AMicroseismic Signal Denoising Algorithm Combining VMD and Wavelet Threshold Denoising Optimized by BWOA

The denoising of microseismic signals is a prerequisite for subsequent analysis and research.In this research,a new microseismic signal denoising algorithm called the Black Widow Optimization Algorithm(BWOA)optimized VariationalMode Decomposition(VMD)jointWavelet Threshold Denoising(WTD)algorithm(BVW)is proposed.The BVW algorithm integrates VMD and WTD,both of which are optimized by BWOA.Specifically,this algorithm utilizes VMD to decompose the microseismic signal to be denoised into several Band-Limited IntrinsicMode Functions(BLIMFs).Subsequently,these BLIMFs whose correlation coefficients with the microseismic signal to be denoised are higher than a threshold are selected as the effective mode functions,and the effective mode functions are denoised using WTD to filter out the residual low-and intermediate-frequency noise.Finally,the denoised microseismic signal is obtained through reconstruction.The ideal values of VMD parameters and WTD parameters are acquired by searching with BWOA to achieve the best VMD decomposition performance and solve the problem of relying on experience and requiring a large workload in the application of the WTD algorithm.The outcomes of simulated experiments indicate that this algorithm is capable of achieving good denoising performance under noise of different intensities,and the denoising performance is significantly better than the commonly used VMD and Empirical Mode Decomposition(EMD)algorithms.The BVW algorithm is more efficient in filtering noise,the waveform after denoising is smoother,the amplitude of the waveform is the closest to the original signal,and the signal-to-noise ratio(SNR)and the root mean square error after denoising are more satisfying.The case based on Fankou Lead-Zinc Mine shows that for microseismic signals with different intensities of noise monitored on-site,compared with VMD and EMD,the BVW algorithm ismore efficient in filtering noise,and the SNR after denoising is higher.

Denoising of seismic data via multi-scale ridgelet transform

Noise has traditionally been suppressed or eliminated in seismic data sets by the use of Fourier filters and, to a lesser degree, nonlinear statistical filters. Although these methods are quite useful under specific conditions, they may produce undesirable effects for the low signal to noise ratio data. In this paper, a new method, multi-scale ridgelet transform, is used in the light of the theory of ridgelet transform. We employ wavelet transform to do sub-band decomposition for the signals and then use non-linear thresholding in ridgelet domain for every block. In other words, it is based on the idea of partition, at sufficiently fine scale, a curving singularity looks straight, and so ridgelet transform can work well in such cases. Applications on both synthetic data and actual seismic data from Sichuan basin, South China, show that the new method eliminates the noise portion of the signal more efficiently and retains a greater amount of geologic data than other methods, the quality and consecutiveness of seismic event are improved obviously as well as the quality of section is improved.

The Second-generation Wavelet Transform and its Application in Denoising of Seismic Data

This paper discusses the principle and procedures of the second-generation wavelet transform and its application to the denoising of seismic data. Based on lifting steps, it is a flexible wavelet construction method using linear and nonlinear spatial prediction and operators to implement the wavelet transform and to make it reversible. The lifting scheme transform -includes three steps： split, predict, and update. Deslauriers-Dubuc （4, 2） wavelet transforms are used to process both synthetic and real data in our second-generation wavelet transform. The processing results show that random noise is effectively suppressed and the signal to noise ratio improves remarkably. The lifting wavelet transform is an efficient algorithm.

Coupling denoising algorithm based on discrete wavelet transform and modified median filter for medical image

