Wavelet Thresholding Technique Research Articles

Representation error reduction in compressive sensing using generative models with pivotal tuning

Reducing the transmitted data volume is essential for implementing networks with resource limited and energy-constrained devices. In this sense, compressive sensing becomes a powerful alternative as it moves the most computationally complex task to the central server node, in contrast to the traditional compression scheme. Recently a combination of compressive sensing and generative models has appeared, giving rise to Compressive Sensing using Generative Models (CSGM). Although CSGM reduce reconstruction errors, they introduce the so-called representation error. This paper proposes CSGM-Pivotal Tuning Inversion (CSGM-PTI), a technique based on model retraining in decompression time to reduce the representation error in CSGM. The idea of CSGM-PTI is to expand the scope of the generative model to include the desired signal. The results show robustness to noise and performance gains in signal reconstruction of up to 20% compared with Deep Image Prior (DIP), standalone CSGM, and Wavelet Thresholding (WT) techniques, all traditionally used in the related literature.

Harmonic Detection Method Based on Parameter Optimization VMD-IWT Combined Noise Reduction

Aiming at the problem that the existing harmonic detection methods are susceptible to noise interference in the actual working environment, which leads to the reduction of detection accuracy, this paper introduces a novel harmonic detection technique utilizing a RIME optimization algorithm (RIME) to enhance variational mode decomposition (VMD) combined with an improved wavelet threshold (IWT) approach. Initially, RIME optimization refines VMD for the decomposition of harmonic current signals, yielding several modal components. Subsequently, a correlation coefficient method distinguishes between effective and ineffective modal components, discarding the latter. The effective components undergo noise reduction through an enhanced wavelet thresholding technique, and these denoised components are then reconstructed to produce the final noise-reduced signal. Finally, the Hilbert transform is applied to the denoised signal to extract harmonic parameters. Verification through both simulated and actual signal measurements demonstrates that the proposed method not only surpasses other noise reduction algorithms in signal-to-noise ratio and root-mean-square error, but also shows superior accuracy and robustness compared to alternative detection techniques. This method effectively filters out signal noise under noise interference, minimizes detection errors, and achieves precise harmonic signal detection with improved accuracy.

EMD AND WAVELET-BASED ECG SIGNAL DENOISING AND QRS COMPLEX DETECTION

This project presents a novel method for noise removal and QRS complex detection in electrocardiogram (ECG) signals, employing Empirical Mode Decomposition (EMD), windowing, and wavelet thresholding techniques. Noise is added to the ECG signal, and EMD is applied to obtain denoised components. Local minima detection and peak matching identify QRS complex boundaries. Windowing isolates the QRS regions, followed by wavelet thresholding for further denoising. Evaluation metrics like improved Signal-to-Noise Ratio, Mean Square Error, and Percent Root Mean Square Difference are calculated at different input SNR values, demonstrating the method's effectiveness in preserving the QRS complex while removing noise.. Keywords: ECG signal processing, QRS complex detection, Empirical Mode Decomposition (EMD), Windowing, Wavelet thresholding, QRS complex extraction, Signal-to-Noise Ratio (SNR), Mean Square Error (MSE), Percent Root Mean Square Difference (PRD).

De-noising classification method for financial time series based on ICEEMDAN and wavelet threshold, and its application

This paper proposes a classification method for financial time series that addresses the significant issue of noise. The proposed method combines improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and wavelet threshold de-noising. The method begins by employing ICEEMDAN to decompose the time series into modal components and residuals. Using the noise component verification approach introduced in this paper, these components are categorized into noisy and de-noised elements. The noisy components are then de-noised using the Wavelet Threshold technique, which separates the non-noise and noise elements. The final de-noised output is produced by merging the non-noise elements with the de-noised components, and the 1-NN (nearest neighbor) algorithm is applied for time series classification. Highlighting its practical value in finance, this paper introduces a two-step stock classification prediction method that combines time series classification with a BP (Backpropagation) neural network. The method first classifies stocks into portfolios with high internal similarity using time series classification. It then employs a BP neural network to predict the classification of stock price movements within these portfolios. Backtesting confirms that this approach can enhance the accuracy of predicting stock price fluctuations.

