De-noising mechanical signals by hybrid thresholding

In this article, we developed and analyzed a thresholding method in which soft thresholding estimators are independently expanded by empirical scaling values. The scaling values have a common hyper-parameter that is an order of expansion of an ideal scaling value that achieves hard thresholding. We simply call this estimator a scaled soft thresholding estimator. The scaled soft thresholding is a general method that includes the soft thresholding and non-negative garrote as special cases and gives an another derivation of adaptive LASSO. We then derived the degree of freedom of the scaled soft thresholding by means of the Stein's unbiased risk estimate and found that it is decomposed into the degree of freedom of soft thresholding and the reminder connecting to hard thresholding. In this meaning, the scaled soft thresholding gives a natural bridge between soft and hard thresholding methods. Since the degree of freedom represents the degree of over-fitting, this result implies that there are two sources of over-fitting in the scaled soft thresholding. The first source originated from soft thresholding is determined by the number of un-removed coefficients and is a natural measure of the degree of over-fitting. We analyzed the second source in a particular case of the scaled soft thresholding by referring a known result for hard thresholding. We then found that, in a sparse, large sample and non-parametric setting, the second source is largely determined by coefficient estimates whose true values are zeros and has an influence on over-fitting when threshold levels are around noise levels in those coefficient estimates. In a simple numerical example, these theoretical implications has well explained the behavior of the degree of freedom. Moreover, based on the results here and some known facts, we explained the behaviors of risks of soft, hard and scaled soft thresholding methods.

The aim of this study was to investigate the application of wavelet denoising in noise reduction for multifunction myoelectric control system. Six upper limb motions including hand open, hand close, wrist extension, wrist flexion, pronation, and supination. For each motion, two channels of electrodes were applied. A comparative study of four classical denoising algorithms including universal thresholding, SURE thresholding, hybrid thresholding, and minimax thresholding have been used to remove white Gaussian noise at various signal-to-noise ratios (SNRs) from EMG signals. Applications of soft and hard thresholding as well as threshold rescaling methods were considered and the whole procedures of noise reduction were applied with different wavelet functions and different decomposition levels. Evaluations of the performance of noise reduction are determined using mean squared error (MSE). The results show that Daubechies wavelet with second orders (db2) provides marginally better performance than other possibilities. Suitable number of decomposition levels is four. Universal and soft thresholding is the best of wavelet denoising algorithms from eight possible denoising processes under investigation. In addition, the threshold using a level-dependent estimation of level noise showed better than others.

Wavelet denoising techniques with applications to experimental geophysical data

A wavelet-based method for improving signal-to-noise ratio and contrast in MR images

Partial Discharge (PD) signal measurement is very significant tool in analyzing condition of the electrical insulation. The PD information is lost in the presence of various noises. The wavelet transform (WT) based denoising provides a better platform for pre and post processing of PD signal. The wavelet adaptive Thresholding de-noising techniques are well suited for reducing the noise. This paper adopts the various adaptive thresholding techniques such as VisuShrink, SureShrink, combination of the two called Heursure, minimax thresholding and BayesShrink, which are broadly classified as Global and Local thresholding methods. The algorithm presents the comparative analysis for the selection of optimal mother wavelet. Once the optimal mother wavelet is chosen, selection of the best thresholding rule is identified by comparing the values of signal to noise ratio (SNR), mean square error (MSE) and Peak Signal to Noise ratio (PSNR) of all the techniques. The algorithm also presents the comparison between Hard and Soft thresholding. It is shown that the soft thresholding is best suited to remove the noise compared to hard thresholding. The simulated Damped Exponential Pulse (DEP) and Damped Oscillatory Pulse (DOP) has been used. Three sets of PD data are considered to check the performance of the algorithm.

In order to overcome the discontinuance of the hard thresholding function and the defect of seriously slashing singularity in the soft thresholding function, improve the denoising effect and detect the transformer partial discharge signal more accurately, in this paper an improved wavelet threshold denoising method is put forward through analyzing the interference noise of transformer partial discharge signals and studying various wavelet threshold denoising method, especially the wavelet threshold denoising method that overcomes the shortcomings of the hard and soft threshold. Simulation results show that the denoising effect of this method has been greatly improved than the traditional hard and soft threshold method. This method can be widely used in practical transformer partial discharge signal denoising.

This paper investigates the negative pressure waves generated when the pipeline leaks based on the negative pressure wave localization method, adopts a boosted wavelet transform method that does not depend on the Fourier transform, selects the noise reduction threshold based on the Birgé-Massart strategy, introduces a soft and hard threshold compromise noise reduction algorithm to process the noise-containing signals, and finally uses the negative pressure waves collected from field experiments to test and apply the above algorithm, and compares the effect and error analysis with the traditional soft threshold method and hard threshold method. The results show that the denoising effect and the root mean square error after signal processing of the algorithm established in this paper are better than the traditional algorithms, and have good application value in pipeline leakage signal noise reduction.

Image denoising and quality measurements by using filtering and wavelet based techniques

A large amount of noise is mixed in the actual process industrial data, which leads to a decline in data quality, which in turn affects the diagnosis results. In reality, the wavelet threshold method is generally used to remove noise. However, the hard threshold method which is in the wavelet threshold method has the disadvantages of poor signal continuity and signal oscillating. The soft threshold method has the disadvantages of constant deviation and large error of reconstructed signal. To this end, we propose a random soft-hard threshold algorithm which can combine hard and soft thresholds. Then the new algorithm is combined with the principal component analysis for fault diagnosis of the TE (Tennessee Eastman) process. The MATLAB simulation results show that the above method can effectively denoise, identify and detect faults more accurately, and can better find the variables that have the greatest impact on the fault.