In order to overcome the phenomenon of image blur and edge loss in the process of collecting and transmitting medical image,a denoising method of medical image based on discrete wavelet transform(DWT)and modified median filter for medical image coupling denoising is proposed.The method is composed of four modules:image acquisition,image storage,image processing and image reconstruction.Image acquisition gets the medical image that contains Gaussian noise and impulse noise.Image storage includes the preservation of data and parameters of the original image and processed image.In the third module,the medical image is decomposed as four sub bands(LL,HL,LH,HH)by wavelet decomposition,where LL is low frequency,LH,HL,HH are respective for horizontal,vertical and in the diagonal line high frequency component.Using improved wavelet threshold to process high frequency coefficients and retain low frequency coefficients,the modified median filtering is performed on three high frequency sub bands after wavelet threshold processing.The last module is image reconstruction,which means getting the image after denoising by wavelet reconstruction.The advantage of this method is combining the advantages of median filter and wavelet to make the denoising effect better,not a simple combination of the two previous methods.With DWT and improved median filter coefficients coupling denoising,it is highly practical for high-precision medical images containing complex noises.The experimental results of proposed algorithm are compared with the results of median filter,wavelet transform,contourlet and DT-CWT,etc.According to visual evaluation index PSNR and SNR and Canny edge detection,in low noise images,PSNR and SNR increase by 10%–15%;in high noise images,PSNR and SNR increase by 2%–6%.The experimental results of the proposed algorithm achieved better acceptable results compared with other methods,which provides an important method for the diagnosis of medical condition.

NEW TECHNOLOGY FOR FAULT DIAGNOSIS BASED ON WAVELET DENOISING AND MODIFIED EXPONENTIAL TIME-FREQUENCY DISTRIBUTION

Fast wavelet multi-resolution analysis (wavelet MRA) provides a effective tool for analyzing and canceling disturbing components in original signal. Because of its exponential frequency axis, this method isn't suitable for extracting harmonic components. The modified exponential time-frequency distribution ( MED) overcomes the problems of Wigner distribution( WD) ,can suppress cross-terms and cancel noise further more. MED provides high resolution in both time and frequency domains, so it can make out weak period impulse components fmm signal with mighty harmonic components. According to the 'time' behavior, together with 'frequency' behavior in one figure,the essential structure of a signal is revealed clearly. According to the analysis of algorithm and fault diagnosis example, the joint of wavelet MRA and MED is a powerful tool for fault diagnosis.

Wavelet Denoising of Flight Flutter Testing Data for Improvement of Parameter Identification

The accuracy of modal parameter estimation plays a crucial role in flutter boundary prediction. A new wavelet denoising method is introduced for flight flutter testing data, which can improve the estimation of frequency domain identification algorithms. In this method, the testing data is first preprocessed with a gradient inverse weighted filter to initially lower the noise. The redundant wavelet transform is then used to decompose the signal into several levels. A “clean” input is recovered from the noisy data by level dependent thresholding approach, and the noise of output is reduced by a modified spatially selective noise filtration technique. The advantage of the wavelet denoising is illustrated by means of simulated and real data.

SAR image denoising based on wavelet-fractal analysis

Wavelet-fractal based SAR （synthetic aperture radar） image processing is one of the advanced technologies in image processing. The main concept of analysis is that after wavelet transformation, multifractal spectrum of the signal is different from that of noise. This difference is used to alleviate the noise produced by SAR image.The method to denoise SAR image using the process based on wavelet-fractai analysis is discussed in detail. Essentially, the present method focuses on adjusting the Hoelder exponent α of multifractal spectrum. After simulation, α should be adjusted to 1.72-1.73. The more the value of α exceeds 1.73, the less distinctive the edges of SAR image become. According to the authors denoising is optimal at α=1.72-1.73. In other words, when α =1.72-1.73, a smooth and denoised SAR image is produced.

Translation-invariant wavelet denoising of full-tensor gravity-gradiometer data

Denoising of full-tensor gravity-gradiometer data involves detailed information from field sources, especially the data mixed with high-frequency random noise. We present a denoising method based on the translation-invariant wavelet with mixed thresholding and adaptive threshold to remove the random noise and retain the data details. The novel mixed thresholding approach is devised to filter the random noise based on the energy distribution of the wavelet coefficients corresponding to the signal and random noise. The translation- invariant wavelet suppresses pseudo-Gibbs phenomena, and the mixed thresholding better separates the wavelet coefficients than traditional thresholding. Adaptive Bayesian threshold is used to process the wavelet coefficients according to the specific characteristics of the wavelet coefficients at each decomposition scale. A two-dimensional discrete wavelet transform is used to denoise gridded data for better computational efficiency. The results of denoising model and real data suggest that compared with Gaussian regional filter, the proposed method suppresses the white Gaussian noise and preserves the high-frequency information in gravity-gradiometer data. Satisfactory denoising is achieved with the translation-invariant wavelet.

