Hard Threshold Function Research Articles

Speech Enhancement Based on Student <formula formulatype="inline"><tex Notation="TeX">$t$</tex></formula> Modeling of Teager Energy Operated Perceptual Wavelet Packet Coefficients and a Custom Thresholding Function

This paper presents a speech enhancement approach, where an adaptive threshold is statistically determined based on Student $t$ Modeling of Teager energy (TE) operated perceptual wavelet packet (PWP) coefficients of noisy speech. In order to obtain an enhanced speech, the threshold thus derived is applied upon the PWP coefficients by employing a Student $t$ pdf dependent custom thresholding function, which is designed based on a combination of modified hard and semisoft thresholding functions. Extensive simulations are carried out using the NOIZEUS database to evaluate the effectiveness of the proposed method for car and multi-talker babble noise corrupted speech signals. Several standard objective measures and subjective evaluations including formal listening tests show that the proposed method outperforms some of the state-of-the-art speech enhancement methods at high as well as low levels of SNRs.

Wavelet-based hybrid thresholding method for ultrasonic liver image denoising

This paper presents a wavelet-based hybrid threshold method according to the soft- and hard-threshold functions proposed by Donoho. The wavelet-based hybrid threshold method may help doctors to know more details on the liver disease through denoising the ultrasound image of the liver. First of all, an analytical expression for the hybrid threshold function is discussed. The wavelet-based hybrid threshold method is then investigated for ultrasound image of the liver. Finally, we test the influence of this parameter on the proposed method with the real ultrasound image corrupted by speckle noise with different variances. Moreover, we compare the proposed method under the varying parameters with the soft-threshold function and the hard-threshold function. Three metrics, which are correlation coefficient, edge preservation index and structural similarity index, are measured to quantify the denoised results of ultrasound liver image. Experimental results demonstrate the potential of the proposed method for ultrasound liver image denosing.

A New Wavelet Thresholding Function Based on Hyperbolic Tangent Function

Thresholding function is an important part of the wavelet threshold denoising method, which can influence the signal denoising effect significantly. However, some defects are present in the existing methods, such as function discontinuity, fixed bias, and parameters determined by trial and error. In order to solve these problems, a new wavelet thresholding function based on hyperbolic tangent function is proposed in this paper. Firstly, the basic properties of hyperbolic tangent function are analyzed. Then, a new thresholding function with a shape parameter is presented based on hyperbolic tangent function. The continuity, monotonicity, and high-order differentiability of the new function are theoretically proven. Finally, in order to determine the final form of the new function, a shape parameter optimization strategy based on artificial fish swarm algorithm is given in this paper. Mean square error is adopted to construct the objective function, and the optimal shape parameter is achieved by iterative search. At the end of the paper, a simulation experiment is provided to verify the effectiveness of the new function. In the experiment, two benchmark signals are used as test signals. Simulation results show that the proposed function can achieve better denoising effect than the classical hard and soft thresholding functions under different signal types and noise intensities.

Noise reduction of nuclear magnetic resonance (NMR) transversal data using improved wavelet transform and exponentially weighted moving average (EWMA)

NMR logging and core NMR signals acts as an effective way of pore structure evaluation and fluid discrimination, but it is greatly contaminated by noise for samples with low magnetic resonance intensity. Transversal relaxation time (T(2)) spectrum obtained by inversion of decay signals intrigued by Carr-Purcell-Meiboom-Gill (CPMG) sequence may deviate from the truth if the signal-to-noise ratio (SNR) is imperfect. A method of combing the improved wavelet thresholding with the EWMA is proposed for noise reduction of decay data. The wavelet basis function and decomposition level are optimized in consideration of information entropy and white noise estimation firstly. Then a hybrid threshold function is developed to avoid drawbacks of hard and soft threshold functions. To achieve the best thresholding values of different levels, a nonlinear objective function based on SNR and mean square error (MSE) is constructed, transforming the problem to a task of finding optimal solutions. Particle swarm optimization (PSO) is used to ensure the stability and global convergence. EWMA is carried out to eliminate unwanted peaks and sawtooths of the wavelet denoised signal. With validations of numerical simulations and experiments, it is demonstrated that the proposed approach can reduce the noise of T(2) decay data perfectly.

The Application of the Improved Threshold Method in Wavelet Image De-Noising

The key of wavelet image threshold de-noising is the choice of the threshold function and the threshold value. To overcome the shortcomings of constant deviation existing between estimated wavelet coefficients and decomposition coefficients in the soft threshold function and discontinuity of the hard threshold function, a new threshold function based on wavelet shrinkage in image de-noising is presented in this paper. Threshold values of images with different edges and texture degrees are fine-tuned when the threshold value is set. Furthermore, a self-adaption optimal threshold which is fit to all scale levels is designed based on features of multiscale and multiresolution of wavelet transform. Simulation results show that the proposed methods are efficient to reduce the noise while preserving the detail information of the image.

