Wavelet Packet Threshold Research Articles

Application of Weak Signal Denoising Based on Improved Wavelet Threshold

In this Study, the application of wavelet threshold denoising in weak signal detection of underwater targets under complex sea conditions is discussed. Firstly, the basic principle and steps of wavelet threshold denoising method based on Mallat decomposition are analyzed. Then a new threshold function is proposed to overcome the shortcomings of traditional Donoho hard and soft thresholds. The denoising effects of wavelet and wavelet packet threshold denoising methods under hard threshold, soft threshold and new threshold functions are simulated, and the signal-to-noise ratio (SNR) and mean square error (MSE) after denoising are taken as evaluation indexes. The results show that the improved threshold denoising method outperforms the traditional threshold denoising methods.

Laser Doppler Signal Denoising Based on Wavelet Packet Thresholding Method

In laser Doppler velocimeter (LDV), calculation precision of Doppler shift is affected by noise contained in Doppler signal. In order to restrain the noise interference and improve the precision of signal processing, wavelet packet threshold denoising methods are proposed. Based on the analysis of Doppler signal, appropriate threshold function and decomposition layer number are selected. Heursure, sqtwolog, rigrsure, and minimaxi rules are adopted to get the thresholds. Processing results indicate that signal-to-noise ratio (SNR) and root mean square error (RMSE) of simulated signals with original SNR of 0 dB, 5 dB, and 10 dB in both low- and high-frequency ranges are significantly improved by wavelet packet threshold denoising. A double-beam and double-scattering LDV system is built in our laboratory. For measured signals obtained from the experimental system, the minimum relative error of denoised signal is only 0.079% (using minimaxi rule). The denoised waveforms of simulated and experimental signals are much more smooth and clear than that of original signals. Generally speaking, denoising effects of minimaxi and saqtwolog rules are better than those of heursure and rigrsure rules. As shown in the processing and analysis of simulated and experimental signals, denoising methods based on wavelet packet threshold have ability to depress the noise in laser Doppler signal and improve the precision of signal processing. Owing to its effectiveness and practicability, wavelet packet threshold denoising is a practical method for LDV signal processing.

Extraction of Partial Discharge Pulses from the Complex Noisy Signals of Power Cables Based on CEEMDAN and Wavelet Packet

While both periodic narrowband noise and white noise are significant sources of interference in the detection and localization of partial discharge (PD) signals in power cables, existing research has focused nearly exclusively on white noise suppression. This paper addresses this issue by proposing a new signal extraction method for effectively detecting random PD signals in power cables subject to complex noise environments involving both white noise and periodic narrowband noise. Firstly, the power cable signal was decomposed using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), and the periodic narrowband noise and frequency aliasing in the obtained signal components were suppressed using singular value decomposition. Then, signal components contributing significantly to the PD signal were determined according to the cross-correlation coefficient between each component and the original PD signal, and the PD signal was reconstructed solely from the obtained significant components. Finally, the wavelet packet threshold method was used to filter out residual white noise in the reconstructed PD signal. The performance of the proposed algorithm was demonstrated by its application to synthesized PD signals with complex noise environments composed of both Gaussian white noise and periodic narrowband noise. In addition, the time-varying kurtosis method was demonstrated to accurately determine the PD signal arrival time when applied to PD signals extracted by the proposed method from synthesized signals in complex noise environments with signal-to-noise ratio (SNR) values as low as −6 dB. When the SNR was reduced to −23 dB, the arrival time error of the PD signal was only one sampling point.

