soft thresholding
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Sensors ◽  
2021 ◽  
Vol 21 (23) ◽  
pp. 7973
Author(s):  
Shengli Zhang ◽  
Jifei Pan ◽  
Zhenzhong Han ◽  
Linqing Guo

Signal features can be obscured in noisy environments, resulting in low accuracy of radar emitter signal recognition based on traditional methods. To improve the ability of learning features from noisy signals, a new radar emitter signal recognition method based on one-dimensional (1D) deep residual shrinkage network (DRSN) is proposed, which offers the following advantages: (i) Unimportant features are eliminated using the soft thresholding function, and the thresholds are automatically set based on the attention mechanism; (ii) without any professional knowledge of signal processing or dimension conversion of data, the 1D DRSN can automatically learn the features characterizing the signal directly from the 1D data and achieve a high recognition rate for noisy signals. The effectiveness of the 1D DRSN was experimentally verified under different types of noise. In addition, comparison with other deep learning methods revealed the superior performance of the DRSN. Last, the mechanism of eliminating redundant features using the soft thresholding function was analyzed.


Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5271
Author(s):  
Kang Peng ◽  
Hongyang Guo ◽  
Xueyi Shang

Signal denoising is one of the most important issues in signal processing, and various techniques have been proposed to address this issue. A combined method involving wavelet decomposition and multiscale principal component analysis (MSPCA) has been proposed and exhibits a strong signal denoising performance. This technique takes advantage of several signals that have similar noises to conduct denoising; however, noises are usually quite different between signals, and wavelet decomposition has limited adaptive decomposition abilities for complex signals. To address this issue, we propose a signal denoising method based on ensemble empirical mode decomposition (EEMD) and MSPCA. The proposed method can conduct MSPCA-based denoising for a single signal compared with the former MSPCA-based denoising methods. The main steps of the proposed denoising method are as follows: First, EEMD is used for adaptive decomposition of a signal, and the variance contribution rate is selected to remove components with high-frequency noises. Subsequently, the Hankel matrix is constructed on each component to obtain a higher order matrix, and the main score and load vectors of the PCA are adopted to denoise the Hankel matrix. Next, the PCA-denoised component is denoised using soft thresholding. Finally, the stacking of PCA- and soft thresholding-denoised components is treated as the final denoised signal. Synthetic tests demonstrate that the EEMD-MSPCA-based method can provide good signal denoising results and is superior to the low-pass filter, wavelet reconstruction, EEMD reconstruction, Hankel–SVD, EEMD-Hankel–SVD, and wavelet-MSPCA-based denoising methods. Moreover, the proposed method in combination with the AIC picking method shows good prospects for processing microseismic waves.


2021 ◽  
Author(s):  
Amroabadi S. Hashemi

In this thesis, we develop various methods for the purpose of data denoising. We propose a method for Mean Square Error (MSE) estimation in Soft Thresholding. The MSE estimator is based on Minimum Noiseless Data Length (MNDL). Our simulation results show that this MSE estimate is a valuable comparison measure for different soft thresholding methods. Two denoising methods are proposed for analog domain: Mean Square Error EstiMation (MSEEM) which minimizes the worst case MSE estimate, and Noise Invalidation Denoising (NIDe) method which is based on the newly prosposed idea of noise signature. While MSEEM shown to be the optimum denoising method for non-sparse signals, NIDe approach outperforms the other well known denoising methods in presence of colored noise. In digital domain we address two interesting problems: 1) simultaneous denoising and quantization method, 2) denoising a digital signal in digital domain. For problem one, we propose a new method that generalizes the idea of dead zone estimation to a multi-level noise removal. An example of this method is shown for hyperspectral image denoising and compression. A digital domain denoising approach pioneers in answering the second problem with only one prior knowledge on the desired signal, that it is digital. The method provides the optimum reconstruction levels in the MSE sense. One of the critical steps of denoising process is the noise variance estimation. As a part of this thesis, we propose a novel noise variance estimation method for BayesShrink that outperforms conventional MAD-based noise variance estimation. Although BayesShrink is one of the most efficient denoising methods, no analytical analysis is available for it. Here, we study Bayes estimators for General Gaussian Distribued (GGD) data and provide the theoretical justification for BayesShrink. This study enables us to generalize the BayesShrink threshold to Generalized BayesShrink which outperforms the BayesShrink itself.


