A New Wavelet Threshold Function and Denoising Application

Lu, Jingyi; Lin, Hong; Ye, Dong; Zhang, Yansheng

doi:10.1155/2016/3195492

Cited by 95 publications

(37 citation statements)

References 11 publications

(12 reference statements)

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“…Thus, it can be concluded that Ψ Ψ is always positive semidefinite. Positive semidefinite property guarantees that MSE(X, ) is convex while invertible of Ψ Ψ makes the optimal solution of a in the form of (10), (12) and (29), (33). It must be full rank to ensure invertible Ψ Ψ, so we can deduce that Ψ must be full row or column rank because of rank(Ψ) = rank(Ψ Ψ).…”

Section: Optimal Solution Guaranteementioning

confidence: 99%

“…In addition, the more important drawback is that soft and hard threshold functions do not have continuous derivatives. Various improvements had been proposed by exploring new threshold functions [1,[10][11][12][13][14][15][16][17], but the nonnegative garrotelike functions [10][11][12][13][14] are still not differentiable. Zhang [1,15], Nasri and Nezamabadi-pour [16], and Wu et al [17], respectively, proposed a series of threshold functions with adjustable parameters.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Supervised and Unsupervised Subband Adaptive Denoising Frameworks with Polynomial Threshold Function

Gong¹,

Yang²,

Wang³

et al. 2017

Mathematical Problems in Engineering

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Unlike inflexible structure of soft and hard threshold function, a unified linear matrix form with flexible structure for threshold function is proposed. Based on the unified linear flexible structure threshold function, both supervised and unsupervised subband adaptive denoising frameworks are established. To determine flexible coefficients, a direct mean-square error (MSE) minimization is conducted in supervised denoising while Stein’s unbiased risk estimate as a MSE estimate is minimized in unsupervised denoising. The SURE rule requires no hypotheses or a priori knowledge about clean signals. Furthermore, we discuss conditions to obtain optimal coefficients for both supervised and unsupervised subband adaptive denoising frameworks. Applying an Odd-Term Reserving Polynomial (OTRP) function as concrete threshold function, simulations for polynomial order, denoising performance, and noise effect are conducted. Proper polynomial order and noise effect are analyzed. Both proposed methods are compared with soft and hard based denoising technologies—VisuShrink, SureShrink, MiniMaxShrink, and BayesShrink—in denoising performance simulation. Results show that the proposed approaches perform better in both MSE and signal-to-noise ratio (SNR) sense.

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Section: Optimal Solution Guaranteementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Supervised and Unsupervised Subband Adaptive Denoising Frameworks with Polynomial Threshold Function

Gong¹,

Yang²,

Wang³

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…(4) Thresholding Function. The basis thresholding functions are soft and hard thresholding functions [18]; the soft thresholding function is as follows:…”

Section: Key Factors Of Wavelet Threshold Denoising Methodmentioning

confidence: 99%

Wavelet Denoising of Vehicle Platform Vibration Signal Based on Threshold Neural Network

Li¹,

Wang²,

Luo³

et al. 2017

Shock and Vibration

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Vehicle Platform Vibration Signal (VPVS) denoising is essential to achieve high measurement accuracy of precise optical measuring instrument (POMI). A method to denoise the VPVS is proposed based on the wavelet coefficients thresholding and threshold neural network (TNN). According to the characteristics of VPVS, a novel thresholding function is constructed, and then its optimized threshold is selected through unsupervised learning of TNN. The original VPVS mixed in trend and random noise is constructed as VPVS model. A VPVS denoising flow is proposed based on the power spectral and energy distribution of the VPVS model. The simulation shows that the proposed denoising method achieves better results, compared to the previous denoising methods using the indexes of SNR and RMSE. The experiment demonstrates that it is efficient for denoising VPVS polluted by the trend and random noise.

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“…In addition, it can be integrated with other smoothing methods to improve the denoising outputs of sensors' measurements [31,32]. The energy of wavelet decompositions is the main parameter for signal denoising [33,34]. The analyzed signal can be decomposed into high and low wavelet energy components according to the oscillatory behavior of the signal components.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Wavelet and Principal Component Analyses Approach for Extracting Dynamic Motion Characteristics from Displacement Series Derived from Multipath-Affected High-Rate GNSS Observations

et al. 2019

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Nowadays, the high rate GNSS (Global Navigation Satellite Systems) positioning methods are widely used as a complementary tool to other geotechnical sensors, such as accelerometers, seismometers, and inertial measurement units (IMU), to evaluate dynamic displacement responses of engineering structures. However, the most common problem in structural health monitoring (SHM) using GNSS is the presence of surrounding structures that cause multipath errors in GNSS observations. Skyscrapers and high-rise buildings in metropolitan cities are generally close to each other, and long-span bridges have towers, main cable, and suspender cables. Therefore, multipath error in GNSS observations, which is typically added to the measurement noise, is inevitable while monitoring such flexible engineering structures. Unlike other errors like atmospheric errors, which are mostly reduced or modeled out, multipath errors are the largest remaining unmanaged error sources. The high noise levels of high-rate GNSS solutions limit their structural monitoring application for detecting load-induced semi-static and dynamic displacements. This study investigates the estimation of accurate dynamic characteristics (frequency and amplitude) of structural or seismic motions derived from multipath-affected high-rate GNSS observations. To this end, a novel hybrid model using both wavelet-based multiscale principal component analysis (MSPCA) and wavelet transform (MSPCAW) is designed to extract the amplitude and frequency of both GNSS relative- and PPP- (Precise Point Positioning) derived displacement motions. To evaluate the method, a shaking table with a GNSS receiver attached to it, collecting 10 Hz data, was set up close to a building. The table was used to generate various amplitudes and frequencies of harmonic motions. In addition, 50-Hz linear variable differential transformer (LVDT) observations were collected to verify the MSMPCAW model by comparing their results. The results showed that the MSPCAW could be efficiently used to extract the dynamic characteristics of noisy dynamic movements under seismic loads. Furthermore, the dynamic behavior of seismic motions can be extracted accurately using GNSS-PPP, and its dominant frequency equals that extracted by LVDT and relative GNSS positioning method. Its accuracy in determining the amplitude approaches 91.5% relative to the LVDT observations.

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A New Wavelet Threshold Function and Denoising Application

Cited by 95 publications

References 11 publications

Supervised and Unsupervised Subband Adaptive Denoising Frameworks with Polynomial Threshold Function

Supervised and Unsupervised Subband Adaptive Denoising Frameworks with Polynomial Threshold Function

Wavelet Denoising of Vehicle Platform Vibration Signal Based on Threshold Neural Network

Hybrid Wavelet and Principal Component Analyses Approach for Extracting Dynamic Motion Characteristics from Displacement Series Derived from Multipath-Affected High-Rate GNSS Observations

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