Block Compressive Sensing for Solder Joint Images With Wavelet Packet Thresholding

This paper provides a novel method that can achieve better results in solder joint imagery compression and reconstruction. Wavelet packet decomposition is used to generate some frequency coefficients of images. The higher and lower frequency coefficients of the reconstruction signal are used separately to improve the reconstruction performance. A threshold that only relates to the higher frequency coefficients is defined to remove the noise in the reconstruction result in each iteration. A new control factor is further defined to control the threshold value. The control factor relates to the wavelet packet low-frequency coefficients and is updated by the wavelet packet low-frequency coefficients in each iteration. The experimental results reveal that the proposed algorithm is able to improve the performance in terms of peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) compared with classical algorithms in reconstruction of different types of solder joint images. When the sample rate is increased, the proposed method improves the reconstruction results and maintains low computational cost. The proposed algorithm can retain more image structure and achieve better results than some common methods.

Noise Suppression Method of Microseismic Signal Based on Complementary Ensemble Empirical Mode Decomposition and Wavelet Packet Threshold

Aiming at the situation that complementary ensemble empirical mode decomposition (CEEMD) noise suppression method may produce redundant noise and wavelet transform easily loses high-frequency detail information, considering wavelet packet transform can be used to perform better time-frequency localization analysis on signals containing a large amount of medium and high frequency information, according to the noise and useful signal components of both the characteristic of self-correlation function is different, the CEEMD and wavelet packet threshold jointed method is proposed. The method uses the energy concentration ratio to find noise and useful signal component demarcation point to denoise the microseismic signals. Firstly, we utilize adaptively decompose the signal from high frequency to low frequency by the CEEMD; Secondly, using the self-correlation method to select the intrinsic mode function (IMF) that needs noise suppression, the wavelet suppression method is used to suppress the noise of several high-frequency components whose self-correlation coefficient is below the critical value K; Finally, the IMF component after the wavelet packet threshold noise suppression is reconstructed with the noise-free IMF component. In order to verify the effectiveness of the proposed method on the noise suppression of microseismic signal, we added a Gaussian white noise to the Ricker wavelet signal similar to the microseismic signal. The experimental results show that the signal-to-noise ratio (SNR) of the signal is raised more than 10dB. The energy percentage is higher than 92%. In practical engineering, our proposal achieves an effective noise suppression effect on the microseismic signal.

An SVM-Based Recognition Method for Safety Monitoring Signals of Oil and Gas Pipeline

An SVM-based recognition method for the safety of oil and gas pipeline was proposed due to limitation of the traditional learning methods based on empirical risk minimization. The vibration signals along the pipelines are obtained with the distributed optical fiber vibration sensor on the basis of Mach-Zehnder optical fiber interferometer theory. The wavelet packet threshold denoising is used to preprocess the signal. Then the eigenvectors of vibration signals were extracted through the energy-pattern method based on wavelet packet decomposition. At last the vibration signals were recognized by support vector machine (SVM) through the eigenvectors with a view to detecting whether abnormal events happened along the pipelines.

CT image denoising using NLM and correlation‐based wavelet packet thresholding

The impact of radiation dose is directly related to the quality of computed tomography (CT) images. Low-dose CT images are degraded with the noise and other factors. Noise reduction methods are very helpful to enhance the noisy CT images with a possibility to increase the signal-to-noise ratio (SNR) and have a scope for further reduction of radiation dose. In this study, a denoising scheme is proposed which is applicable only for two identical images with uncorrelated noise. In the proposed scheme, a non-local means (NLM) filter is used to denoise the first input image and a wavelet packet thresholding to denoise the second input image. Results of NLM filter are analysed and found excellent for noise suppression but missing the small structures of the input image. To recover that, the proposed scheme is using correlation-based wavelet packet thresholding. The final outcomes of the proposed scheme are excellent in terms of noise suppression and structure preservation. The proposed scheme is compared with existing methods and it is observed that performance of the proposed method is superior to existing methods in terms of visual quality, image quality index, peak SNR and entropy difference.

