Thresholding Of Wavelet Coefficients Research Articles

Automatic P-Phase-Onset-Time-Picking Method of Microseismic Monitoring Signal of Underground Mine Based on Noise Reduction and Multiple Detection Indexes.

The underground pressure disaster caused by the exploitation of deep mineral resources has become a major hidden danger restricting the safe production of mines. Microseismic monitoring technology is a universally recognized means of underground pressure monitoring and early warning. In this paper, the wavelet coefficient threshold denoising method in the time-frequency domain, STA/LTA method, AIC method, and skew and kurtosis method are studied, and the automatic P-phase-onset-time-picking model based on noise reduction and multiple detection indexes is established. Through the effect analysis of microseismic signals collected by microseismic monitoring system of coral Tungsten Mine in Guangxi, automatic P-phase onset time picking is realized, the reliability of the P-phase-onset-time-picking method proposed in this paper based on noise reduction and multiple detection indexes is verified. The picking accuracy can still be guaranteed under the severe signal interference of background noise, power frequency interference and manual activity in the underground mine, which is of great significance to the data processing and analysis of microseismic monitoring.

Effectiveness of Wavelet Denoising on Secondary Ion Mass Spectrometry Signals

Wavelet theory has already achieved huge success. For Secondary Ions Mass Spectrometry (SIMS) signals, denoising the secondary signal, which is altered by the measurement, is considered that an essential step prior to applying such a signal processing technique that aims enhance the SIMS signals.The most efficient and widely used wavelet denoising method is based on wavelet coefficient thresholding. This process involves three important steps; wavelet decomposition: the input signals are decomposed into wavelet coefficients, thresholding: the wavelet coefficients are modified according to a threshold, and reconstruction: the modified coefficients are used in an inverse transform to obtain the noise-free-signal. Several researchers have used thresholding wavelet denoising techniques.
 The choice of wavelet type and the level of resolution can have a significant influence; it is important to note that the choice of resolution level depends on the type of signal we are dealing with, the nature of the present noise, and our specific goals for the denoised signal. It is generally recommended to test different resolution levels and evaluate their impact on the quality of the denoised signal before making a final decision. Moreover, the results obtained in wavelet denoising can be significantly influenced by the selection of wavelet types. The chosen wavelet type plays a crucial role in the extraction of signal details. Indeed, the effectiveness of denoising the MD6 sample has been demonstrated by the results obtained with sym4, db8, Haar and coif5 wavelets? These wavelets have effectively reduced noise while preserving crucial signal information, leading to an enhancement in the quality of the denoised signal.

Microseismic data denoising in the sychrosqueezed domain by integrating the wavelet coefficient thresholding and pixel connectivity

SUMMARY Microseismic monitoring is crucial for risk assessment in mining, fracturing and excavation. In practice, microseismic records are often contaminated by undesired noise, which is an obstacle to high-precision seismic locating and imaging. In this study, we develop a new denoising method to improve the signal-to-noise ratio (SNR) of seismic signals by combining wavelet coefficient thresholding and pixel connectivity thresholding. First, the pure background noise range in the seismic record is estimated using the ratio of variance (ROV) method. Then, the synchrosqueezed continuous wavelet transform (SS-CWT) is used to project the seismic records onto the time–frequency plane. After that, the wavelet coefficient threshold for each frequency is computed based on the empirical cumulative distribution function (ECDF) of the coefficients of the pure background noise. Next, hard thresholding is conducted to process the wavelet coefficients in the time–frequency domain. Finally, an image processing approach called pixel connectivity thresholding is introduced to further suppress isolated noise on the time–frequency plane. The wavelet coefficient threshold obtained by using pure background noise data is theoretically more accurate than that obtained by using the whole seismic record, because of the discrepancy in the power spectrum between seismic waves and background noise. After hard thresholding, the wavelet coefficients of residual noise exhibit isolated and lower pixel connectivity in the time–frequency plane, compared with those of seismic signals. Thus, pixel connectivity thresholding is utilized to deal with the residual noise and further improve the SNR of seismic records. The proposed new denoising method is tested by synthetic and real seismic data, and the results suggest its effectiveness and robustness when dealing with noisy data from different acquisition environments and sampling rates. The current study provides a useful tool for microseismic data processing.