Study on Denoising Based on the Wavelet Transform

The wavelet transform has remarkable advantages and wide applications in denoising because of its characteristic of good time-frequency. Based on the analysis of traditional wavelet denoising methods, which are based on Fourier transform, an improved method is proposed. It overcomes the shortcomings of the traditional Fourier denoising method. In this paper, the denoising procedures are introduced respectively based on the wavelet transform and the method of connecting the wavelet threshold with the wavelet basis is adopted. Through Matlab simulation and concrete data, it arrives at the conclusion that the method of signal denoising based on the wavelet transform is obviously more effective and better than the traditional method based on Fourier transform.

Image denoising algorithm of refuge chamber by combining wavelet transform and bilateral filtering

In order to preferably identify infrared image of refuge chamber, reduce image noises of refuge chamber and retain more image details, we propose the method of combining two-dimensional discrete wavelet transform and bilateral denoising. First, the wavelet transform is adopted to decompose the image of refuge chamber, of which low frequency component remains unchanged. Then, three high-frequency components are treated by bilateral filtering, and the image is reconstructed. The result shows that the combination of bilateral filtering and wavelet transform for image denoising can better retain the details which are included in the image, while providing better visual effect. This is superior to using either bilateral filtering or wavelet transform alone. It is useful for perfecting emergency refuge system of coal mines.

Multi-level denoising and enhancement method based on wavelet transform for mine monitoring

Based on low illumination and a large number of mixed noises contained in coal mine, denoising with one method usually cannot achieve good results, so a multi-level image denoising method based on wavelet correlation relevant inter-scale is presented. Firstly, we used directional median filter to effectively reduce impulse noise in the spatial domain, which is the main cause of noise in mine. Secondly, we used a Wiener filtration method to mainly reduce the Gaussian noise, and then finally used a multi-wavelet transform to minimize the remaining noise of low-light images in the transform domain. This multi-level image noise reduction method combines spatial and transform domain denoising to enhance benefits, and effectively reduce impulse noise and Gaussian noise in a coal mine, while retaining good detailed image characteristics of the underground for improving quality of images with mixing noise and effective low-light environment.

Radar emitter signal recognition based on multi-scale wavelet entropy and feature weighting

In modern electromagnetic environment, radar emitter signal recognition is an important research topic. On the basis of multi-resolution wavelet analysis, an adaptive radar emitter signal recognition method based on multi-scale wavelet entropy feature extraction and feature weighting was proposed. With the only priori knowledge of signal to noise ratio(SNR), the method of extracting multi-scale wavelet entropy features of wavelet coefficients from different received signals were combined with calculating uneven weight factor and stability weight factor of the extracted multi-dimensional characteristics. Radar emitter signals of different modulation types and different parameters modulated were recognized through feature weighting and feature fusion. Theoretical analysis and simulation results show that the presented algorithm has a high recognition rate. Additionally, when the SNR is greater than-4 d B, the correct recognition rate is higher than 93%. Hence, the proposed algorithm has great application value.

A Dual Tree Complex Discrete Cosine Harmonic Wavelet Transform (ADCHWT) and Its Application to Signal/Image Denoising

A new simple and efficient dual tree analytic wavelet transform based on Discrete Cosine Harmonic Wavelet Transform DCHWT (ADCHWT) has been proposed and is applied for signal and image denoising. The analytic DCHWT has been realized by applying DCHWT to the original signal and its Hilbert transform. The shift invariance and the envelope extraction properties of the ADCHWT have been found to be very effective in denoising speech and image signals, compared to that of DCHWT.