A study on Fault Diagnosis Method of Rolling Bearing Based on Wavelet Packet and Improved BP Neural Network

In this paper, rolling bearing fault diagnosis method is proposed based on wavelet packet threshold de-noising and improved BP neural network. It achieves the goal of signal de-noising by setting the appropriate threshold, and then the denoised signal is decomposed into three layers by wavelet packet. The energy characteristics of the 8 frequency bands are calculated respectively. Levenberg-Maquardt algorithm which is improved the traditional BP neural network to improve the diagnosis efficiency of BP neural network, is proposed. Taking the outer ring fault of rolling bearings as an example, the experimental results show that the wavelet packet threshold de-noising can effectively improve the signal-to-noise ratio. Compared with the traditional BP neural network, the improved BP neural network has better diagnosis efficiency.

An NMR log echo data de-noising method based on the wavelet packet threshold algorithm

To improve the de-noising effects of low signal-to-noise ratio (SNR) nuclear magnetic resonance (NMR) log echo data, this paper applies the wavelet packet threshold algorithm to the data. The principle of the algorithm is elaborated in detail. By comparing the properties of a series of wavelet packet bases and the relevance between them and the NMR log echo train signal, ‘sym7’ is found to be the optimal wavelet packet basis of the wavelet packet threshold algorithm to de-noise the NMR log echo train signal. A new method is presented to determine the optimal wavelet packet decomposition scale; this is within the scope of its maximum, using the modulus maxima and the Shannon entropy minimum standards to determine the global and local optimal wavelet packet decomposition scales, respectively. The results of applying the method to the simulated and actual NMR log echo data indicate that compared with the wavelet threshold algorithm, the wavelet packet threshold algorithm, which shows higher decomposition accuracy and better de-noising effect, is much more suitable for de-noising low SNR–NMR log echo data.

Research on Blasting Vibration Signal Denoising Based on Lifting Scheme

Considering lifting scheme and traditional wavelet packet transform principle, The optimal lifting wavelet packet threshold denoising algorithm was introduced. Experimental blasting vibration signal was decomposed by optimal lifting wavelet packet, and noise components in blasting vibration measured signals were filtered successfully. Research shows that, lifting wavelet package transform can effectively remove noise components, and it laid an important foundation for lifting algorithm will be introduced into the analysis field of blasting vibration effects and other mechanical vibration signal.

A New Adaptive Image Denoising Method Based on Neighboring Coefficients

Many good techniques have been discussed for image denoising that include NeighShrink, improved adaptive wavelet denoising method based on neighboring coefficients (IAWDMBNC), improved wavelet shrinkage technique for image denoising (IWST), local adaptive wiener filter (LAWF), wavelet packet thresholding using median and wiener filters (WPTMWF), adaptive image denoising method based on thresholding (AIDMT). These techniques are based on local statistical description of the neighboring coefficients in a window. These methods however do not give good quality of the images since they cannot modify and remove too many small wavelet coefficients simultaneously due to the threshold. In this paper, a new image denoising method is proposed that shrinks the noisy coefficients using an adaptive threshold. Our method overcomes these drawbacks and it has better performance than the NeighShrink, IAWDMBNC, IWST, LAWF, WPTMWF, and AIDMT denoising methods.

Study on Noise Reduction Using a Wavelet Packet for Ultrasonic Flaw Detection Signal of a Small Diameter Steel Pipe with a Thick Wall

Ultrasonic detection technology is an important tool that is used to ensure the safe operation of equipment. However, when carrying out ultrasonic testing, especially in the ultrasonic detection of small-diameter steel pipes with thick walls, a mass of structural noise causes the useful information to get lost. This is problematic because the quality of ultrasonic echo signals is the foundation for the pipeline flaw-identification and feature extraction. At present, the wavelet packet thresholding method is the most widely used in signal de-noising processes. In this paper, a de-noising method of a wavelet packet based on the threshold is proposed for the limitation of both soft and hard thresholds. The ultrasonic wave pipeline detection signal that is often contaminated by noise is de-noised by this method. Moreover, the contrastive analysis is performed among the wavelet packet transform based on an adjusted threshold, the original ultrasonic echo signal, and the default threshold. Experiment results show that the noise reduction effect of the wavelet packet based on the adjusted threshold is the most reasonable one, and the signal-to-noise ratio (SNR) of the signals is also improved.