An Effective Denoising Method Based on Cumulative Distribution Function Thresholding and its Application in the Microseismic Signal of a Metal Mine With High Sampling Rate (6 kHz)

Microseismic events can be used to analyze the risk of tunnel collapse, rock burst, and other mine hazards in space and time. In practice, the artificial activities and other signals at the mining site can seriously interfere with the microseismic waveforms, reducing the signal-to-noise ratio. In this study, we propose a denoising method based on the threshold of the cumulative distribution function (CDF) of the wavelet coefficients in the wavelet domain using synchrosqueezed continuous wavelet transform (SS-CWT). First, the ratio of microseismic signal variance between two adjacent time windows is used to determine the range of background noise. Then, the microseismic signal is transformed into a wavelet domain using SS-CWT, and the threshold of wavelet coefficients at each scale is estimated based on the cumulative distribution function (CDF) of background noise. At last, a post-processing step is applied by utilizing an amplitude smoothing function, to further suppress the noise. The proposed denoising method is tested by both synthetic and filed microseismic data recorded in a metal mine. The results show that the method is effective in denoising and can improve the SNR of mine microseismic data with a high sampling rate.

Fetal phonocardiogram signals denoising using improved complete ensemble (EMD) with adaptive noise and optimal thresholding of wavelet coefficients.

Although fetal phonocardiogram (fPCG) signals have become a good indicator for discovered heart disease, they may be contaminated by various noises that reduce the signals quality and the final diagnosis decision. Moreover, the noise may cause the risk of the data to misunderstand the heart signal and to misinterpret it. The main objective of this paper is to effectively remove noisefrom the fPCG signal to make it clinically feasible. So,we proposed a novel noise reduction method based on Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), wavelet threshold and Crow Search Algorithm (CSA). This noise reduction method, named ICEEMDAN-DWT-CSA, has three major advantages. They were, (i) A better suppress of mode mixing and a minimized number of IMFs, (ii) A choice of wavelet corresponding to the study signal proven by the literature and (iii) Selection of the optimal threshold value. Firstly, the noisy fPCG signal is decomposed into Intrinsic Mode Functions (IMFs) by the (ICEEMDAN). Each noisy IMFs were decomposed by the Discrete Wavelet Transform (DWT). Then, the optimal threshold value using the (CSA) technique is selected and the thresholding function is carried out in the detail's coefficients. Secondly, each denoised (IMFs) is reconstructed by applying the Inverse Discrete Wavelet Transform (IDWT). Finally, all these denoised (IMFs) are combined to get the denoised fPCG signal. The performance of the proposed method has been evaluated by Signal to Noise Ratio (SNR), Mean Square Error (MSE) and the Correlation Coefficient (COR). The experiment gave a better result than some standard methods.

Welding Defects Detection in Radiographic Images Using an Improved Denoising Technique Combined with an Enhanced Chan-Vese Model

The detection of welding defects is becoming an important operation in the industry and the field of non-destructive testing. Among the most used techniques in the detection of weld defects, it is radiography. The radiographic images acquired are generally of low contrast, poor quality, and uneven lighting. Therefore, the detection of welding defects becomes a difficult task. In this work, a new hybrid approach based on the combination of several techniques is proposed. It consists of three stages: firstly, we define the region of interest (ROI). Secondly, a preprocessing operation based on an improved version of denoising by soft thresholding of wavelet coefficients and an optimized threshold is applied to improve the image quality (noise reduction, contrast enhancement). Thirdly, an enhanced Chan-Vese model is proposed to segment the denoised ROI region. This enhanced model is based on the choice of a cluster obtained by the Fuzzy C-Mean algorithm (FCM) as the initial contour. The proposed approach is applied to the various radiographic welding images from the GDxray database to extract the characteristics of the welding defects. The results obtained clearly show the effectiveness of the proposed approach compared to conventional techniques.

Optimum value of scale and threshold for compression of 99mTc-MDP bone scan images using Haar wavelet transform

