Performance Evaluation of Wavelet De-Noising Schemes for Suppression of Power Line Noise in Electrocardiogram Signals

Power line noise introduces distortions to recorded electrocardiogram (ECG) signals. These distortions compromise the integrity and negatively affect the interpretation of the ECG signals. Despite the fact that the amplifiers used in biomedical signal processing have high common mode rejection ratio (CMRR), ECG recordings are still often corrupted with residual Power Line Interference (PLI) noise. Further improvement in the hardware solutions do not have significant achievements in PLI noise suppression but rather introduce other adverse effects. Software approach is necessary to refine ECG data. Evaluation of PLI noise suppression in ECG signal in the wavelet domain is presented. The performance of the Hard Threshold Shrinkage Function (HTSF), the Soft Threshold Shrinkage Function (STSF), the Hyperbola Threshold Shrinkage Function (HYTSF), the Garrote Threshold Shrinkage Function (GTSF), and the Modified Garrote Threshold Shrinkage Function (MGTSF) for the suppression of PLI noise are evaluated and compared with the aid of an algorithm. The optimum tuning constant for the Modified Garrote Threshold Shrinkage Function (MGTSF) is found to be 1.18 for PLI noise. GTSF is found to have best performance closely followed by MGTSF in term of filtering Gain. HTSF recorded the lowest Gain. Filtering against PLI noise in the wavelet domain preserves the key features of the signal such as the QRS complex.

Rolling Bearing Fault Diagnosis Using Improved Deep Residual Shrinkage Networks

To improve feature learning ability and accurately diagnose the faults of rolling bearings under a strong background noise environment, we present a new shrinkage function named leaky thresholding to replace the soft thresholding in the deep residual shrinkage networks (DRSNs). In this work, we discover that such improved deep residual shrinkage networks (IDRSNs) can be realized by using a group searching method to optimize the slope value of leaky thresholding, and leaky thresholding in the IDRSNs can more effectively eliminate the noise of signal features. We highlight that our techniques can significantly improve the performance on various fundamental tasks. Experimental results show that IDRSNs achieve better fault diagnosis results on noised vibration signals compared with DRSNs. Moreover, we also provide a normalized processing to further improve the fault diagnosing accuracy of rolling bearing under a strong background noise environment.

A New Method of Measurement Matrix Optimization for Compressed Sensing Based on Alternating Minimization

In this paper, a new method of measurement matrix optimization for compressed sensing based on alternating minimization is introduced. The optimal measurement matrix is formulated in terms of minimizing the Frobenius norm of the difference between the Gram matrix of sensing matrix and the target one. The method considers the simultaneous minimization of the mutual coherence indexes including maximum mutual coherence μmax, t-averaged mutual coherence μave and global mutual coherence μall, and solves the problem that minimizing a single index usually results in the deterioration of the others. Firstly, the threshold of the shrinkage function is raised to be higher than the Welch bound and the relaxed Equiangular Tight Frame obtained by applying the new function to the Gram matrix is taken as the initial target Gram matrix, which reduces μave and solves the problem that μmax would be larger caused by the lower threshold in the known shrinkage function. Then a new target Gram matrix is obtained by sequentially applying rank reduction and eigenvalue averaging to the initial one, leading to lower. The analytical solutions of measurement matrix are derived by SVD and an alternating scheme is adopted in the method. Simulation results show that the proposed method simultaneously reduces the above three indexes and outperforms the known algorithms in terms of reconstruction performance.

Image Denoising Based on Bivariate Distribution

The literature has shown that the performance of the de-noising algorithm was greatly influenced by the dependencies between wavelet coefficients. In this paper, the bivariate probability density function (PDF) was proposed which was symmetric, and the dependencies between the coefficients were considered. The bivariate Cauchy distribution and the bivariate Student’s distribution are special cases of the proposed bivariate PDF. One of the parameters in the probability density function gave the estimation method, and the other parameter can take any real number greater than 2. The algorithm adopted a maximum a posteriori estimator employing the dual-tree complex wavelet transform (DTCWT). Compared with the existing best results, the method is faster and more efficient than the previous numerical integration techniques. The bivariate shrinkage function of the proposed algorithm can be expressed explicitly. The proposed method is simple to implement.

