Bridging between Soft and Hard Thresholding by Scaling

Wavelet denoising techniques with applications to experimental geophysical data

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.

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.

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.

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

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.

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.

Purpose: Parallel imaging methods in MRI have resulted in faster acquisition times and improved noise performance. ESPIRiT is one such technique that estimates coil sensitivity maps from the auto-calibration region using an eigenvalue-based method. This method requires choosing several parameters for the the map estimation. Even though ESPIRiT is fairly robust to these parameter choices, occasionally, poor selection can result in reduced performance. The purpose of this work is to automatically select parameters in ESPIRiT for more robust and consistent performance across a variety of exams. Theory and Methods: Stein's unbiased risk estimate (SURE) is a method of calculating an unbiased estimate of the mean squared error of an estimator under certain assumptions. We show that this can be used to estimate the performance of ESPIRiT. We derive and demonstrate the use of SURE to optimize ESPIRiT parameter selection. Results: Simulations show SURE to be an accurate estimator of the mean squared error. SURE is then used to optimize ESPIRiT parameters to yield maps that are optimal in a denoising/data-consistency sense. This improves g-factor performance without causing undesirable attenuation. In-vivo experiments verify the reliability of this method. Conclusion: Simulation experiments demonstrate that SURE is an accurate estimate of expected mean squared error. Using SURE to determine ESPIRiT parameters allows for automatic parameter selections.In-vivo results are consistent with simulation and theoretical results.

Ultrasound (US) image quality often suffers from random and speckle noise. Especially in the case of difficult patients, increased presence of random noise leads to compromised signal to noise ratio (SNR). The proposed technique removes random or speckle noise by promoting the low rank component of temporal US image sequences comprising of RF-data or envelope-detected data, respectively. This approach leverages the fact that due to tissue connectedness, tissue motion tends to exhibit limited temporal profiles. An approach to approximate the low rank component of the image sequence involves truncating its singular value decomposition. In the proposed algorithm, this is performed in a block-wise manner. Additionally, an adaptive singular value threshold is proposed based on Stein's unbiased risk estimator. This paper presents applications of this methodology on sequences of RF-data and envelope-detected data.

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.

This paper addresses the problem of Bayesian wavelet estimating the mean vector of multivariate normal distribution under a multivariate normal prior distribution based on linear and nonlinear exponential balanced loss functions. The covariance matrix of multivariate normal distribution is considered known. Bayes estimators of mean vector parameter of multivariate normal distribution are achieved. Then two soft shrinkage wavelet threshold estimators based on Stein’s unbiased risk estimate (SURE) and Bayes estimators are provided. Finally, the performance of the soft shrinkage wavelet estimators was checked through simulation study and Electrical Grid Stability Simulated data set. Simulation and real data results showed the better performance of SURE thresholds based on linear and nonlinear exponential balanced loss functions compared to other classical wavelet methods. Also, they showed better performance for SURE threshold based on nonlinear exponential balanced loss function in multivariate normal distribution with small dimensions.

Since the infrared image has the problem of poor contrast, edge blur, low noise ratio, noisy and other shortcomings, this paper presents an improved threshold denoising algorithm based on curvelet transform, using a combination of hard and soft threshold methods to form a new threshold based functions. Compare to the conventional hard threshold, soft threshold, de-noising based on wavelet transform method, the proposed denoising method can obtain better PSNR and visual characteristics, retain more details

A new thresholding method, based on L-statistics and called order thresholding, is proposed as a technique for improving the power when testing against high-dimensional alternatives. The new method allows great flexibility in the choice of the threshold parameter. This results in improved power over the soft and hard thresholding methods. Moreover, order thresholding is not restricted to the normal distribution. An extension of the basic order threshold statistic to high-dimensional ANOVA is presented. The performance of the basic order threshold statistic and its extension is evaluated with extensive simulations.

Recently, total variation (TV)-based regularization has become a standard technique for signal denoising. The reconstruction quality is generally sensitive to the value of regularization parameter. In this work, based on Cham-bolle's algorithm, we develop two data-driven optimization schemes based on minimization of Stein's unbiased risk estimate (SURE)-statistically equivalent to mean squared error (MSE). First, we propose a recursive evaluation of SURE to monitor the estimation error during Chambolle's iteration; the optimal value is then identified by the minimum SURE. Second, for fast optimization, we perform alternating update between regularization parameter and solution within Chambolle's iteration. We exemplify the proposed methods with both 1-D and 2-D signal denoising. Numerical experiments show that the proposed methods lead to highly accurate estimate of regularization parameter and nearly optimal denoising performance.

We consider geostatistical regression models to predict spatial variables of interest, where likelihood‐based methods are used to estimate model parameters. It is known that parameters in the Matérn covariogram cannot be estimated well, even when increasing amounts of data are collected densely in a fixed domain. Although a best linear unbiased predictor has been proposed when model parameters are known, a predictor with estimated parameters is nonlinear and may be not the best in practice. Therefore, we propose an adjusted procedure for the likelihood‐based estimates to improve the predicted ability of the nonlinear spatial predictor. The adjusted parameter estimators based on minimizing a corrected Stein's unbiased risk estimator tend to have less bias than the conventional likelihood‐based estimators, and the resulting spatial predictor is more accurate and more stable. Statistical inference for the proposed method is justified both theoretically and numerically. To verify the practicability of the proposed method, a groundwater data set in Bangladesh is analyzed.