Introduction:Wavelet transforms of an image result in set of wavelet coefficients. Thresholding eliminates insignificant coefficients while retaining the significant ones (resulting in matrix having few nonzero elements that need to be stored). The compressed image is reconstructed by applying inverse wavelet transform. The quality of compressed image deteriorates with increase in compression. Hence, finding optimum value of scale and threshold is a challenging task. The objective of the study was to find the optimum value of scale and threshold for compressing 99mTc-methylene diphosphonate (99 mTc-MDP) bone scan images using Haar wavelet transform.Materials and Methods:Haar wavelet transform at scale 1–8 was applied on 106 99 mTc-MDP whole-body bone scan images, and wavelet coefficients were threshold at 90, 95, 97, and 99 percentiles, followed by inverse wavelet transform to get 3392 compressed images. Nuclear medicine physician (NMP) compared compressed image with its corresponding input to label it as acceptable or unacceptable. The values of scale and threshold that resulted in majority of acceptable images were considered to be optimum. The quality of compressed image was also evaluated using perception image quality evaluator (PIQE) image quality metrics. Compression ratio was calculated by dividing the number of nonzero elements after thresholding wavelet coefficients by the number of nonzero elements in Haar decomposed matrix.Results:NMP found quality of compressed images (obtained at scale 2 and 90 percentile threshold) identical to the quality of the corresponding input images. As per PIQE score, quality of compressed images was perceptually better than that of the corresponding input images.Conclusions:The optimum values of scale and threshold were determined to be 2 and 90 percentiles, respectively.

Feature extraction for functional time series: Theory and application to NIR spectroscopy data

We propose a novel method to extract global and local features of functional time series. The global features concerning the dominant modes of variation over the entire function domain, and local features of function variations over particular short intervals within function domain, are both important in functional data analysis. Functional principal component analysis (FPCA), though a key feature extraction tool, only focus on capturing the dominant global features, neglecting highly localized features. We introduce a FPCA-BTW method that initially extracts global features of functional data via FPCA, and then extracts local features by block thresholding of wavelet (BTW) coefficients. Using Monte Carlo simulations, along with an empirical application on near-infrared spectroscopy data of wood panels, we illustrate that the proposed method outperforms competing methods including FPCA and sparse FPCA in the estimation functional processes. Moreover, extracted local features inheriting serial dependence of the original functional time series contribute to more accurate forecasts. Finally, we develop asymptotic properties of FPCA-BTW estimators, discovering the interaction between convergence rates of global and local features.

Medical image denoising using optimal thresholding of wavelet coefficients with selection of the best decomposition level and mother wavelet

AbstractMedical images have become omnipresent in diagnosis and therapy. However, they can be affected by various types of noise that reduce image quality and make the final diagnostic decision difficult. The main objective of this research is to effectively remove the noise while preserving the important image characteristics. This paper proposes a novel approach for image denoising based on discrete wavelet transform (DWT) with the selection of the best decomposition level and mother wavelet. Then, the thresholding function is carried out in the detail coefficients. Optimal thresholding is done using new optimization techniques such as the crow search algorithm and social spider optimization techniques. Finally, the inverse of DWT is applied to reconstruct the denoised image. The proposed method is evaluated using peak signal to noise ratio, mean square error, and the structural similarity index measure. The experimental results show the efficiency of the optimization‐based denoising method over standard methods. Interesting results are obtained with all kinds of noise, and improvements about 30 dB can be reached with the Rician noise.

Denoising Images by Dual–Tree Complex Wavelet Transform Combined With Meta Heuristic Optimization Algorithms

Denoising is a prime objective technique for processing images. Image denoising techniques removes the noises present in an image without interrupting its features and contents. The image gets interrupted by channel or processing noise depending on the applications. Thus, the contaminated noises produce degradable image qualities with respect to subjective and objective approach. To overcome this, image denoising approaches were suggested. In the present research, Dual–Tree Complex Wavelet transform (DTCWT) is utilized to achieve image denoising since they perform multi resolution decomposition by two DWT trees. Soft and hard thresholding methods are used to threshold wavelet coefficients. The present research proposes a novel technique to denoise images which gives image information clearly by thresholding and optimization technique. The optimization is carried through different Meta-heuristic optimization Algorithms Genetic Algorithm (GA) and Grey-wolf optimization (GWO) algorithm. Optimization of threshold value is performed after Bayesian method and the observed output produces better results when compared to other techniques involving Visu shrink, Sure shrink and Bayes shrinkbased on peak signal to noise ratio (PSNR) and visual qualities.

