The Research of Infrared Image Denoising Algorithm Based on Curvelet Transform

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.

Wavelet denoising techniques with applications to experimental geophysical data

Curvelet transform (CT), proposed by E. Candes et al. (1999), is used for speckle reduction of SAR images. The CT is useful for speckle reduction through its subband images and the speckle reduction is obtained by thresholding the subband-image coefficients of the digitized SAR images. Two thresholding methods are used; hard thresholding and soft thresholding. The denoising method shows great promise for speckle removal and hence provides good detection performance for SAR based recognition.

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

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 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.

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.

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.

This paper presents a hybrid wavelet thresholding approach for reducing white Gaussian noise in mechanical fault signals to offset the deficiencies of hard and soft thresholding. We observed that it is not appropriate to use the mean squared error (MSE) as the only criterion in the evaluation of the de-noising results of mechanical signals. As such, we proposed a combined criterion incorporating both MSE and false identification energy (E/sub false/) to evaluate the de-noising results. In our simulation studies, the proposed hybrid thresholding approach outperforms both the soft- and hard-thresholding methods in terms of the combined criterion. The proposed approach is then successfully applied to noise reduction and fault feature extraction of bearing signals.

Wavelet de-noising method is often used in the processing of magnetotelluric (MT) signal, and the wavelet hard and soft threshold de-noising method are the most popular although there is much room for improvement in the threshold function selection and threshold determination. A new adaptive wavelet threshold de-noising method was proposed by selecting a new threshold function and presenting an adaptive method for obtaining optimal threshold based on the multi-resolution Stein unbiased risk estimation. New threshold function and an adaptive method to determine threshold were discussed, and the principle and implementation of the algorithm were given. The simulated signal and the measured MT data contaminated by impulse interference were analyzed, and the obtained results were compared with those of the conventional wavelet hard and soft threshold de-noising methods. The results show that the proposed method overcomes the defects of the traditional wavelet soft and hard threshold due to a new threshold function, and a new method to determine the threshold of each layer is applied and provides an adaptive method for filtering MT data in the wavelet domain that requires a minimum of human intervention. The presented de-noising method is very suitable for suppressing the impulse interference for MT data and can get higher signal-to-noise ratio than the traditional wavelet threshold de-noising methods. After de-noising, the accurate data is loaded for further impedance estimation and geological interpretation.

The shrinkage function has an important effect on the image denoising results. An adaptive shrinkage function is developed in this paper to shrink the small coefficients properly for image denoising based on neighborhood characteristics. The shrinkage function is determined by the number of large coefficients near the current signal coefficients. In this way, different shrinkage functions can be adaptively used to deal with different coefficients in the process of image denoising, instead of using fixed shrinkage functions. Experimental results show that the SNR of the image processed by the adaptive shrink function algorithm is better than that processed by the soft threshold, hard threshold, and neighborhood shrink algorithm. Moreover, compared with the traditional soft threshold, hard threshold and neighborhood shrink algorithm, the PSNR of the algorithm using adaptive shrink function increases by 3.68dB, 2.28dB and 0.61dB, respectively. In addition, the proposed new algorithms, soft threshold and hard threshold, are combined with empirical Wiener filtering and shift invariant (TI) scheme to compare their image noise reduction effects. The results show that the PSNR can be improved significantly by using the adaptive shrink function algorithm combined with empirical Wiener filtering and shift invariant (TI) scheme.

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

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.