The simulation and the field trial results demonstrate that the presented method is applicable to the in-motion initial alignment, and it can serve as a nice initial alignment method in the follow-on fine alignment process and navigation process. [ABSTRACT FROM AUTHOR]

Highlights • A new adaptive denoising is proposed for tomographic image reconstruction. • The method combines the wavelet techniques and the Non Local Means (NLM) filter. • The numerical experiments show that the method can reduce various forms of noise. • Robustness tests prove that the approach is more stable than state-of-the-art methods. Many methods of image acquisition from medical multidimensional data rely on continuous techniques whereas in fact they are used in a finite discrete field. The discretization step is often accompanied by residuals diminishing the quality of the produced images. In addition, the acquisition phase does not occur in an ideal way and may cause artifacts and nonstandard noise. Therefore, denoising is mandatory for many algorithms in computer vision and image processing. In this paper, we propose a new denoising strategy for the tomographic image reconstruction. The method is based on a coupling of the wavelet techniques with the well-known Non Local Means (NLM) filter and operates adaptively during the data acquisition stage. Unlike other well-known denoising techniques, which are mainly based on the smoothing of the resultant image, this approach is instead based on the sinogram preprocessing. The numerical simulations show that the tomographic reconstruction based on the new denoising strategy is able to reduce enough noises present in various forms in the data. Additional robustness tests prove that the proposed approach is more stable than the basic NLM and other homologous methods. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes methods for super resolving single noisy low resolution images. Even if single image super resolution has been a topic of research for last few decades, super resolution of noisy low resolution images is still a challenging problem. Most of the state of the art super resolution algorithms will fail to perform if significant amount of noise is present in the observed image. In this paper, we propose a denoised patch dictionary based single image super resolution algorithm. To enhance the robustness to noise performance, this method is further modified by using a wavelet based fusion algorithm which combines the result of proposed method with direct super resolved image, and super resolved image after denoising to preserve the finer details of the super resolved image. The proposed methods are applied on the commonly used test images. The results validate that the proposed methods show improvement over the existing techniques. [ABSTRACT FROM AUTHOR]

Abstract: A threshold‐free denoising procedure of acquired discrete Atomic‐force microscopy (AFM) signals using the discrete wavelet transform (DWT) method is presented in this article. The integration of a denoising procedure into a control structure is extremely important for each kind of system to be controlled. The detection of unavoidable measurement noise in the acquired data of the AFM signal is done by using orthogonal wavelets (Daubechies and Symmlet) and with different polynomial approximation order for each family. The proposed denoising algorithm, based on the free wavelet toolboxes from the WaveLab 850 library of the Stanford University (USA), compares the usefulness of Daubechies and Symmlet wavelets with different vanishing moments. With the help of a seminorm the noise of a sequence is defined as a coherent and incoherent part of the AFM signal. In the first step of the procedure the algorithm analyzes the frequency subspaces of the wavelet packets tree and searches for small or opposing components in the wavelet domains. In the second step of the procedure the incoherent components in the low‐ and high frequency domains are localized and the incoherent is then removed from the AFM signal. The proposed algorithm structure is used to improve the quality of the AFM signals and it can be easily integrated into the existing AFM control hard‐ and software structures. The effectiveness of the proposed denoising algorithm is validated with real measurements. [ABSTRACT FROM AUTHOR]