Heart sound classification using wavelet scattering transform and support vector machine

OBJECTIVE: A representation of the sound recordings that are associated with the movement of the entire cardiac structure is termed the Phonocardiogram (PCG) signal. In diagnosing such diverse diseases of the heart, PCG signals are helpful. Nevertheless, as recording PCG signals are prone to several surrounding noises and other disturbing signals, it is a complex task. Thus, prior to being wielded for advanced processing, the PCG signal needs to be denoised. This work proposes an improved heart sound classification by utilizing two-stage Low pass filtering and Wavelet Threshold (WT) technique with subsequent Feature Extraction (FE) using Wavelet Scatter Transform and further classification utilizing the Cubic Polynomial Support Vector Machine (SVM) technique for CVD. METHOD: A computer-aided diagnosis system for CVD detection centered on PCG signal analysis is offered in this work. Initially, by heavily filtering the signal, the raw PCG signals obtained using the database were pre-processed. Then, to remove redundant information and noise, it is denoised via the WT technique. From the denoised PCG, wavelet time scattering features were extracted. After that, by employing SVMs, these features were classified for pathology. RESULTS: For the analysis, the PCG signal obtained from the Physionet dataset was considered. Heavy low-pass filtering utilizing a Low-Pass Butterworth Filter (LPBF) is entailed in the pre-processing step. This removed 98% of the noise inherently present in the signal. Further, the signal strength was ameliorated by denoising it utilizing the WT technique. Promising results with maximum noise removal of up to 99% are exhibited by the method. From the PCG, Wavelet Scattering (WS) features were extracted, which were later wielded to categorize the PCG utilizing SVMs with 99.72% accuracy for different sounds. DISCUSSION: The Classification accuracies are analogized with other classification techniques present in the literature. This technique exhibited propitious outcomes with a 3% improvement in the F1 score when weighed against the top-notch techniques. The improvement in the metrics is attributed to the usage of the pre-processing stage comprising of Low-pass filter and WT method, WS Transform (WST), and SVMs. CONCLUSION: The superiority of the proposed technique is advocated by the comparative investigation with prevailing methodologies. The system revealed that Coronary Artery Disease (CAD) can be implemented with superior methods to achieve high accuracy.

Wavelet and Earth Mover’s Distance Coupling Denoising Techniques

The widely used wavelet-thresholding techniques (DWT-H and DWT-S) have a near-optimal behavior that cannot be enhanced by any local denoising filter, but they cannot utilize the similarity of small-size image patches to enhance the denoising performance. Two of the latest improvements (WNLM and NLMW) introduced the Euclidean distance to measure the similarity of image patches, and then used the non-local meaning of similar patches for further denoising. Since the Euclidean distance is not a good similarity measurement, these two improvements are limited. In this study, we introduced the earth mover’s distance (EMD) as the similarity measure of small-scale patches within the wavelet sub-bands of noisy images. Moreover, at higher noise levels, we further incorporated joint bilateral filtering, which can filter both the spatial domain and the intensity domain of images. Denoising simulation experiments on BSDS500 demonstrated that our algorithm outperformed the DWT-H, DWT-S, WNLM, and NLMW algorithms by 4.197 dB, 3.326 dB, 2.097 dB, and 1.162 dB in terms of the average PSNR, and by 0.230, 0.213, 0.132, and 0.085 in terms of the average SSIM.

A method for noninvasive beat-by-beat visualization of His bundle signals.

Invasive recording of His bundle signals (HBS) in electrophysiological study (EPS) is important in determining HV interval, the time taken to activate the ventricles from the His bundle. Noninvasive surface measurements of HBS are attempted by averaging typically 100-200 cardiac cycles of ECG time series in body surface potential mapping (BSPM) and in magnetocardiography (MCG) which records weak cardiac magnetic fields by highly sensitive detectors. However, noninvasive beat-by-beat extraction of HBS is challenged by ramp-like atrial signals and noise in PR segment of the cardiac cycle. By making use of a signal-averaged trace showing prominent HBS as a guide trace, we developed a method combining interval-dependent wavelet thresholding (IDWT) and signal space projection (SSP) technique to eliminate artifacts from single beats. The method was applied on MCG recorded on 21 subjects with known HV intervals based on EPS and noninvasive signal-averaging, including five subjects with BSPM recorded subsequently. The method was also applied on stress-MCG of a subject featuring autonomic dynamics. HBS could be extracted from 19 out of 21 subjects by signal-averaging whose timing differed from EPS between -8 and 11 ms as tested by 2 observers. HBS in single beats were seen as aligned patterns in inter-beat contours and were appreciable in stress-MCG and conspicuous than BSPM. The performance of the method was evaluated on simulated and measured MCG to be adequate if the signal-to-noise ratio was at least 20 dB. These results suggest the use of this method for noninvasive assessments on HBS.