2021 ◽  
Author(s):  
Nima Nikvand

In this thesis, the problem of data denoising is studied, and two new denoising approaches are proposed. Using statistical properties of the additive noise, the methods provide adaptive data-dependent soft thresholding techniques to remove the additive noise. The proposed methods, Point-wise Noise Invlaidating Soft Thresholding (PNIST) and Accumulative Noise Invalidation Soft Thresholding (ANIST), are based on Noise Invalidation. The invalidation exploits basic properties of the additive noise in order to remove the noise effects as much as possible. There are similarities and differences between ANIST and PNIST. While PNIST performs better in the case of additive white Gaussian noise, ANIST can be used with both Gaussian and non Gaussian additive noise. As part of a data denoising technique, a new noise variance estimation is also proposed. The thresholds proposed by NIST approaches are comparable to the shrinkage methods, and our simulation results promise that the new methods can outperform the existing approaches in various applications. We also explore the area of image denoising as one of the main applications of data denoising and extend the proposed approaches to two dimensional applications. Simulations show that the proposed methods outperform common shrinkage methods and are comparable to the famous BayesShrink method in terms of Mean Square Error and visual quality.


2021 ◽  
Author(s):  
Amroabadi S. Hashemi

In this thesis, we develop various methods for the purpose of data denoising. We propose a method for Mean Square Error (MSE) estimation in Soft Thresholding. The MSE estimator is based on Minimum Noiseless Data Length (MNDL). Our simulation results show that this MSE estimate is a valuable comparison measure for different soft thresholding methods. Two denoising methods are proposed for analog domain: Mean Square Error EstiMation (MSEEM) which minimizes the worst case MSE estimate, and Noise Invalidation Denoising (NIDe) method which is based on the newly prosposed idea of noise signature. While MSEEM shown to be the optimum denoising method for non-sparse signals, NIDe approach outperforms the other well known denoising methods in presence of colored noise. In digital domain we address two interesting problems: 1) simultaneous denoising and quantization method, 2) denoising a digital signal in digital domain. For problem one, we propose a new method that generalizes the idea of dead zone estimation to a multi-level noise removal. An example of this method is shown for hyperspectral image denoising and compression. A digital domain denoising approach pioneers in answering the second problem with only one prior knowledge on the desired signal, that it is digital. The method provides the optimum reconstruction levels in the MSE sense. One of the critical steps of denoising process is the noise variance estimation. As a part of this thesis, we propose a novel noise variance estimation method for BayesShrink that outperforms conventional MAD-based noise variance estimation. Although BayesShrink is one of the most efficient denoising methods, no analytical analysis is available for it. Here, we study Bayes estimators for General Gaussian Distribued (GGD) data and provide the theoretical justification for BayesShrink. This study enables us to generalize the BayesShrink threshold to Generalized BayesShrink which outperforms the BayesShrink itself.


2021 ◽  
Author(s):  
Nima Nikvand

In this thesis, the problem of data denoising is studied, and two new denoising approaches are proposed. Using statistical properties of the additive noise, the methods provide adaptive data-dependent soft thresholding techniques to remove the additive noise. The proposed methods, Point-wise Noise Invlaidating Soft Thresholding (PNIST) and Accumulative Noise Invalidation Soft Thresholding (ANIST), are based on Noise Invalidation. The invalidation exploits basic properties of the additive noise in order to remove the noise effects as much as possible. There are similarities and differences between ANIST and PNIST. While PNIST performs better in the case of additive white Gaussian noise, ANIST can be used with both Gaussian and non Gaussian additive noise. As part of a data denoising technique, a new noise variance estimation is also proposed. The thresholds proposed by NIST approaches are comparable to the shrinkage methods, and our simulation results promise that the new methods can outperform the existing approaches in various applications. We also explore the area of image denoising as one of the main applications of data denoising and extend the proposed approaches to two dimensional applications. Simulations show that the proposed methods outperform common shrinkage methods and are comparable to the famous BayesShrink method in terms of Mean Square Error and visual quality.


2021 ◽  
Vol 69 ◽  
pp. 101987
Author(s):  
Xinlin Zhang ◽  
Hengfa Lu ◽  
Di Guo ◽  
Lijun Bao ◽  
Feng Huang ◽  
...  

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