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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]

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Gao, Li, Wang and Cai.)