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This work proposes a wavelet shrinkage rule under asymmetric LINEX loss function and a mixture of a point mass function at zero and the logistic distribution as prior distribution to the wavelet coefficients in a nonparametric regression model with gaussian error. Underestimation of a significant wavelet coefficient can lead to the bad detection of features of the unknown function, such as peaks, discontinuities, and oscillations. It can also occur under asymmetrically distributed wavelet coefficients. Thus, the proposed rule is suitable when overestimation and underestimation have asymmetric losses. Statistical properties of the rule, such as squared bias, variance, frequentist, and bayesian risks, are obtained. Simulation studies are conducted to evaluate the performance of the rule against standard methods and an application in a real dataset involving infrared spectra is provided.

In this paper, we consider aggregated functional data composed by a linear combination of component curves and the problem of estimating these component curves. We propose the application of a bayesian wavelet shrinkage rule based on a mixture of a point mass function at zero and the logistic distribution as prior to wavelet coefficients to estimate mean curves of components. This procedure has the advantage of estimating component functions with important local characteristics such as discontinuities, spikes and oscillations for example, due the features of wavelet basis expansion of functions. Simulation studies were done to evaluate the performance of the proposed method, and its results are compared with a spline-based method. An application on the so-called Tecator dataset is also provided. [ABSTRACT FROM AUTHOR]

Wavelet shrinkage estimators are widely applied to analyse datasets in wavelet domain from several fields of science. They typically act by reducing magnitudes of empirical coefficients in a discrete wavelet transformation to estimate wavelet coefficients. In nonparametric regression problems, most of the shrinkage rules are derived from models composed of an unknown function with additive Gaussian noise. Although Gaussian noise assumption is reasonable in several real data analysis, mainly for large sample sizes, it is not general. Contaminated data with positive noise can occur in practice and nonparametric regression models with positive noise bring challenges in wavelet shrinkage point of view. In this sense, this work proposes bayesian shrinkage rules to estimate wavelet coefficients from a nonparametric regression framework with additive and strictly positive noise under exponential and lognormal distributions. Computational aspects are discussed and simulation studies to analyse the performances of the proposed shrinkage rules and compare them with standard techniques are done. An application for winning times Boston Marathon dataset is also provided. [ABSTRACT FROM AUTHOR]

Nonlinear diffusion has been proved to be an indispensable approach for the removal of noise in image processing. In this paper, we employ nonlinear diffusion for the purpose of denoising audio signals in order to have this approach also recognized as a powerful tool for audio signal processing. We apply nonlinear diffusion to wavelet coefficients obtained from different filters associated with orthogonal and biorthogonal wavelets. We use wavelet decomposition to keep signal components well-localized in time. We compare denoising results using nonlinear diffusion with wavelet shrinkage for different wavelet filters. Our experiments and results show that the denoising is much improved by using the nonlinear diffusion process. [ABSTRACT FROM AUTHOR]

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The present work describes simulation studies to compare the performances in terms of averaged mean squared error of bayesian wavelet shrinkage methods in estimating component curves from aggregated functional data. Five bayesian methods available in the literature were considered to be compared in the studies: The shrinkage rule under logistic prior, shrinkage rule under beta prior, large posterior mode (LPM) method, amplitude-scale invariant Bayes estimator (ABE) and Bayesian adaptive multiresolution smoother (BAMS). The so called Donoho-Johnstone test functions, logit and SpaHet functions were considered as component functions and the scenarios were defined according to different values of sample size and signal to noise ratio in the datasets. It was observed that the signal to noise ratio of the data had impact on the performances of the methods. An application of the methodology and the results to the tecator dataset is also done. [ABSTRACT FROM AUTHOR]

