A Novel Adaptive Wavelet Thresholding with Identical Correlation Shrinkage Function for ECG Noise Removal

EOG artifact removal using a wavelet neural network

The shrinkage function has an important effect on the image denoising results. An adaptive shrinkage function is developed in this paper to shrink the small coefficients properly for image denoising based on neighborhood characteristics. The shrinkage function is determined by the number of large coefficients near the current signal coefficients. In this way, different shrinkage functions can be adaptively used to deal with different coefficients in the process of image denoising, instead of using fixed shrinkage functions. Experimental results show that the SNR of the image processed by the adaptive shrink function algorithm is better than that processed by the soft threshold, hard threshold, and neighborhood shrink algorithm. Moreover, compared with the traditional soft threshold, hard threshold and neighborhood shrink algorithm, the PSNR of the algorithm using adaptive shrink function increases by 3.68dB, 2.28dB and 0.61dB, respectively. In addition, the proposed new algorithms, soft threshold and hard threshold, are combined with empirical Wiener filtering and shift invariant (TI) scheme to compare their image noise reduction effects. The results show that the PSNR can be improved significantly by using the adaptive shrink function algorithm combined with empirical Wiener filtering and shift invariant (TI) scheme.

Partial Discharge (PD) signal measurement is very significant tool in analyzing condition of the electrical insulation. The PD information is lost in the presence of various noises. The wavelet transform (WT) based denoising provides a better platform for pre and post processing of PD signal. The wavelet adaptive Thresholding de-noising techniques are well suited for reducing the noise. This paper adopts the various adaptive thresholding techniques such as VisuShrink, SureShrink, combination of the two called Heursure, minimax thresholding and BayesShrink, which are broadly classified as Global and Local thresholding methods. The algorithm presents the comparative analysis for the selection of optimal mother wavelet. Once the optimal mother wavelet is chosen, selection of the best thresholding rule is identified by comparing the values of signal to noise ratio (SNR), mean square error (MSE) and Peak Signal to Noise ratio (PSNR) of all the techniques. The algorithm also presents the comparison between Hard and Soft thresholding. It is shown that the soft thresholding is best suited to remove the noise compared to hard thresholding. The simulated Damped Exponential Pulse (DEP) and Damped Oscillatory Pulse (DOP) has been used. Three sets of PD data are considered to check the performance of the algorithm.

In this article, we developed and analyzed a thresholding method in which soft thresholding estimators are independently expanded by empirical scaling values. The scaling values have a common hyper-parameter that is an order of expansion of an ideal scaling value that achieves hard thresholding. We simply call this estimator a scaled soft thresholding estimator. The scaled soft thresholding is a general method that includes the soft thresholding and non-negative garrote as special cases and gives an another derivation of adaptive LASSO. We then derived the degree of freedom of the scaled soft thresholding by means of the Stein's unbiased risk estimate and found that it is decomposed into the degree of freedom of soft thresholding and the reminder connecting to hard thresholding. In this meaning, the scaled soft thresholding gives a natural bridge between soft and hard thresholding methods. Since the degree of freedom represents the degree of over-fitting, this result implies that there are two sources of over-fitting in the scaled soft thresholding. The first source originated from soft thresholding is determined by the number of un-removed coefficients and is a natural measure of the degree of over-fitting. We analyzed the second source in a particular case of the scaled soft thresholding by referring a known result for hard thresholding. We then found that, in a sparse, large sample and non-parametric setting, the second source is largely determined by coefficient estimates whose true values are zeros and has an influence on over-fitting when threshold levels are around noise levels in those coefficient estimates. In a simple numerical example, these theoretical implications has well explained the behavior of the degree of freedom. Moreover, based on the results here and some known facts, we explained the behaviors of risks of soft, hard and scaled soft thresholding methods.

An adaptive level dependent wavelet thresholding for ECG denoising

Wavelet denoising techniques with applications to experimental geophysical data

The aim of this study was to investigate the application of wavelet denoising in noise reduction for multifunction myoelectric control system. Six upper limb motions including hand open, hand close, wrist extension, wrist flexion, pronation, and supination. For each motion, two channels of electrodes were applied. A comparative study of four classical denoising algorithms including universal thresholding, SURE thresholding, hybrid thresholding, and minimax thresholding have been used to remove white Gaussian noise at various signal-to-noise ratios (SNRs) from EMG signals. Applications of soft and hard thresholding as well as threshold rescaling methods were considered and the whole procedures of noise reduction were applied with different wavelet functions and different decomposition levels. Evaluations of the performance of noise reduction are determined using mean squared error (MSE). The results show that Daubechies wavelet with second orders (db2) provides marginally better performance than other possibilities. Suitable number of decomposition levels is four. Universal and soft thresholding is the best of wavelet denoising algorithms from eight possible denoising processes under investigation. In addition, the threshold using a level-dependent estimation of level noise showed better than others.

Synthetic Aperture Radar (SAR) is a coherent microwave imaging method used for mapping scattering properties of Earth's surface. Speckle is a granular disturbance, modeled as a multiplicative noise, that affects all types of coherent images. Most of the applications demand speckle reduction to be carried out in real-time and require computationally simple and efficient techniques. The paper presents a combination of spatial and frequency domain techniques for removing speckle noise. The algorithm uses a Wiener filter as a preprocessing stage in the spatial domain and adaptive soft thresholding of Wavelet transform coefficients in the frequency domain. Considering multiplicative model for speckle noise, logarithmic transform is applied to Wiener filtered image. Threshold value at each decomposition level and subband is computed from the corresponding standard deviation. Simulation results show that the proposed method is efficient in removing speckle noise compared to an existing algorithm. The results are quantitatively analysed using Peak Signal-to-Noise Ratio (PSNR) and Structural SIMilarity (SSIM) metrics.