Wavelet thresholding techniques implementation in retinal images for suppressing noises

In medical image processing, noise plays a major role of reducing the details of the images and blurs the features which are important for the diagnosis of the disease. Retinal images are high resolution images. Gaussian noise, Salt & Pepper noise affects certain important features of them which are needed for proper diagnosis of the retinal diseases. So removing noises in these images is a kind of difficulty that all researcher experiences. The main objective is to reduce the effect of Gaussian noise and Salt & Pepper noise in retinal images. Recently, wavelet transform is being used in all areas of image processing and especially in medical image denoising, it is highly used because it has multi resolution property and sparsity. So here, wavelet thresholding techniques such as Visu shrink, SURE Shrink and Bayes shrink are implemented to remove Gaussian noise and Salt & Pepper noise. The performance of all the three methods are evaluated using PSNR (Peak Signal to Noise Ratio), MSE (Mean Square Error), NK (Normalized cross correlation) and Time elapsed. Also, the performances of all the thresholding techniques were compared using above mentioned metrics.

Speech Enhancement using a Variable Level Decomposition DWT

The wavelet transform shows a promising solution for a non-stationary signal. The denoising of a noisy speech signal carried with a wavelet thresholding technique. The noisy signal decomposed into different frequency bands, and this decomposition level (DL) decided independent of non-stationary noise. In this letter, a new DL detection procedure presented, and it decides the decomposition level based on signal energy and speech dominance. The proposed DL applies to the speech denoising model, and the obtained results compared with the unversal thresholding technique and the minimum mean square error algorithm. The performance of the enhanced speech signal measures with speech intelligibility measure (STOI), and speech quality measure (PESQ). The experimental results revealed that the proposed scheme outperforms the conventional methods in all SNR and non-stationary environments.

Wavelet Transform Based Estimation of 1 Dimensional Signal

The key idea of this manuscript is denoising of noisy biological signals. For this wavelet thresholding technique is suggested. To eliminate the noise existing in the signal, mixed thresholding function is considered which is the median of Hard, Soft and Garrote functions. The mixed thresholding function is applied by degraded white gaussian noise Electrocardiogram signal. Two methods that are used to calculate the threshold value is FDR technique and Visu shrink technique. The outcomes of mixed functions are compared with remaining functions using Signal to Noise Ratio (SNR) and Mean Square Error (MSE). It is obvious that the mixed function performs superior than remaining functions using Visu shrink technique and performs better than only Hard function using FDR technique.

Examination of Skin Cancer Images using Wavelet De-noising

The objective of this paper is de-noising of melanoma images using wavelets because, dermatoscopy images are corrupted by noise, which leads to fault diagnosis. Hence de-noising is essential in melanoma skin cancer image to remove the salt and pepper noise(impulse noise) by preserving the melanoma image original information. The wavelet thresholding techniques are used in this paper to de-noise the melanoma image and improved the quality of an image. Wavelet de-noising algorithm has been developed employing soft and hard thresholding techniques. It works on Daubechies, Symlet, biorthogonal wavelets at decomposition level5. Image objective performance metrics like peak signal to noise ratio, mean square error and statistical performance metrics like mean, median, standard deviation, L1 norm, L2 norm are observed and analyzed for melanoma images

Dynamic monitoring of a super high-rise structure based on GNSS-RTK technique combining CEEMDAN and wavelet threshold analysis

To capture the dynamic characteristics of a super high-rise structure under construction (i.e. Tianjin 117 Tower), multi-constellation GNSS-RTK (global navigation satellite system – real time kinematic) sensors are employed to derive the displacement information of the structure. A combined approach (CEEMDAN–WT) of complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and wavelet threshold (WT) technique is put forward to weaken the influence of background noise of sensors. For the sake of testing the effect of noise reduction via employing CEEMDAN–WT, a nonlinear signal with additive noise is introduced. Subsequently, the natural frequencies and the corresponding damping ratios of the structure are extracted based on the fast Fourier transform (FFT) and random decrement technique. In addition, the finite element model (FEM) of the structure is built to forecast the natural frequencies via modal analysis. The results show that: (1) The dynamic displacement information of super high-rise structures can be effectively determined based on GNSS-RTK technique; (2) The presented CEEMDAN–WT approach outperforms the single CEEMDAN and WT approaches; (3) The result obtained via the field measurement coincides with the FEM.