IMAGE WAVELET DENOISING USING THE ROBUST LOCAL THRESHOLD

This paper suggests a scheme of image denoising based on two-dimensional discrete wavelet transform. The denoising algorithm is described with some operators. By thresholding the wavelet transform coefficients of noisy images, the original image can be reconstructed correctly. Different threshold selections and thresholding methods are discussed. A new robust local threshold scheme is proposed. Quantifying the performance of image denoising schemes by using the mean square error, the performance of the robust local threshold scheme is demonstrated and is compared with the universal threshold scheme. The experiment shows that image denoising using the robust local threshold performs better than that using the universal threshold.

Lift fin stabilizers based on data fusion with wavelet denoising technology

Fin stabilizers with fin-lift feedback control can shield the mapping error of calculation between the fin angle and fin lift force,which is in the fin stabilizer with fin-angle feedback control.In practice,there are some technical difficulties in lift fin stabilizers,such as lift force detection and lift force sensor installation,so it cannot achieve the good antirolling performance.Therefore,a fin stabilizer system with fin-lift/fin-angle integrated control is brought forward.Data fusion based on wavelet denoising technology is employed in the system,which combines lift with fin angle local information from two sensors with different frequency ranges in order to eliminate redundant and contradictory information,and using complementary information to obtain the relative integrity of the lift force signal.The system model is established in this paper,and the fusion signal and the antirolling performance of this model are simulated respectively.The result shows that the control system can meet the antirolling need in different sea situations.

New Wavelet Threshold Denoising Method in Noisy Blind Source Separation

In general conditions, most blind source separation algorithms are established on noisy-free model and ignore the noise that affects the quality of separated sources. Firstly, this paper introduces an improved natural gradient algorithm based on bias removal technology to estimate the demixing matrix under noisy environment. Then the discrete wavelet transform technology is applied to the separated signals to further remove noise. In order to improve the separation effect, this paper analyzes the deficiency of hard threshold and soft threshold, and proposes a new wavelet threshold function based on the wavelet decomposition and reconfiguration. The simulations have verified that this method improves the signal noise ratio （SNR） of the separation results and the separation precision.

Active Depths of Main Faults in the Ying-Qiong Basin Investigated by Multi-Scale Wavelet Decomposition of Bouguer Gravity Anomalies and Power Spectral Methods

The Ying-Qiong Basin is located on the northwestern margin of the South China Sea and at the junction of the South China Block and the Indochina Block.It is characterized by complex geological structures.The existing seismic data in the study area is sparse due to the lack of earthquake activities.Because of the limited source energy and poor coverage of seismic data,the knowledge of deep structures in the area,including the spatial distribution of deep faults,is incomplete.Contrarily,satellite gravity data cover the entire study area and can reveal the spatial distribution of faults.Based on the wavelet multi-scale decomposition method,the Bouguer gravity field in the Ying-Qiong Basin was decomposed and reconstructed to obtain the detailed images of the first-to sixth-order gravitational fields.By incorporating the known geological features,the gravitational field responses of the main faults in the Ying-Qiong Basin were identified in the detailed fields,and the power spectrum analysis yielded the depths of 1.4,8,15,26.5,and 39 km for the average burial depths of the bottom surfaces from the first-to fifth-order detailed fields,respectively.The four main faults in the Yinggehai Basin all have a large active depth range:fault A(No.1)is between 5 and 39 km,fault B is between 26.5 and 39 km,and faults C and D are between 15 and 39 km.However,the depth of active faults in the Qiongdongnan Basin is relatively shallow,mainly between 8 and 26.5 km.

Multi-scale phase average waveform of electroencephalogram signals in childhood absence epilepsy using wavelet transformation