Wavelet threshold denoising can easily cause edge blur, while total variational denoising is insufficient to achieve image smooth area denoising. Therefore, this paper proposes a new denoising method combining the total variational model and the adaptive wavelet threshold. Firstly, the original noisy image is processed by the total variational model, the improved Prewitt operator is used to extract the edge of the processed image, and the edge denoising image is obtained. Then, the original noisy image is divided into edge and non-edge images by the improved Prewitt operator, and the non-edge image is de-noised by the adaptive wavelet threshold method to obtain the non-edge denoising image. Finally, after denoising, the edge image and non-edge image are superimposed to achieve high-definition restoration of medical images. Experimental results show that the proposed method can effectively denoise medical images and preserve the original edges and details in the images.KeywordsImage denoisingTotal variational modelPrewitt operatorWavelet transform

Wavelet de-noising method is often used in the processing of magnetotelluric (MT) signal, and the wavelet hard and soft threshold de-noising method are the most popular although there is much room for improvement in the threshold function selection and threshold determination. A new adaptive wavelet threshold de-noising method was proposed by selecting a new threshold function and presenting an adaptive method for obtaining optimal threshold based on the multi-resolution Stein unbiased risk estimation. New threshold function and an adaptive method to determine threshold were discussed, and the principle and implementation of the algorithm were given. The simulated signal and the measured MT data contaminated by impulse interference were analyzed, and the obtained results were compared with those of the conventional wavelet hard and soft threshold de-noising methods. The results show that the proposed method overcomes the defects of the traditional wavelet soft and hard threshold due to a new threshold function, and a new method to determine the threshold of each layer is applied and provides an adaptive method for filtering MT data in the wavelet domain that requires a minimum of human intervention. The presented de-noising method is very suitable for suppressing the impulse interference for MT data and can get higher signal-to-noise ratio than the traditional wavelet threshold de-noising methods. After de-noising, the accurate data is loaded for further impedance estimation and geological interpretation.

The method of wavelet thresholding for removing noise, or denoising, has been researched extensively due to its effectiveness and simplicity. Much of the work has been concentrated on finding the best uniform threshold or best basis. However, not much has been done to make this method adaptive to spatially changing statistics which is typical of a large class of images. This work proposes a spatially adaptive wavelet thresholding method based on context modeling, a common technique used in image compression to adapt the coder to the non-stationarity of images. We model each coefficient as a random variable with the generalized Gaussian prior with unknown parameters. Context modeling is used to estimate the parameters for each coefficient, which are then used to adapt the thresholding strategy. Experimental results show that spatially adaptive wavelet thresholding yields significantly superior image quality and lower MSE than optimal uniform thresholding.

Block matching 3D filtering (BM3D) algorithm is more effective than traditional denoising methods especially for Gaussian noise. However, the traditional hard-threshold used in BM3D algorithm can not recognize the noise intensity in the process of removing additive noise with BM3D, some image details will be lost. Aiming at this problem, an improved BM3D algorithm is proposed. Firstly, the traditional hard-thresholding of the BM3D method is substituted by an adaptive filtering technique. This technique has a high capacity to acclimate and can change according to the noise intensity. Secondly, when the noise intensity is less than the threshold, the new TV model is used to replace the hard-threshold filtering, when the noise intensity exceeds the threshold, the hard and soft thresholding algorithm is used to replace the hard-threshold filtering. Through the adaptive threshold, the high noise and low noise image feature areas are screened out, targeted denoising is carried out, and the edge details are preserved. Experimental results show that the performance of the improved BM3D method is better than traditional methods.

The main aim of the presented paper is to explore all types of all wavelet families at all possible decomposition levels to find the best decomposition level as well as the best wavelet family to denoise an ECG signal from a specific type of noise which is the white Gaussian noise. The universal hard and soft thresholding of Donoho & Johnston is used to shrink extracted details. The MIT-BIH signal database is used to test our programs. The experiments revealed that the Most interesting wavelet level decomposition is level 5, and, Daubechie Family has proved its performance in denoising ECG signal when comparing the Signal to Noise Ratio (SNR) measure. These two findings are well confirmed by an expert in the domain.

The denoising of medical images degraded by various types of noises is a major problem in medical image processing. A very good tradeoff between detail preservation and noise removal is obtained while implementing with various successive filtering procedures. This paper presents a wavelet-based multiscale products thresholding and spatial based Bilateral Filter scheme for noise removal of magnetic resonance images. In the first stage, the noisy image is passed through Bilateral Filter (BF) and some amount of noise is reduced but the image becomes blurred, hence adaptive wavelet thresholding is applied with multiscale product rule in the second stage. Rather than using Wavelet Transform, Dyadic Wavelet Transform is employed. After apply the Dyadic Wavelet Transform, wavelet interscale dependencies is exploited by multiply the adjacent wavelet subbands to preserve edge structures while suppressing noise. An adaptive threshold is calculated and implemented on the multiscale products rather than on the wavelet coefficients. Hence to identify important features like edges, curves and textures the thresholding is applied to multiscale products. The proposed method for medical image denoising is performed through a recursive application of simple steps and demonstrated on a number of standard medical images. The results obtained with the proposed method outperform other methods both visually and in terms of objective quality peak-signal-to-noise ratio (PSNR).

This paper describes subband dependent adaptive shrinkage function that generalizes hard and soft shrinkages proposed by Donoho and Johnstone (1994). The proposed new class of shrinkage function has continuous derivative, which has been simulated and tested with normal and abnormal ECG signals with added standard Gaussian noise using MATLAB. The recovered signal is visually pleasant compared with other existing shrinkage functions. The implication of the proposed shrinkage function in denoising and data compression is discussed.