In this paper, we consider the generalized Bayes estimator of mean vector parameter for multivariate normal distribution with Unknown mean vector and covariance matrix under reflected normal loss function. We also prove admissibility and minimaxity of the generalized Bayes estimator. We obtain stein’s unbiased risk estimator (SURE) threshold based on generalized Bayes estimator and we find the wavelet shrinkage generalized bayes SURE estimator. At the end, we check the performance of this estimator and we provide two real examples. [ABSTRACT FROM AUTHOR]

The parameter that is of most interest in applications of stable distributions is the stability index α, which determines how "heavy" the tail is. For applications when the main interest is on the tail, we develop an estimator of α for univariate symmetric stable distributions, based on the characteristic function and on the principle of wavelet shrinkage. We analyze the proposed estimator by the Monte Carlo simulations and prove that it is a consistent estimator. The presence of human-made explosions in a seismic catalog leads to errors in the statistical analysis of seismicity. Here, we also proposed the CWS coefficient, based on the proposed estimator, like an additional classification tool to discriminate between natural tectonic earthquakes and human-made explosions. [ABSTRACT FROM AUTHOR]

Nonlinear diffusion has been proved to be an indispensable approach for the removal of noise in image processing. In this paper, we employ nonlinear diffusion for the purpose of denoising audio signals in order to have this approach also recognized as a powerful tool for audio signal processing. We apply nonlinear diffusion to wavelet coefficients obtained from different filters associated with orthogonal and biorthogonal wavelets. We use wavelet decomposition to keep signal components well-localized in time. We compare denoising results using nonlinear diffusion with wavelet shrinkage for different wavelet filters. Our experiments and results show that the denoising is much improved by using the nonlinear diffusion process.

Consider the nonparametric curve estimation problem. Wavelet shrinkage methods are applied to the data in the wavelet domain for noise reduction. After denoising, the function can be estimated by wavelet basis expansion. The present paper proposes a Bayesian approach for wavelet shrinkage with the use of a mixture of a point mass function at zero and the logistic distribution symmetric around zero as the prior distribution to the wavelet coefficients of an unknown function in models with additive Gaussian errors. Statistical properties such as bias, classical and Bayesian risks of the rules are analyzed and performances of the proposed rules are obtained in simulations studies involving the Donoho-Johnstone test functions. Application in a mass spectrometry real data set is done. [ABSTRACT FROM AUTHOR]

To avoid the problems of relative overlap and low signal-to-noise ratio (SNR) of segmented three-dimensional (3D) multimodal medical images, which limit the effect of medical image diagnosis, a 3D multimodal medical image segmentation algorithm using reinforcement learning and big data analytics is proposed. Bayesian maximum a posteriori estimation method and improved wavelet threshold function are used to design wavelet shrinkage algorithm to remove high-frequency signal component noise in wavelet domain. The low-frequency signal component is processed by bilateral filtering and the inverse wavelet transform is used to denoise the 3D multimodal medical image. An end-to-end DRD U-Net model based on deep reinforcement learning is constructed. The feature extraction capacity of denoised image segmentation is increased by changing the convolution layer in the traditional reinforcement learning model to the residual module and introducing the multiscale context feature extraction module. The 3D multimodal medical image segmentation is done using the reward and punishment mechanism in the deep learning reinforcement algorithm. In order to verify the effectiveness of 3D multimodal medical image segmentation algorithm, the LIDC-IDRI data set, the SCR data set, and the DeepLesion data set are selected as the experimental data set of this article. The results demonstrate that the algorithm's segmentation effect is effective. When the number of iterations is increased to 250, the structural similarity reaches 98%, the SNR is always maintained between 55 and 60 dB, the training loss is modest, relative overlap and accuracy all exceed 95%, and the overall segmentation performance is superior. Readers will understand how deep reinforcement learning and big data analytics test the effectiveness of 3D multimodal medical image segmentation algorithm.