The aim of this study is providing a comprehensive background information related to the roots of both Fourier Transform (FT) and Wavelet Transform (WT) along with an experiment related to applications of WT techniques. The paper describes several applications of WT and provides background information on FT. Fourier Transform (FT) is a concept that has a long history yet several issues related to resolution and uncertainty of time-frequency. Even though there are several adapted forms of FT such as Short Time Fourier Transform (STFT), which intend to solve the problems, certain limitations remain. Wavelet Transform (WT) is an alternative transformation technique emerged in order to fully tackle these diverse and complicated issues. In this paper, the background information related to the roots of FT and WT are given. Some of the problems that WT addresses are examined. WT is a tool that has many advantages among them is noise reduction and compression. We reviewed several studies that use the noise reduction capability of WT alone or combined with other signal processing tools. Discrete Wavelet Transform (DWT) based algorithm is also examined as a noise reduction technique and carried out in MATLAB setting. Analysis on a speech signal which contaminated with keyboard sound also a number spelling female voice containing unknown noise are performed. Different types of thresholding and mother wavelets were in consideration and it was revealed that Daubechies family along with the soft thresholding technique suited our application the most. [ABSTRACT FROM AUTHOR]

Arrhythmia, also known as dysrhythmia, is a condition involving an irregular heartbeat. A problem in the heart may cause problems in other organs, and as time passes, this will lead to more severe problems. Arrhythmia must be detected at an early stage to prevent such a problem occurring in the heart. Detection of arrhythmia from an electrocardiogram is an easy method that does not need much equipment and does not harm the patient. The purpose of this research is to find a faster and more accurate system to classify nine classes of arrhythmia. The St. Petersburg Institute of Cardiological Technics 12-lead arrhythmia database was used for training and testing. Data were compressed and preprocessed (denoising, trend elimination, baseline correction, and normalization) before being sent to the system for feature calculation. The wavelet coefficients that displayed the most significant effect on classification were chosen and used as features. Standard deviation and variance were also added to the feature set. Later, principal component analysis (PCA) was used to reduce the number of features further. After deciding the features, the performance of the basic classification methods and spiking neural network was checked to determine whether there was a better classifier to be used for our research. Tenfold cross-validation was applied to the training dataset. Bagged trees were found to produce better results. The classifiers' performance was tested by sensitivity, specificity, and accuracy. [ABSTRACT FROM AUTHOR]

The construction quality of the bolt is directly related to the safety of the project, and, as such, it must be tested. In this paper, the improved complete ensemble empirical mode decomposition (ICEEMD) method is introduced to the bolt detection signal analysis. The ICEEMD is used in order to decompose the anchor detection signal according to the approximate entropy of each intrinsic mode function (IMF). The noise of the IMFs is eliminated by the wavelet soft threshold denoising technique. Based on the approximate entropy and the wavelet denoising principle, the ICEEMD-De anchor signal analysis method is proposed. From the analysis of the vibration analog signal, as well as the bolt detection signal, the result shows that the ICEEMD-De method is capable of correctly separating the different IMFs under noisy conditions and also that the IMF can effectively identify the reflection signal of the end of the bolt. [ABSTRACT FROM AUTHOR]

Aiming at the problem that the wavelet threshold algorithm is poor denoising effect in traditional pulse measuring instrument, an adaptive filtering algorithm of improved wavelet threshold function and threshold estimation is proposed in this system. This algorithm is used to eliminate the constant deviation of soft threshold function and the discontinuous shortcomings of hard threshold function by constructing a new threshold function and threshold estimation method and adjusting the adaptive adjustment coefficient, thus filtering out the interference noise in photoplethysmograph signals. The light intensity signals acquired by the photoelectric sensor are sequentially processed by signal amplifying circuit and filter circuit, the photoplethysmography signals are transmitted into LPC2103 for further processing, the results are displayed on the LCD screen. Experiments show that the improved wavelet threshold algorithm not only preserves the useful signal, but also avoids the oscillation. The algorithm is employed to denoise the pulse wave, which effectively improves the accuracy of the pulse measuring instrument. [ABSTRACT FROM AUTHOR]