A novel curvelet thresholding denoising method based on chi-squared distribution

In this paper, we first explored the advantages and disadvantages of the classical curvelet thresholding functions. To circumvent the inherent drawbacks of them, we introduced the chi-squared cumulative distribution to develop a novel thresholding function. The theoretical analysis and mathematical proofs show that the proposed thresholding function represents a compromise between soft and hard thresholding function and offers potential advantages of generally less sensitivity to small perturbations in the data over hard thresholding function and smaller bias and overall reconstruction error over soft thresholding function. Additionally, the proposed function is comparable to the semisoft thresholding function, while the latter requires two thresholds. Moreover, our proposed function can adjust flexibly between the hard and soft thresholding function through the parameter \(n\), providing a better balance between noise removal and detail preservation. Numerical experiments also demonstrate that the proposed thresholding function outperforms the three classical ones in terms of PSNR and visual quality.

An Improvement Based on Wavelet Transform Speech Denoising Threshold Function

The wavelet threshold denoising method is widely researched and used, the hard threshold and soft threshold which exist different advantages and disadvantages are two kinds commonly used threshold function; the threshold function was improved between hard threshold and soft threshold by using the exponential function. The smooth curve is monotonically increasing, no discontinuity and thus will not produce oscillation. Overcoming shortcomings that the hard threshold function and soft threshold function to be zero in wavelet coefficient is small and soft threshold exist constant deviation, and when the absolute value is greater than the threshold coefficient, soft threshold function is disposed with the same contraction method. After the simulation results prove that compared with traditional speech enhancement algorithms, the new threshold function has been improved to a certain extent.

Adaptive Wavelet Threshold Function for Fingerprint Image De-noising

Based on the characteristics of fingerprint image as well as the traditional soft and hard threshold functions for the fingerprint image de-noising, this paper puts forward a new threshold function. The result of the experiment confirms that if the parameter of the new threshold function is appropriately defined, the de-noising performance is better than those methods [1-3]. In the simulation experiment, a fitting model about the noise intensity and the decomposition level is proposed on the basis of a large number of experiment data. The model can adaptively avoid the noise. Hence the new threshold function is supposed to help to improve the efficiency of the fingerprint image de-noising and to have certain application value.

Application of an Improved Algorithm for Denoising of Wavelet Threshold in Palmprint Recognition

In the acquisition process of palmprint image, the image is often subject to interference from the outside noise.This noise will affect the future of Palmprint feature extraction. Denoising of wavelet is a common method for denoising of palmprint image. The defect of traditional soft and hard threshold functions in image denoising is analyzed. An improved threshold function is proposed on the basis of soft and hard threshold functions. The conventional hard, soft threshold functions and the improved function are used respectively in image denosing. Experiments prove that the improved wavelet threshold function is better than conventional soft, hard threshold function in denoising effect.

Method of Ultrasonic Signal De-Noising Based on Lifting Wavelet Improved Threshold

The article established the mathematical model of ultrasonic flaw echo signals. First, the basic theory of wavelet transform is introduced, the principle of the wavelet threshold de-noising method is analyzed; Then on the basis of soft and hard threshold function, the paper proposes a method based on lifting wavelet de-noising. And from two aspects of signal-to-noise ratio (SNR) and mean square error (MSE) the de-noising performance is analysed. The results show that the method improved the shortcomings of soft and hard threshold de-noising method, and got a better de-noising performance and higher signal-to-noise ratio. So in real-time signal de-noising aspect the lifting wavelet has a very good application prospect.

Application of an Improved Wavelet Threshold Denoising Method for Vibration Signal Processing

Vibration signal analysis has been widely used in the fault detection and condition monitoring of rotation machinery. But the practical signals are easily polluted by noises in their transmission process. The raw signals should be processed to reduce noise and improve the quality before further analyzing. In this paper an improved wavelet threshold denosing method for vibration signal processing is proposed. Firstly, a new threshold is developed based on the VisuShrink threshold. The effect of noise standard deviation and wavelet coefficient is retained, and the correlation of wavelet decomposition scale is considered. Then, a new threshold function is defined. The new algorithm is able to overcome the discontinuity in hard threshold denoising method and reduce the distortion caused by permanent bias of wavelet coefficient in soft threshold denoising method. At last five kinds of threshold principles and three kinds of threshold functions are compared in processing the same signal, which is simulated as the mechanical vibration signal added white noises. The results show that the improved threshold is superior to the traditional threshold principles and the new threshold function is more effective than soft and hard threshold function in improving SNR and decreasing RMSE.