In this paper, we present a new wavelet shrinkage operator to remove noise for non-linear time series. Like other improvements, the proposed operator is used to address the discontinuity of the hard operator as well as the large bias of the soft operator. The special of this operator is that it introduces the universal threshold to divide the details of signal and noise. Such that the operator can identify those coefficients with noise, and then shrink larger for them, otherwise, shrink small. We test the denoising performance of the new operator in the chaotic time series generated by the Lorenz system. The results show that the new method successfully reduces the noise in nonlinear time series. Also, we applied our approach to improving the classification accuracy of the bearing fault in the noisy environment. The bearing fault datasets come from the Case Western Reserve University (CWRU) bearing data center and Paderborn University respectively. Experimental results show that the proposed operator effectively reduces the error rate on both traditional classifier models and deep learning models. Comparisons with the three existing shrinkage operators demonstrate the superiority of the proposal. [ABSTRACT FROM AUTHOR]

In bayesian wavelet shrinkage, the already proposed priors to wavelet coefficients are assumed to be symmetric around zero. Although this assumption is reasonable in many applications, it is not general. The present paper proposes the use of an asymmetric shrinkage rule based on the discrete mixture of a point mass function at zero and an asymmetric beta distribution as prior to the wavelet coefficients in a non-parametric regression model. Statistical properties such as bias, variance, classical and bayesian risks of the associated asymmetric rule are provided and performances of the proposed rule are obtained in simulation studies involving artificial asymmetric distributed coefficients and the Donoho-Johnstone test functions. Application in a seismic real dataset is also analyzed. [ABSTRACT FROM AUTHOR]

Wavelet thresholding (or shrinkage) attempts to remove the noises existing in the signals while preserving inherent pattern characteristics in the reconstruction of true signals. For data-denoising purpose, we present a new wavelet thresholding procedure which employs the step-down testing idea of identifying active contrasts in unreplicated fractional factorial experiments. The proposed method employs bootstrapping methods to a step-down test for thresholding wavelet coefficients. By introducing the concept of a false discovery error rate in testing wavelet coefficients, we shrink the wavelet coefficients with p-values higher than the error rate. The error rate controls the expected proportion of wrongly accepted coefficients among chosen wavelet coefficients. Bootstrap samples are used to approximate the p-value for computational efficiency. We also present some guidelines for selecting the values of hyper-parameters which affect the performance in the step-down thresholding procedure. Based on some common testing signals and an air-conditioner sounds example, the comparison of our proposed procedure with other thresholding methods in the literature is performed. The analytical results show that the proposed procedure has a potential in data-denoising and data-reduction in a variety of signal reconstruction applications.

We describe the lifting dual tree complex wavelet transform (LDTCWT), a type of lifting wavelets remodeling that produce complex coefficients by employing a dual tree of lifting wavelets filters to get its real part and imaginary part. Permits the remodel to produce approximate shift invariance, directionally selective filters and reduces the computation time (properties lacking within the classical wavelets transform). We describe a way to estimate the accuracy of this approximation and style appropriate filters to attain this. These benefits are often exploited among applications like denoising, segmentation, image fusion and compression. The results of applications shrinkage denoising demonstrate objective and subjective enhancements over the dual tree complex wavelet transform (DTCWT). The results of the shrinkage denoising example application indicate empirical and subjective enhancements over the DTCWT. The new transform with the DTCWT provide a trade-off between denoising computational competence of performance, and memory necessities. We tend to use the PSNR (peak signal to noise ratio) alongside the structural similarity index measure (SSIM) and the SSIM map to estimate denoised image quality. [ABSTRACT FROM AUTHOR]

The present work aims at developing a new approach towards the analysis of the crack path through the access to the information from the infrared (IR) video imaging of the steady fatigue crack growth. We first test some commonly available infrared image filtering techniques, and then we introduce a new robust algorithm to identify the position of the dynamic crack. The proposed procedure performs the local analysis of the temperature distribution around the fatigue crack tip in the 316L stainless steel. The developed MATLAB framework simplifies the routine processing and permits analyzing multiple experiments reasonably easily. Two filtering procedures - Gaussian and wavelet shrinkage - were implemented and applied successively to denoise the IR images. Both filters produce comparable and good quality results. The new algorithm capable of automatically locating the crack tip position from consecutive filtered IR images is proposed. Remarkably successful results are demonstrated with only small errors caused by materials distortion.