Analytical and Simple Form of Shrinkage Functions for Non-Convex Penalty Functions in Fused Lasso Algorithm

In some circumstances, the performance of machine learning (ML) tasks are based on the quality of signal (data) that is processed in these tasks. Therefore, the pre-processing techniques, such as reconstruction and denoising methods, are important techniques in ML tasks. In reconstructed (estimated) method, the fused lasso algorithm with non-convex penalty function is an efficient method when the signal corrupted by additive white Gaussian noise (AWGN) is considered. Therefore, this paper proposes new shrinkage functions for non-convex penalty functions, modified arctangent and exponential models, in fused lasso formulation. A lot of works present the shrinkage function for arctangent penalty function. Unfortunately, there is no closed-form solution. The numerical solution is required for shrinkage function of this penalty function. However, the analytical solution is derived in this paper. Moreover, the shrinkage function of modified exponential penalty function is proposed. This shrinkage function obtains from simple iterative method, fixed-point algorithm. We demonstrate the proposed methods through simulations with standard one-dimensional signals contaminated by AWGN. The proposed techniques are compared with traditional estimation methods, such as total variation (TV) and wavelet denoising methods. In experimental results, our proposed methods outperform several exiting methods both visual quality and in terms of root mean square error (RMSE). In fact, the proposed methods can better preserve the feature of noise-free signal than the compared methods. The denoised signals produced by the proposed methods are less smooth than the denoised signals produced by the compared methods.

Despeckling method of ultrasound images using closed-form shrinkage function based on cauchy distribution in wavelet domain

Speckle suppression and elimination are very important to improve the visual quality of ultrasound image and the diagnostic ability of the diseases. An effective technique of image denoising based on discrete wavelet transform is to employ a Bayesian maximum a posteriori (MAP) estimator. To suppress and remove the speckle noise using MAP estimator effectively, it must assign correctly the shrinkage function based on appropriate probability density functions (PDFs) for the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise. In this paper, we introduce a new closed-form shrinkage function that is an analytical solution of a Bayesian MAP estimator for despeckling of the ultrasound images effectively in wavelet domain. We employ a Cauchy prior and Gaussian PDF to model the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise, respectively. Firstly, we derive the CauchyShrinkGMAP that is a closed-form shrinkage function. In addition, we estimate the noise variance and parameter of MAP estimator. Next, we evaluate the despeckling performance of wavelet image denoising method using the CauchyShrinkGMAP compared to various despeckling method using median and Wiener filters, hard and soft thresholding and GaussShrinkGMAP and MCMAP3N shrinkage function. The experiment results show that PSNR of new closed-form shrinkage function is highest, MSE is smallest, and the correlation coefficient ([Formula: see text]) and SSIM are closer to one than the other existing image denoising methods for noisy synthetic ultrasound images at different speckle noise levels. Also, experiment results show that ENL of new closed-form shrinkage function is highest and that of EN and SD is smallest than the other existing image denoising methods for noisy real ultrasound image.

Multi-scales Image Denoising Method Based on Joint Confidence Probability of Coefficients

Background: It is a classic problem that we estimate the original coefficient from the known coefficient disturbed with noise. Methods: This paper proposes an image denoising method which combines the dual-tree complex wavelet with good direction selection and translation invariance. Firstly, we determine the expression of probability density function through estimating the parameters by the variance and the fourth-order moment. Secondly, we propose two assumptions and calculate the joint confidence probability of original coefficient under the situation that the disturbed parental and present coefficients from neighborhood scale are known. Finally, we set the joint confidence probability as shrinkage function of coefficient for implementing the image denoising. Results: The simulation experiment results show that, compared to these traditional methods, this new method can reserve more detail information. Conclusion: Compared to the current methods, our novel algorithm can remove the most noise and reserve the detail texture in denoising results, which can make better visualization. In addition, our algorithm also shows advantage in PSNR.