BACKGROUND： Recent studies have focused on various methods of wavelet transformation for electroencephalogram （EEG） signals. However, there are very few studies reporting characteristics of multi-scale phase waves during epileptic discharge.OBJECTIVE： To extract multi-scale phase average waveforms from childhood absence epilepsy EEG signals between time and frequency domains using wavelet transformation, and to compare EEG signals of absence seizure with pre-epileptic seizure and normal children, and to quantify multi-scale phase average waveforms from childhood absence epilepsy EEG signals. DESIGN, TIME AND SETTING： The case-comparative experiment was performed at the Department of Neuroelectrophysiology, Tianjin Medical University from August 2002 to May 2005. PARTICIPANTS： A total of 15 patients with childhood absence epilepsy from the General Hospital of Tianjin Medical University were enrolled in the study. The patients were not administered anti-epileptic drugs or sedatives prior to EEG testing. In addition, 12 healthy, age- and gender-matched children were also enrolled.METHODS： EEG signals were tested on 15 patients with childhood absence epilepsy and 12 normal children. Epileptic discharge signals during clinical and subclinical seizures were collected 10 and 20 times, respectively. The collected EEG signals were treated with wavelet transformation to extract multi-scale characteristics during absence epilepsy seizure using a conditional sampling method. Multi-scale phase average waveforms were collected using a conditional phase averaging technique. Amplitude of phase average waveform from EEG signals of epilepsy seizure, subclinical epileptic discharge, and EEG signals of normal children were compared and statistically analyzed in the first half-cycle.MAIN OUTCOME MEASURES： Multi-scale wavelet coefficient and the evolution of EEG signals were observed during childhood absence epilepsy seizures using wavelet transformation. Multi-scale phase average waveforms from EEG signals were observed using a conditional sampling method and phase averaging technique.RESULTS： Multi-scale characteristics of EEG signals demonstrated that 12-scale （3 Hz） rhythmical activity was significantly enhanced during childhood absence epilepsy seizure and co-existed with background structure （〈1 Hz, low frequency discharge）. The phase average wave exhibited opposed phase abnormal rhythm at 3 Hz. Prior to childhood absence epilepsy seizure, EEG detected opposed abnormal a rhythm and 3 Hz composition, which were not detected with traditional EEG. Compared to EEG signals from normal children, epileptic discharges from clinical and subclinical childhood absence epilepsy seizures were positive and amplitude was significantly greater （P〈0.05）.CONCLUSION： Wavelet transformation was used to analyze EEG signals from childhood absence epilepsy to obtain multi-scale quantitative characteristics and phase average waveforms. Multi-scale wavelet coefficients of EEG signals correlated with childhood absence epilepsy seizure, and multi-scale waveforms prior to epilepsy seizure were similar to characteristics during the onset period. Compared to normal children, EEG signals during epilepsy seizure exhibited an opposed phase model.

Online Wavelet Denoising via a Moving Window

在这份报纸，在即时信号处理降噪的传统的小浪的缺点被讨论，联机降噪的要求被考虑，并且一扇动人的窗户被介绍进传统的小浪变换。用动人的窗户，降噪途径的联机小浪被建议。联机降噪的一些问题例如边阶失真和 pseudo-Gibbs 现象，被讨论。为了解决这些问题，窗户延期和窗户，周期旋转也被建议。不同途径被广泛地在降噪域使用的信号测试。视觉结果和量的措施被介绍加亮新途径的可获得性。

Denoising Method for Partial Discharge Signal of Switchgear Based on Continuous Adaptive Wavelet Threshold

Partial discharge(PD)is an important reason for the insulation failure of the switchgear.In the process of PD detection,PD signal is often annihilated in strong noise.In order to improve the accuracy of PD detection in power plant switchgear,a method based on continuous adaptive wavelet threshold switchgear PD signals denoising is proposed in this paper.By constructing a continuous adaptive threshold function and introducing adjustment parameters,the problems of over⁃processing of traditional hard threshold functions and incomplete denoising of soft threshold functions can be improved.The analysis results of simulated signals and measured signals show that the continuous adaptive wavelet threshold denoising method is significantly better than the traditional denoising method for the PD signal.The proposed method in this paper retains the characteristics of the original signal.Compared with the traditional denoising methods,after denoising the simulated signals,the signal⁃to⁃noise ratio(SNR)is increased by more than 30%,and the root⁃mean⁃square error(RMSE)is reduced by more than 30%.After denoising the real signal,the noise suppression ratio(NRR)is increased by more than 40%.The recognition accuracy rate of PD signal has also been improved to a certain extent,which proves that the method has a certain practicability.