Partial Discharge (PD) measurements of large generators are extremely affected and hampered by noise, making the denoising of PD signal an inevitable issue. Wavelet shrinkage is the most commonly employed method for PD signal denoising. The appropriate mother wavelet and decomposition level are critically important for the denoising performance. In consideration of the PD signal characteristics of large generators, a novel wavelet shrinkage scheme for PD signal denoising is presented. In the scheme, a scale dependent wavelet selection method is proposed; the core idea is that the optimum wavelet at each scale is selected as the one maximizing the energy ratio of coefficients beside and inside the range formed by the threshold, which correspond to the signal to be reserved and noise to be removed, respectively. In addition, taking into account the influence of mother wavelet at each scale on the decomposition level, an approach for decomposition level determination is put forward based on the energy composition after decomposition at each scale. The application results on the simulated signals with different SNR obtained by combining the various pulses and measured signal on-site show the effectiveness of the proposed scheme. Besides, the denoising results are compared with that of the existing wavelet selection methods and the proposed wavelet selection method shows an obvious advantage. [ABSTRACT FROM AUTHOR]

Many existing non-local means (NLM) methods either use Euclidean distance to measure the similarity between patches, or compute weight $\omega _{ij}$ only once and keep it unchanged during the subsequent denoising iterations, or use only the structure information of the denoised image to update weight $\omega _{ij}$. These may lead to the limited denoising performance. To address these issues, this paper proposes the non-local adaptive means (NLAM) for image denoising. NLAM treats weight $\omega _{ij}$ as an optimization variable and iteratively updates its value. We then introduce three unbiased distances, namely, pixel–pixel, patch–patch, and coupled unbiased distances. These unbiased distances are more robust to measure the image pixel/patch similarity than Euclidean distance. Using the coupled unbiased distance, we propose the unbiased distance non-local adaptive means (UD-NLAM). Because UD-NLAM uses only a single patch size to compute weight $\omega _{ij}$ , we introduce multipatch UD-NLAM (MUD-NLAM) to adapt different noise levels. To further improve denoising performance, we then propose a new denoising method called MUD-NLAM with wavelet shrinkage (MUD-NLAM-WS). Experimental results show that the proposed NLAM, UD-NLAM, and MUD-NLAM outperform existing NLM methods, and MUD-NLAM-WS achieves a better performance than the state-of-the-art denoising methods. [ABSTRACT FROM AUTHOR]

The paper is devoted to the new model for image decomposition, that splits an image $f$ into three components $u+v+\omega$, with $u$ a piecewise-smooth or the ``cartoon'' component, $v$ a texture component and $\omega$ the noise part in variational approach. This decomposition model is in fact incorporates the advantages of two preceding models: the second-order total variation minimization of Rudin-Osher-Fatemi (ROF2), and wavelet shrinkage for oscillatory functions. This decomposition model is presented as an extension of the three components decomposition algorithm of Aujol et al. in \cite{JAC}. It also continues the idea introduced previously by authors in \cite{TPB}, for two components decomposition model. The ROF2 model was first proposed by Bergounioux et al. in \cite{BP}, it is an improved regularization method to overcome the undesirable staircasing effect. The wavelet shrinkage is well combined to separate the oscillating part due to texture from that due to noise. Experimental results validate the proposed algorithm and demonstrate that the image decomposition model presents effective and comparable performance to other state-of-the-art models.