Characterization of Environmental Drivers Controlling the Baseline of Soil Surface CO2 Flux using Wavelet-based Multiresolution State-Space Model and Wavelet Denoising

Multivariate environmental time series including soil surface CO2 flux (FCO2) have non-stationarity and mutual interdependence, and thus the i.i.d assumption-based conventional regression techniques inevitably lead to spurious regression or lose the dynamic characteristics in the process of variable transformation. In this paper, we adopted a wavelet threshold technique for our newly developed wavelet-based multiresolution state-space model (MRSSM) to overcome such limitations and to quantitatively evaluate the environmental drivers (EDs) controlling the baseline of FCO2. First, the structural characteristics and the potential EDs (PEDs) of FCO2 were explored by wavelet denoised (threshold) SSM for complex environmental observation data. Then, the major EDs (MEDs) were identified using the scale localized correlation and the wavelet coherence analysis between PEDs and observation data. Next, the contribution of MEDs to FCO2 was quantitatively evaluated by calculating the effective dynamic efficiency using the wavelet energy ratio of the maximum-correlation time-frequency bands. Finally, the effectiveness of the wavelet threshold method for MRSSM was discussed. The proposed wavelet denoising method is expected to improve the performance of MRSSM which is effective to identify, evaluate and predict the main environmental factors inherent in the observation data from complex environmental systems where physicochemical and biological processes of various spatio-temporal scales occur simultaneously.

A wavelet technique for the study of economic socio-political situations in a textual analysis framework

PurposeThe purpose of this paper is to apply the wavelet thresholding technique in order to analyze economic socio-political situations in Tunisia using textual data sets. This technique is used to remove noise from contingency table. A comparative study is done on correspondence analysis and classification results (using k-means algorithm) before and after denoising.Design/methodology/approachTextual data set is collected from an electronic newspaper that offers actual economic news about Tunisia. Both the hard and the soft-thresholding techniques are applied based on various Daubechies wavelets with different vanishing moments.FindingsThe results obtained have proved the effectiveness of wavelet denoising method in textual data analysis. On one hand, this technique allowed reducing the loss of information generated by correspondence analysis, ensured a better quality of representation of the factorial plan, neglected the interest of lemmatization in textual analysis and improved the results of classification by k-means algorithm. On the other hand, the proximities provided by the factorial visualization validate the economic situation of Tunisia during the studied period showing mainly a stable situation before the revolution and a deteriorated one after the revolution.Originality/valueThe results are the first to analyze economic socio-political relations using textual data. The originality of this paper comes also from the joint use of correspondence analysis and wavelet thresholding in textual data analysis.

An integrated acoustic echo and noise cancellation system using cross-band adaptive filters and wavelet thresholding of multitaper spectrum

An efficient integrated system for acoustic echo and noise cancellation in hands free devices is proposed in this paper. Adaptive filters are usually employed in such systems for the acoustic echo cancellation. In order to reduce the computational complexity, sub band adaptive filters are commonly used since the order of filter required will be less but at the cost of distortion due to aliasing effect. In this work, cross-band adaptive filters are developed in wavelet domain/wavelet packet domain in tune with psychoacoustic model, to reduce the above distortion and thereby effectively estimate the echo and cancel it. The system uses wavelet thresholding technique for smoothening the log multitaper spectrum which eliminates the annoying musical noise in the processed output. To achieve efficient echo and noise cancellation, a novel switching mechanism to switch between wavelet filter bank and perceptual wavelet packet filter bank with most matching wavelet basis, from a dictionary of wavelet bases, depending on the type of noise present in each frame of the noisy speech is designed and developed in this work. The performance of the proposed integrated system is evaluated in terms of Acoustic Interference Cancellation (AIC) and Noise Attenuation (NA) under different Signal to Noise Ratio (SNR) conditions. The system exhibits very good performance even at very low SNRs close to −10 dB when compared with other such competitive systems.

Vibrational and hydroacoustic signal processing in the frequency domain and its software-hardware implementation

The paper discusses an algorithm for spectral density estimation in the frequency domain using wavelet-based smoothing by wavelet thresholding techniques. The suggested algorithm can be applied to vibrational and hydroacoustic signal processing in order to estimate signal parameters in the frequency domain. The algorithm can be applied to the Fourier periodogram without using signal samples in the time domain. We also propose a technique aimed at working with signals of arbitrary length by applying the maximal overlap discrete wavelet transform. We also study software-hardware implementation of the developed algorithms.