Energy-Efficient IoT-Health Monitoring System using Approximate Computing

Wireless Body Sensor Nodes (WBSN) are frequently used for real time IoT-based health monitoring of patients outside the hospital environment. These WBSNs involve bio-sensors to capture signals from a patient’s body and wireless transmitters to transmit the collected signals to a server located in private/public cloud in real time. These WBSNs include hardware for processing of signals before being transmitted to the cloud. Simultaneous occurrence of all these processes inside energy constrained WBSNs results in considerable amount of power consumption, thus limiting their operational lifetime. Due to the inherent error-resilience in signal processing algorithms, most of these data reaching the servers are redundant in nature and hence of not much clinical importance. Transmission and storage of these excess data result in inefficient usages of transmission bandwidth and storage capabilities. In this paper, we develop a real time encoding scheme that performs iterative thresholding and approximation of wavelet coefficients for sparse encoding of bio-signals (ECG signals), thereby reducing the energy and bandwidth consumption of the WBSN. The encoding scheme compresses bio-signals (ECG signals), while still maintaining the clinically important features. We optimize various process parameters to model a low power hardware prototype for the implementation of our algorithm on a real time microcontroller based IoT platform that operates as an end-to-end WBSN system in real time. Experimental results show a system-level energy improvement of 96% with a negligible impact on signal quality (2%).

A Step-Down Test Procedure for Wavelet Shrinkage Using Bootstrapping

Wavelet thresholding (or shrinkage) attempts to remove the noises existing in the signals while preserving inherent pattern characteristics in the reconstruction of true signals. For data-denoising purpose, we present a new wavelet thresholding procedure which employs the step-down testing idea of identifying active contrasts in unreplicated fractional factorial experiments. The proposed method employs bootstrapping methods to a step-down test for thresholding wavelet coefficients. By introducing the concept of a false discovery error rate in testing wavelet coefficients, we shrink the wavelet coefficients with $p$ -values higher than the error rate. The error rate controls the expected proportion of wrongly accepted coefficients among chosen wavelet coefficients. Bootstrap samples are used to approximate the $p$ -value for computational efficiency. We also present some guidelines for selecting the values of hyper-parameters which affect the performance in the step-down thresholding procedure. Based on some common testing signals and an air-conditioner sounds example, the comparison of our proposed procedure with other thresholding methods in the literature is performed. The analytical results show that the proposed procedure has a potential in data-denoising and data-reduction in a variety of signal reconstruction applications.

An improved infrared image processing method based on adaptive threshold denoising

This paper combines the image adaptive threshold denoising algorithm and performs double threshold mapping processing to the infrared image, which effectively reduces the influence of these phenomena to the infrared image and improves the quality of the image. In this paper, the infrared image denoising technology is studied, and an infrared image denoising method based on the wavelet coefficient threshold processing is proposed. This method is based on the noise distribution characteristics of infrared images, the multiplicative noise in the infrared image is transformed into an additive noise, and the wavelet transform coefficient of the transformed infrared image is processed to denoise the image. On this basis, the advantages and disadvantages of the soft and hard threshold functions are deeply analyzed, and an adaptive threshold function with adjustable parameter is constructed. At the same time, in order to suppress the Gibbs visual distortion caused by the absence of translation invariance of the orthogonal wavelet transform, the two-input wavelet transform with translation invariance is introduced, and a double threshold mapping infrared image processing method based on the adaptive threshold denoising algorithm based on the two-input wavelet transform is formed. Simulation results show that the method proposed in this paper has a better suppression of noise, maintains the integrity of image details, and improves the image quality to a certain extent.

Adaptive thresholding of wavelet coefficients using generalised false discovery rate to compress ECG signal

Adaptive thresholding of wavelet coefficients using generalised false discovery rate to compress ECG signal

Adaptive thresholding of wavelet coefficients using generalised false discovery rate to compress ECG signal

In signal compression the selection of an appropriate threshold is the challenging task. The paper proposes an algorithm to determine the signal adaptive threshold based on estimating wavelet coefficients by generalised False Discovery Rate (FDR) to compress ECG signal. The hypothesis testing and thresholding are closely related. So, multiple hypotheses testing is used to determine an adaptive threshold called as False Discovery Threshold (FDT). The p-value of each wavelet detail coefficient is computed and arranged in an ascending manner. The dynamic critical significance levels are calculated using k-FWER and k-FDR. These significance levels are compared with the corresponding p-value to satisfy desired FDR, which provides the FDT. The run length encoding followed by Huffman coding provides compression. The paper also proposes a new performance evaluation parameter: mean Structural Similarity Index (mSSIM) to check the similarity between original and reconstructed ECG signals. Generalised FDR-based thresholding provides very less PRD value compared to standard codecs in the literature and structural similarity very close to one, which signifies better reconstruction of the signal.