Because of the serious electromagnetic interference environments where the displacement sensors work, the wavelet transform method is used to reduce influences the electromagnetic interference. And in this paper, the wavelet fuzzy threshold method is proposed to de-noising, which can overcome the disadvantages of using the hard threshold method or soft threshold solely. Besides, in order to make the estimation accuracy of uncertainty interference higher, the variance estimation method is used to improve the denoising performances. By simulating and analyzing, the sensor signal with serious noise produced by the electromagnetic interference was reconstructed well by disassembled to 6 levels used the sym8 wavelet function. On the basis of this, the noise was reduced by the wavelet fuzzy threshold method. Compared with soft threshold de-noising and hard threshold de-noising, fuzzy threshold de-noising way can restrain EMI better. Finally, the variance estimation method is proved to be able to identify the type of interference signals.

Based on multi-resolution analysis of wavelet, this article is aimed at building a new soft threshold function for wavelet de-noising, to overcome the discontinuous disadvantage of the hard threshold function. In the area adjacent to the threshold, continuously adjustable nonlinear functions are introduced in piecewise to process the wavelet coefficients more carefully in this area. Consequently, large deviation caused by super-compression of wavelet coefficients when using traditional soft threshold could be avoided, and the nonlinearity of the system is able to be effectively kept. Using both signal to noise ratio (SNR) and mean square error (MSE) as the evaluation indicators, simulation results show that the improved method is more effective than the method based on traditional hard and soft threshold.

In order to improve the effects of denoising, this paper introduces the basic principles of wavelet threshold denoising and traditional structures threshold functions. Meanwhile, it proposes wavelet threshold function and fixed threshold formula which are both improved here. First, this paper studies the problems existing in the traditional wavelet threshold functions and introduces the adjustment factors to construct the new threshold function basis on soft threshold function. Then, it studies the fixed threshold and introduces the logarithmic function of layer number of wavelet decomposition to design the new fixed threshold formula. Finally, this paper uses hard threshold, soft threshold, Garrote threshold, and improved threshold function to denoise different signals. And the paper also calculates signal-to-noise (SNR) and mean square errors (MSE) of the hard threshold functions, soft thresholding functions, Garrote threshold functions, and the improved threshold function after denoising. Theoretical analysis and experimental results showed that the proposed approach could improve soft threshold functions with constant deviation and hard threshold with discontinuous function problems. The proposed approach could improve the different decomposition scales that adopt the same threshold value to deal with the noise problems, also effectively filter the noise in the signals, and improve the SNR and reduce the MSE of output signals.

Acoustic emission (AE) detection, as a non-electrical detection method, is very suitable for effective fault detection of power equipment with a strong electromagnetic field. However, the AE signal collected at industrial sites often contains a lot of interference noise, affecting the analysis and prediction of faults. In this study, a wavelet denoising method based on a new threshold function is proposed, to achieve a noise reduction in the low signal-to-noise ratio (SNR) signals. Simulation experiment results show that the proposed threshold function not only overcomes the shortcomings of the discontinuous hard threshold function, but also solves the constant deviation of the soft threshold function. What’s more, the proposed function achieves a good adaptability. When SNR = 10 dB: The SNR of the new threshold is 20.6622, and the RMSE is 0.0026. The SNR of the hard threshold is 20.2246 and the RMSE is 0.0027, compared with the traditional hard threshold method, the SNR of the new threshold is increased by 2.16% and the root mean square error (RMSE) is reduced by 3.7%; the SNR of the soft threshold is 15.5656, and the RMSE is 0.0047, compared with the traditional soft threshold method, the new threshold has a 32.74% increase in SNR and a 40.43% reduction in RMSE. When SNR = -10 dB: The SNR of the new threshold is 4.2602, and the RMSE is 0.0172. The SNR of the hard threshold is 3.8558 and the RMSE is 0.0182, compared with the traditional hard threshold method, the SNR of the new threshold is increased by 10.49% and the RMSE is reduced by 5.49%; the SNR of the soft threshold is 2.1625, and the RMSE is 0.0212, compared with the soft threshold method, SNR is improved by 97% and RMSE is reduced by 18.87%. Performance analyses have proved that the improved wavelet denoising method can obtain a good noise reduction effect. It is very helpful for AE signal analysis with the generally low SNR, which can improve the accuracy of failure identification in subsequent acts.

Wavelet domain de-noising of time-courses in MR image sequences

This article presents an overview of various denoising methods for optical and synthetic aperture radar (SAR) images. Currently, there are numerous algorithms and techniques to denoise images using adaptive filters in both the spatial as well as wavelet domain. However, in contrast, an algorithm which performs both soft and hard thresholding on a multi-level wavelet transformed image utilizing an adaptive threshold value has been designed and implemented. The threshold value varies for different wavelet regions from image to image and is selected for each region based on certain performance criteria such as Peak Signal to Noise Ratio (PSNR) and Mean Square Error (MSE). This algorithm has been used to denoise SAR images corrupted with multiplicative noise as well as optical images corrupted with White Gaussian additive noise. The results obtained have been compared with existing filters like median filter, Frost filter and Wiener filter. Additionally, we have compared the results of using different wavelet families including family of Daubechies and Biorthogonal filter banks.