Novel and efficient algorithms for early detection of myocardial ischemia

This paper presents the development of novel and efficient algorithms for early detection of cardiac ischemia from ECG signal using different feature extraction techniques. The proposed work mainly involves three stages namely denoising, feature extraction and classification. The removal of noise from ECG signal is achieved by applying wavelet threshold technique. The extraction of clinically useful features is carried out through morphological technique, statistical analysis, principal component analysis (PCA)-based technique and independent component analysis-wavelet packet decomposition (ICA-WPD) technique. The extracted features are used as inputs for artificial neural network (ANN), support vector machines (SVM) and K-nearest neighbour (KNN) classifier models for detecting ischemic beats. The performance of all models are compared and validated with ECG signal acquired from physiobank database in terms of performance indices such as classification accuracy, sensitivity and positive prediction accuracy. The results have confirmed that the ANN model trained and tested with features extracted by ICA-WPD provides highest classification accuracy of 96.85%, PPA of 99.59% and sensitivity of 97.22%. Results clearly demonstrated that the ANN classifier model combined with ICA-WPD-based feature is more effective in diagnosing myocardial ischemia at early stages.

Efficient Algorithm for Early Detection of Myocardial Ischemia using PCA based Features

Objective: The purpose of this work is to develop an efficient algorithm for uncovering the myocardial ischemia at early stages from ECG signal using Principal Component Analysis (PCA). Methods/Statistical Analysis: The proposed work mainly involves three stages namely denoising, extracting features and classification. The removal of noise from ECG signal is achieved by applying wavelet threshold technique. The extraction of clinically useful features is carried out by selecting ST-T complex from ECG beat samples followed by dimensionality reduction using PCA. These features are fed to MLP, SVM and KNN classifier models for diagnosing myocardial ischemia at early stages. The performance of classifier models are validated with ECG data obtained from physiobank database in terms of performance measures such as classification accuracy, sensitivity and positive prediction accuracy. Findings: The comparisons of experimental results have shown that the MLP classifier model has great scope for diagnosing myocardial ischemia at early stages. The MLP classifier model has resulted in classification accuracy of 90.51%, PPA of 93.8% and sensitivity of 96.19%. Application/Improvements: The proposed PCA based method has shown an improved accuracy of 90.51% in comparison with classifiers developed by other researchers.

Wavelet nonparametric estimation from strong spatial correlated high-dimensional data

This paper addresses the problem of spatial prediction from strong spatial correlated high-dimensional data. Two approaches are considered: spatial wavelet kernel penalized nonparametric regression, and wavelet shrinkage. The best performance corresponds to spatial wavelet thresholding techniques applied to coarser scales, when slowly varying data displaying strong spatial correlations are analyzed. Our initial motivation relies on spatial estimation of annual mean ocean surface temperature maps to detect changes in ocean-surface temperatures, that could cause modifications in atmospheric circulation and precipitation. Specifically, we have analyzed daily ocean surface temperature curves from the Hawaii ocean stations, available at latitude–longitude interval [22.7,22.8]×[−158.1,−157.94] during the period 2000–2007, from The World-Wide Ocean Optics Database (WOOD). Additionally, wavelet-based non-linear estimation procedures are compared with wavelet-based Gaussian linear model estimation methods, based on spatial autoregressive Hilbertian processes, and heavy tail covariance processes, solution to fractional pseudodifferential equations.

A Particle Swarm Optimization Technique-Based Parametric Wavelet Thresholding Function for Signal Denoising

The determination of threshold and the construction of thresholding function would directly affect the signal denoising quality in wavelet transform denoising techniques. However, some deficiencies exist in the conventional methods, such as fixed threshold value and the inflexible thresholding functions. To overcome the defects of the traditional wavelet thresholding techniques, a modified particle swarm optimization (MPSO) algorithm-based parametric wavelet thresholding approach is proposed for signal denoising. Firstly, a kind of parametric wavelet thresholding function construction method is proposed on the basis of conventional thresholding functions. With mathematical derivation, the properties of the constructed function are proved. Three dynamic adjustment strategies are then employed to modify the PSO algorithm. The mean square error (MSE) between the original signal and the reconstructed signal is minimized by the MPSO algorithm. Finally, the performances of the proposed approach and the existing methods are simulated by denoising four benchmark signals with different noise levels. The simulation results show that the proposed MPSO-based parametric wavelet thresholding can obtain lower MSE, higher signal-to-noise ratio, and noise suppression ratio compared to the other algorithms. Besides, the denoising visual results also indicate the superiority of the proposed approach in terms of the signal denoising capability.