Satellite Image De-Noising With Harris Hawks Meta Heuristic Optimization Algorithm and Improved Adaptive Generalized Gaussian Distribution Threshold Function

An image may be influenced by noise during capturing and transmitting process. Removing the possible noise from the image has always been a challenging issue due to this fact that further processing will not be possible unless by diminishing the noise from images. Many researchers attempted to remove the noise to improve the qualitative and also the quantitative results but these methods could not preserve the quality of images after applying de-noising techniques. In this paper, in the first stage, we utilized the most recent nature-inspired meta-heuristic optimization algorithm to get the optimal solutions for the parameters of thresholding function. Using the Harris hawk optimization (HHO) algorithm results in obtaining the optimized thresholded wavelet coefficients before applying the inverse wavelet transform. In the second stage, we proposed the improved adaptive generalized Gaussian distribution (AGGD) threshold, which is a data-driven function with an adaptive threshold value. This function can be fitted to any kind of images without using any shape tuning parameter. It is clear that the calculation of the threshold value does not require any optimization and LMS learning algorithm. The qualitative and quantitative results validate the superiority of the proposed method.

An optimization detection algorithm for complex intrusion interference signal in mobile wireless network

At present, when detecting intrusive interference signals in classified form, the effect of channel denoising is very poor, and the characteristics of the extracted signals are not clear, which can not achieve effective detection of intrusion signals. An algorithm based on wavelet packet frequency hopping estimation for complex network intrusion detection is proposed in this paper. The soft and hard threshold method is used for wavelet coefficient decomposition, threshold processing, and signal reconstruction; according to probability statistics, a new sequence is composed of the spectral amplitude corresponding to the same frequency of each random variable in a random process and the spectrum matrix of intrusion interference signal is formed, so as to extract the characteristic spectrum of intrusion interference signal; by using the energy balance method, Gauss stochastic wavelet characteristics of intrusion signal can be simulated. The results of network intrusion detection are obtained by the Gauss additivity of the high-order cumulants of the network intrusion. The three edge centroid positioning method is applied to achieve the high-precision location of the intrusion point. Experiments show that the algorithm effectively improves the network channel denoising and the feature extraction effect of the intrusion signal, and it is also better than the current algorithm for the detection and location of the interference signals.

Nonlinear Regularization of Inverse Problems for Linear Homogeneous Transforms by Stabilized Hard Thresholding

In this paper we consider the problem of inverting linear homogeneous transforms by Vaguelette–Wavelet decomposition and stabilized hard thresholding of noisy wavelet coefficients. We also prove asymptotic normality and strong consistency of the mean-square risk estimate for this method.

An algorithm for wavelet thresholding based image denoising by representing images in hexagonal lattice

The existing method of representation for digital images is using square shaped picture elements called pixels in a rectangular grid. Processing based on hexagonal grid is a new approach in image processing. It has various advantages like symmetry, higher angular resolution, consistent connectivity and higher sampling efficiency. Image processing applications like rotation, scaling, edge detection, and compression in hexagonal domain have already been discussed by many researchers. In this paper we propose an image denoising scheme in hexagonal lattice using wavelet thresholding method. For the thresholding of wavelet coefficients, modified NeighShrink thresholding method is applied. In NeighShrink method, sub-optimal universal threshold and identical neighboring window size in all wavelet sub-bands are used. However, in the proposed method, instead of sub-optimal universal threshold, an optimal threshold is determined for every wavelet sub-band by the Stein’s Unbiased Risk Estimate (SURE). Denoising is performed on images represented in rectangular grid as well as hexagonal grid using modified thresholding method for comparison. MSE, PSNR and SSIM are used for the performance analysis. The obtained results confirm that the proposed method gives better results than existing algorithms.

Limit Theorems for Risk Estimate in Models with Non-Gaussian Noise

The problem of constructing an estimate of a signal function from noisy observations, assuming that this function is uniformly Lipschitz regular, is considered. The thresholding of empirical wavelet coefficients is used to reduce the noise. As a rule, it is assumed that the noise distribution is Gaussian and the optimal parameters of thresholding are known for various classes of signal functions. In this paper a model of additive noise whose distribution belongs to a fairly wide class, is considered. The mean-square risk estimate of thresholding is analyzed. It is shown that under certain conditions, this estimate is strongly consistent and asymptotically normal.