The Research of a Critical Threshold Denoising Method and its Parameters Selection

For soft threshold function are likely to cause a constant deviation with the original signal, hard threshold function can not fully remove noise and the selection of semi threshold function parameters is complex, we presented a critical threshold function, and analyzed the parameter selection for the new threshold. The simulation experiments prove that the denoising of critical threshold method is much better, and it also can make up for the deficiencies of traditional threshold.

Application of Wavelet De-Noising in Non-Stationary Signal Analysis Based on the Parameter Optimization of Improved Threshold Function

Using wavelet analysis for non-stationary signal de-noising of electro-mechanical system is considered to be the best approach, and wavelet threshold de-noising method is the most simple method that needs the minimum amount of calculation. But this method in selecting threshold functions needs to be improved. Based on different domestic and foreign methods of improving threshold function, propose an improved bivariate threshold function. According to the simulation of non-stationary signal de-noising, the results show that the optimal de-noising results of different signals exist by taking different parameters. Compared with all the de-noising effects, application of the bivariate threshold function considering signal-to-noise ratio and mean square error is superior to the traditional soft and hard threshold functions. At the same time, it can significantly improve the filtering precision, and reserve the main signal details while effectively removing the noise well.

A Improved Algorithm of Wavelet Image De-Noising Based on Threshold Function

The relevant properties of the selected classical threshold function and selected threshold were compared and analyzed for the methods of noisy-image wavelet threshold de-noising. On the basis of this, a new wavelet threshold de-noising function was given in this paper. The new defined threshold function overcomes the shortcoming which the hard threshold function and the soft threshold function on higher derivatives are discontinuous by adding a variable. Theoretical analysis and experimental results show that, the constructed wavelet threshold de-noising function possess the better adaptability and de-noising effect. In the case of strong Gauss noise for the image, relatively soft threshold method, the PSNR of a new threshold de-noising method can be improved from 4dB to 6dB.

Wavelet Image Denoising Based on the New Threshold Function

A new threshold function was proposed to overcome that hard threshold function is not continuous, soft threshold function has constant deviation and derivative discontinuity defects. It will be applied to using different thresholds denoising method with different decomposition level based on the D.J global threshold. Experimental results shows that the denoising result of new threshold function is superior to the traditional soft and hard threshold function in minimum mean square error (MSE) and peak signal to noise ratio (PSNR).

The Improved Denoising Algorithms Base on Wavelet Transform for Night Image

In order to effectively improve the imaging quality of the nighttime image, An improved wavelet threshold denoising algorithms which could make up the shortage of soft and hard threshold function was researched in this paper. The denoising effect is much better when the parameter e is adjusted to a certain value. The simulation result shows that the gaussian noise in the night image is removed effectively. The Pseudo-Gibbs, Ringing effects, the lack of details and edge blur were overcome obviously.

Improvement and Simulation Analysis of Threshold Denoising Algorithm

According to the characteristics of image wavelet decomposition and statistical characteristics of high frequency wavelet coefficients after wavelet decomposition, this article improves the traditional threshold function de-noising algorithm. Improved threshold function not only overcomes wavelet coefficient discontinuity caused by hard threshold function de-noising and certain deviation witch always exists between wavelet coefficients caused by soft threshold function de-noising and its real value. The experimental results show that, the improved threshold function de-noising results are better than traditional soft and hard threshold method either in the visual effects, or the PSNR gain.

Research of an Improved Wavelet Threshold Denoising Method for Transformer Partial Discharge Signal

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.

Noisy speech enhancement based on an adaptive threshold and a modified hard thresholding function in wavelet packet domain

This paper proposes a speech enhancement approach, which statistically determines an adaptive threshold using the Teager energy operated WP coefficients of noisy speech. The obtained threshold is employed upon the WP coefficients of the noisy speech by employing a modified hard thresholding function. Extensive simulations in the presence of different noises indicate that this new method is very effective for both white noise and color noise reduction from speech, resulting in enhanced speech with better speech quality. Several standard objective measures and subjective observations show that the proposed method outperforms recent state-of-the-art thresholding based approaches from high to low level SNRs.

An Improved Wavelet Threshold Denoising Method for Transformer Partial Discharge Signal

In order to overcome the discontinuance of the hard thresholding function and the defect of slashing singularity more seriously in the soft thresholding function, and improve the denoising effect and detect the transformer partial discharge signal more accurately, this paper puts forward an improved wavelet threshold denoising method 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 the 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.