The present work aims at developing a new approach towards the analysis of the crack path through the access to the information from the infrared (IR) video imaging of the steady fatigue crack growth. We first test some commonly available infrared image filtering techniques, and then we introduce a new robust algorithm to identify the position of the dynamic crack. The proposed procedure performs the local analysis of the temperature distribution around the fatigue crack tip in the 316L stainless steel. The developed MATLAB framework simplifies the routine processing and permits analyzing multiple experiments reasonably easily. Two filtering procedures - Gaussian and wavelet shrinkage - were implemented and applied successively to denoise the IR images. Both filters produce comparable and good quality results. The new algorithm capable of automatically locating the crack tip position from consecutive filtered IR images is proposed. Remarkably successful results are demonstrated with only small errors caused by materials distortion. [ABSTRACT FROM AUTHOR]

This paper presents an efficient method for recovery of SIMS signals from strongly noised blurred discrete data. This technique is based on Tikhonov-Miller regularization where a priori model of solution is included. The latter is a denoisy signal obtained using the Kalman filter. This is an interesting estimation method, but it can only be used when the system is described precisely. By comparing the results of the proposed technique with those of the literature, our algorithm gives the best results without artifacts and oscillations related to noise and significant improvement of the depth resolution. While, the gain in FWHM is less improved than those obtained by the wavelet technique. Therefore, this new algorithm can push the limits of SIMS measurements towards its ultimate resolution. [ABSTRACT FROM AUTHOR]

Highlights • A novel designed EEG-EOG signal contamination model to quantitatively validate artifact removal from EEGs. • A two-stage wavelet shrinkage method proposed for the quality of the reconstructed EEG signal and evaluated in the frequency spectrum, which represents how much the original specific brain-state characteristic can be reconstructed. • We checked the threshold multiplier at both stage-I, stage-II and L (decomposition level). • Westated the importance of the threshold multiplier and L in the proposed scheme. • We used the real EOG and EEG signal to demonstrate the effectiveness of proposed scheme. Abstract Electroencephalogram (EEG) data inevitably contain large amounts of noise, particularly from ocular potentials in tasks with eye movements, known as electro-oculography (EOG) artifact, which has been a crucial issue in brain–computer-interface studies. This time-frequency characteristic has been substantially dealt with in previous proposed denoising algorithms that relied on a consistent assumption based on the single-noise component model. However, the traditional model is not applicable for biomedical signals that consist of multiple signal components, such as weak EEG signals that are easily recognized as noise because of the signal amplitude with respect to the EOG signal. In consideration of the realistic signal contamination, we designed a novel EEG-EOG signal contamination model to quantitatively validate artifact removal from EEGs. We then proposed the two-stage wavelet shrinkage method with the decomposition of the undecimated wavelet transform (UDWT), which is suitable for signal structure. Open-source clinical intracranial EEGs with the hundred dataset in each behavioral condition were introduced to the validation as "true EEG" before the contamination of artificial EOGs. The quality of the reconstructed EEG signal has evaluated in the frequency spectrum, which represents how much the original specific brain-state characteristic can be reconstructed. Numerical analyses demonstrated that the first stage pursued abrupt changes with high amplitudes provided by assumed EOGs, and the second stage provided the EEG frequency spectrum as observed in the original signal. What the performance exceeded the conventional shrinkage suggests that threshold values is required to be set properly depending on individual amplitudes of contaminated bio-signal sources as our proposed method demonstrated. This result focused on the actual amplitude-frequency structure in the polygenetic signal. It not only provided the decomposition performance, but also revealed how bio-signals are mixed together by using a new standard model for robust validation in the EEG-EOG signal contamination. [ABSTRACT FROM AUTHOR]