The preprocessing of wire rope online testing signals is important for quantifying any wire rope defects. As existing signal denoising methods are inadequate, the present study proposes an adaptive wavelet threshold denoising method based on a novel thresholding function. First, the adaptive denoising method for a coal mine hoisting wire rope magnetic flux leakage testing signal is analysed. Then, the adaptive denoising method for the wire rope magnetic flux leakage testing signal is studied based on Stein's unbiased risk estimate (SURE). On this basis, a new threshold function adapted to the testing signal features of the wire rope magnetic flux leakage is designed. The new function not only has a high-order continuous derivative but also no constant bias, so that it can be run in adaptive iterative form to dynamically find the best threshold. Finally, this work experimentally verifies the new method and the results show that it can effectively identify seven defects that totally conform to the real situation with a signal-to-noise ratio that is 25% higher than that of the traditional method, which also missed two defects. The new method can be more effectively used for denoising. [ABSTRACT FROM AUTHOR]

The precise and efficient noise variance estimation is very important for the processing of all kinds of signals while using the wavelet transform to analyze signals and extract signal features. In view of the problem that the accuracy of traditional noise variance estimation is greatly affected by the fluctuation of noise values, this study puts forward the strategy of using the two-state Gaussian mixture model to classify the high-frequency wavelet coefficients in the minimum scale, which takes both the efficiency and accuracy into account. According to the noise variance estimation, a novel improved wavelet threshold function is proposed by combining the advantages of hard and soft threshold functions, and on the basis of the noise variance estimation algorithm and the improved wavelet threshold function, the research puts forth a novel wavelet threshold de-noising method. The method is tested and validated using random signals and bench test data of an electro-mechanical transmission system. The test results indicate that the wavelet threshold de-noising method based on the noise variance estimation shows preferable performance in processing the testing signals of the electro-mechanical transmission system: it can effectively eliminate the interference of transient signals including voltage, current, and oil pressure and maintain the dynamic characteristics of the signals favorably. [ABSTRACT FROM AUTHOR]

Accurate, fast forecasting of hydro-meteorological time series is presently a major challenge in drought and flood mitigation. This paper proposes a hybrid approach, wavelet de-noising (WD) and Rank-Set Pair Analysis (RSPA), that takes full advantage of a combination of the two approaches to improve forecasts of hydro-meteorological time series. WD allows decomposition and reconstruction of a time series by the wavelet transform, and hence separation of the noise from the original series. RSPA, a more reliable and efficient version of Set Pair Analysis, is integrated with WD to form the hybrid WD-RSPA approach. Two types of hydro-meteorological data sets with different characteristics and different levels of human influences at some representative stations are used to illustrate the WD-RSPA approach. The approach is also compared to three other generic methods: the conventional Auto Regressive Integrated Moving Average (ARIMA) method, Artificial Neural Networks (ANNs) (BP-error Back Propagation, MLP-Multilayer Perceptron and RBF-Radial Basis Function), and RSPA alone. Nine error metrics are used to evaluate the model performance. Compared to three other generic methods, the results generated by WD-REPA model presented invariably smaller error measures which means the forecasting capability of the WD-REPA model is better than other models. The results show that WD-RSPA is accurate, feasible, and effective. In particular, WD-RSPA is found to be the best among the various generic methods compared in this paper, even when the extreme events are included within a time series. [ABSTRACT FROM AUTHOR]

We proposed a single pulse threshold detection method with lifting wavelet denoising algorithm based on modified particle swarm optimization (MPSO). The detection probability and false alarm probability of single pulse fixed threshold, variable threshold and random threshold detection were simulated and analyzed. The results show that in the condition of low signal-to-noise ratio (SNR), false alarm probability can be constant, and the detection probability of the target detection could be effectively enhanced using random threshold detection. But random threshold detection method has defect. Therefore, the modified lifting wavelet adaptive nonlinear denoised algorithm was put forward with MPSO. The simulation and experimental results show that the algorithm can make up defect of random threshold detection and effectively improve the SNR of echo signal. It provides theoretical basis and implementation method for weak echo signal detection. [ABSTRACT FROM AUTHOR]