Adaptive Wavelet Packet-Based De-speckling of Ultrasound Images with Bilateral Filter

A new adaptive wavelet packet-based approach to minimize speckle noise in ultrasound images is proposed. This method combines wavelet packet thresholding with a bilateral filter. Here, the best bases after wavelet packet decomposition are selected by comparing the first singular value of all sub-bands, and the noisy coefficients are thresholded using a modified NeighShrink technique. The algorithm is tested with various ultrasound images, and the results, in terms of peak signal-to-noise ratio and mean structural similarity values, are compared with those for some well-known de-speckling techniques. The simulation results indicate that the proposed method has better potential to minimize speckle noise and retain fine details of the ultrasound image.

Fault diagnosis of diesel engine based on adaptive wavelet packets and EEMD-fractal dimension

In this paper a novel method for de-noising nonstationary vibration signal and diagnosing diesel engine faults is presented. The method is based on the adaptive wavelet threshold (AWT) de-noising, ensemble empirical mode decomposition (EEMD) and correlation dimension (CD). A new adaptive wavelet packet (WP) thresholding function for vibration signal de-noising is used in this paper. To alleviate the mode mixing problem occurring in EMD, ensemble empirical mode decomposition (EEMD) is presented. With EEMD, the components with truly physical meaning can be extracted from the signal. Utilizing the advantage of EEMD, this paper proposes a new AWT–EEMD-based method for fault diagnosis of diesel engine. A study of correlation dimension in engine condition monitoring is reported also. Some important influencing factors relating directly to the computational precision of correlation dimension are discussed. Industrial engine normal and fault vibration signals measured from different operating conditions are analyzed using the above method.These techniques have integrated with our proposed adaptive wavelet threshold de-noising to form a new AWT–EEMD–CD method. The advantage of combining of EEMD and fractal dimension is that it does not require the classifiers to recognize the diesel engine fault types, also the method can solve the difficulty of recognizing fault states when two or more fractal dimensions are close to each other. To verify the effectiveness of the EEMD–CD in detecting the faults, their induced vibrations are collected from a series of generators under normal and faulty engine conditions after de-noising. The results show that this method is capable of extracting the impact signal features induced by vibrations and is able to determine their types of fault accurately even when the impacts have been overwhelmed by other unrelated vibration signals.

An intelligent approach for engine fault diagnosis based on Hilbert–Huang transform and support vector machine

Based on the techniques of Hilbert–Huang transform (HHT) and support vector machine (SVM), a noise-based intelligent method for engine fault diagnosis (EFD), so-called HHT–SVM model, is developed in this paper. The noises of a sample engine under normal and several fault states are first measured and denoised by using the wavelet packet threshold method to initially lower the noise level with negligible signal distortion. To extract fault features of the engine, then, the HHT is selected and applied to the measured noise signals. A nine-dimensional vector, which consists of seven intrinsic mode functions (IMFs) from the empirical mode decomposition (EMD), maximum value of HHT marginal spectrum and its corresponding frequency component, is specified to represent each engine fault feature. Finally, an optimal SVM model is established and trained for engine failure classification by using the fault feature vectors of the noise signals. Cross-validation results show that the proposed noise-based HHT–SVM method is accurate and effective for engine fault diagnosis. Due to outstanding time–frequency characteristics and pattern recognition capacity of the HHT and SVM, the newly proposed HHT–SVM can be used to deal with both the stationary and nonstationary signals, and even the transient ones. In the view of applications, the HHT–SVM technique may be suggested not only to detect the abnormal states of vehicle engines, but also to be extended to other fields for failure diagnosis in engineering.