Partial Discharge (PD) measurements of large generators are extremely affected and hampered by noise, making the denoising of PD signal an inevitable issue. Wavelet shrinkage is the most commonly employed method for PD signal denoising. The appropriate mother wavelet and decomposition level are critically important for the denoising performance. In consideration of the PD signal characteristics of large generators, a novel wavelet shrinkage scheme for PD signal denoising is presented. In the scheme, a scale dependent wavelet selection method is proposed; the core idea is that the optimum wavelet at each scale is selected as the one maximizing the energy ratio of coefficients beside and inside the range formed by the threshold, which correspond to the signal to be reserved and noise to be removed, respectively. In addition, taking into account the influence of mother wavelet at each scale on the decomposition level, an approach for decomposition level determination is put forward based on the energy composition after decomposition at each scale. The application results on the simulated signals with different SNR obtained by combining the various pulses and measured signal on-site show the effectiveness of the proposed scheme. Besides, the denoising results are compared with that of the existing wavelet selection methods and the proposed wavelet selection method shows an obvious advantage.

Time series forecasting is widely used in various areas of human knowledge, especially in the planning and strategic direction of companies. The success of this task depends on the forecasting techniques applied. In this paper, a hybrid approach to project time series is suggested. To validate the methodology, a time series already modeled by other authors was chosen, allowing the comparison of results. The proposed methodology includes the following techniques: wavelet shrinkage, wavelet decomposition at level r, and artificial neural networks (ANN). Firstly, a time series to be forecasted is submitted to the proposed wavelet filtering method, which decomposes it to components of trend and linear residue. Then, both are decomposed via level r wavelet decomposition, generating r + 1 Wavelet Components (WCs) for each one; and then each WC is individually modeled by an ANN. Finally, the predictions for all WCs are linearly combined, producing forecasts to the underlying time series. For evaluating purposes, the time series of Canadian Lynx has been used, and all results achieved by the proposed method were better than others in existing literature.

Biometrics authentication is considered as most secure and reliable method to recognise and identify person's identity. Researchers put efforts to find efficient ways to secure and classify the solutions to biometric problems. In this category, fingerprint recognition (FPR) is most widely used biometric trait for person identification/verification. The present work focuses an FPR technique, which uses the grey‐level difference method, discrete wavelet transforms and edge histogram descriptor for fingerprint representation and matching. Wavelet shrinkage used for noise removal in the image. Ridge flow estimation is calculated using the gradient approach. SVM and Hamming distance similarity measures are used for recognition. The experiment result has been tested on the standard 2000–2004 fingerprint verification competition dataset and the accuracy of proposed algorithm was reported to be well above 98%. [ABSTRACT FROM AUTHOR]

The X-ray angiogram image denoising is always one of the most popular research in the field of computer vision. While the methods removed the noise, the useful structure (such as peripheral vascular) had also been smoothed, the fundamental reason is that the denoising methods cannot efficiently distinguish structural areas from flat areas. In this paper, we have proposed a spatially adaptive image denoising (SAID) method which contains two steps: spatially adaptive gradient descent (SAGD) image denoising and dual-domain filter (DDF). The SAGD denoising method contains the following parts: first of all, the wavelet shrinkage method is used to estimate redundant information which is composed of the noise and useful structures; secondly, according to the characteristic of second order matrix, a spatially adaptive gradient factor (SAGF) has been constructed to distinguish the structure from flat areas; finally, the SAGF replaces the original gradient factor and then the SAGD image denoising method is formed. To further improve the quality of the SAGD image, the SAGD image is re-denoised by a modified DDF which is guided with a rotationally invariant non-local filter (RINLF) in spatial domain and gets structural details by wavelet shrinkage in frequency domain. The results of simulation experiments verify that the proposed SAID method can get well quantitative and qualitative results which are even superior to those using the state-of-the-art denoising methods. Even more, the fluctuation of peak signal-to-noise ratio (PSNR) value is very small with a small disturbance of SAGF, which illustrates that our algorithm is more robust than the prior progressive image denoising (PID) method. Moreover, the comparison results of the extensive experiments on clinical X-ray cardiovascular angiogram images further illustrate that our method can yield clearer cardiovascular images which can provide more useful vascular information for clinicians to analyze and diagnose the cardiovascular diseases. [ABSTRACT FROM AUTHOR]