In Computed Tomography (CT), image degradation such as noise and detail blurring is one of the universal problems due to hardware restrictions. The problem of noise in CT images can be solved by image denoising. The main aim of image denoising is to reduce the noise as well as preserve the important features such as edges, corners, textures and sharp structures. Due to the large capability of noise suppression in noisy signals according to neighborhood pixels or coefficients, this paper presents a new technique to denoise CT images with edge preservation in tetrolet domain (Haar-type wavelet transform) where a locally adaptive shrinkage rule is performed on high frequency tetrolet coefficients in such a way that noise can be reduced more effectively. The experimental results of the proposed scheme are excellent in terms of noise suppression and structure preservation. The proposed scheme is compared with some standard existing methods where it is observed that performance of the proposed scheme is superior to the existing methods in terms of visual quality, MSE, PSNR and Image Quality Index (IQI). [ABSTRACT FROM AUTHOR]

In order to accurately detect the fuzzy anomaly data existing in big data networks, it is necessary to study the localization and recognition algorithm. The current algorithms have problems related to poor noise reduction, low recognition efficiency, high energy consumption and low accuracy. A novel localization and recognition algorithm for fuzzy anomaly data in big data networks is proposed. The multi-wavelet denoising method is used to remove the noise signals existing in the network. The k- means algorithm is utilized for network clustering, and the association mode between nodes and the unitary linearity regression model is adopted to eliminate spatially and temporally redundant data that exist in big data networks. The similarity anomaly detection method based on multi- feature aggregation identifies fuzzy anomaly data existing in big data networks, establishes an anomaly data localization model, and completes the localization and recognition of fuzzy anomaly data. Experimental results show that the proposed method has good noise reduction, high recognition efficiency, low energy consumption and high accuracy of localization and recognition. [ABSTRACT FROM AUTHOR]

We provide an extensive study assessing whether a prior wavelet-based denoising step enhances the forecast accuracy of standard forecasting models. Many combinations of attribute values of the thresholding (denoising) algorithm are explored together with several traditional forecasting models used in economic time series forecasting. The results are evaluated using M3 competition yearly time series. We conclude that the performance of a forecasting model combined with the prior denoising step is generally not recommended, which implies that a straightforward generalisation of some of the results available in the literature (which found the denoising step to be beneficial) is not possible. Even if cross-validation is used to select the value of the threshold, a superior performance of the forecasting model with the prior denoising step does not generally follow. [ABSTRACT FROM AUTHOR]

High-frequency components are often discarded for data denoising when applying pure wavelet multiscale or empirical mode decomposition (EMD) based approaches. Instead, they may raise the problem of energy leakage in vibration signals. Hybrid EMD and wavelet packet (EMD-WP) is proposed to denoise Global Positioning System- (GPS-) based structure monitoring data. First, field observables are decomposed into a collection of intrinsic mode functions (IMFs) with different characteristics. Second, high-frequency IMFs are denoised using the wavelet packet; then the monitoring data are reconstructed using the denoised IMFs together with the remaining low-frequency IMFs. Our algorithm is demonstrated on a synthetic displacement response of a 3-story frame excited by El Centro earthquake along with a set of Gaussian random white noises on different levels added. We find that the hybrid method can effectively weaken the multipath effect with low frequency and can potentially extract vibration feature. However, false modals may still exist by the rest of the noise contained in the high-frequency IMFs and when the frequency of the noise is located in the same band as that of effective vibration. Finally, real GPS observables are implemented to evaluate the efficiency of EMD-WP method in mitigating low-frequency multipath. [ABSTRACT FROM AUTHOR]

This paper presents an intelligent noise reduction algorithm for unbalanced noise fuzzy image. Firstly, a segmentation algorithm based on inter class variance maximization is adopted, and the image is divided into two types of background and target, to determine the threshold value; then, according to the change of the local, noise is adaptively reduced, so as to achieve the purpose of intelligent noise reduction. Experimental results show that the denoising effect of the proposed algorithm is better than that of other algorithms. The edge details are preserved and the visual effect is enhanced. [ABSTRACT FROM PUBLISHER]