Enhancement of Non-Air Conducted Speech Based on Wavelet-Packet Adaptive Threshold

This study developed a new kind of speech detecting method by using millimeter wave. Because of the advantage of the millimeter wave, this speech detecting method has great potential application and may provide some exciting possibility for wide applications. However, the MMW conduct speech is in less intelligible and poor audibility since it is corrupted by additive combined noise. This paper, therefore, also developed an algorithm of wavelet packet threshold by using hard threshold and soft threshold for removing noise based on the good capability of wavelet packet for analyzing time-frequency signal. Comparing to traditional speech enhancement algorithm, the results from both simulation and listening evaluation suggest that the proposed algorithm takes on a better performance on noise removing while the distortion of MMW radar speech remains acceptable, the enhanced speech also sounds more pleasant to human listeners, resulting in improved results over classical speech enhancement algorithms. DOI: http://dx.doi.org/10.11591/telkomnika.v11i1.1879

A Non-Contact Speech Enhancement Algorithm Based on Wavelet Packet Adaptive Threshold

Speech is an important method for human communication. In this paper, we developed a new method for detecting speech signal. Because of the advantage of this speech detecting method, it has great potential application value in many fields. Simultaneously, basing on the good capability of wavelet packet for analyzing time-frequency signal, this paper also developed an algorithm of wavelet packet threshold by using hard threshold and soft threshold for removing noise. Comparing to spectral subtraction and Wiener filter speech enhancement algorithm, the proposed algorithm takes on a better performance on noise removing and speech signal reserving.

Efficient Image Denoising Method Based on a New Adaptive Wavelet Packet Thresholding Function

This paper proposes a statistically optimum adaptive wavelet packet (WP) thresholding function for image denoising based on the generalized Gaussian distribution. It applies computationally efficient multilevel WP decomposition to noisy images to obtain the best tree or optimal wavelet basis, utilizing Shannon entropy. It selects an adaptive threshold value which is level and subband dependent based on analyzing the statistical parameters of subband coefficients. In the utilized thresholding function, which is based on a maximum a posteriori estimate, the modified version of dominant coefficients was estimated by optimal linear interpolation between each coefficient and the mean value of the corresponding subband. Experimental results, on several test images under different noise intensity conditions, show that the proposed algorithm, called OLI-Shrink, yields better peak signal noise ratio and superior visual image quality-measured by universal image quality index-compared to standard denoising methods, especially in the presence of high noise intensity. It also outperforms some of the best state-of-the-art wavelet-based denoising techniques.

Study on Method of Magnetic Flux Leakage Signals De-Noising for Cracks of Bar

During bars manufacturing and using process, the use of bars with cracks influenced the service life and sustainable work, on the premise of certain detection system, the choose of signal de-noising method plays an important part in magnetic flux leakage testing process, for which determining the global performance of testing equipment. This paper studies on magnetic flux leakage signals characteristic of cracks on the bar, analyzed the advantages and disadvantages of wavelet analysis and wavelet packet threshold de-noising, and on this basis, in order to give consideration to both the low and high frequency interference signal removing, adopted an integration method that combines wavelet packet threshold de-noising, wavelet packet decomposition and wavelet reconstruction, which greatly improved signal processing results.

Research of Wavelet Packet Analysis in the De-Noising of Ultrasonic Echo Signal

The quality of ultrasonic flaw echo signal is the foundation of achieving qualitative and quantitative analysis in the in ultrasonic flaw detection. In practice, the flaw echo signals are often contaminated or even annihilation by random noise. According to the characteristics of ultrasonic flaw echo signal, wavelet packet has more accurate local analysis ability in low frequency and high frequency part. This paper discusses de-noising in ultrasonic signals based on wavelet packet analysis, and proposes an improved threshold approach for de-noising. The results show that: It remarkably raises the signal-to-noise ratio of ultrasonic flaw echo signal and improves the quality of signal with improved wavelet packet threshold.