In various fields of information examination, for example, AI, profoundly getting the hang of missing information is a typical issue. Missing qualities should be tended to since they can adversely affect the exactness and adequacy of prescient models. This research investigates how data discretization affects deep learning methods for filling the missing values in datasets with continuous features. They provide a unique method for imputing missing values using deep neural networks (DNNs) called extravagant expectation maximization-deep neural network (EEM-DNN). This approach discretizes continuous features into separate intervals initially. This is justified by treating the issue of missing value imputation as a classification work, with the missing values being considered a distinct class. A DNN, designed explicitly for imputation, is then trained using the discretized data. The expectation maximization concepts are incorporated into the network architecture, and as a result, the network iteratively improves its imputation predictions. They run comprehensive experiments on several datasets from different fields to gauge the efficacy of the suggested strategy. The effectiveness of EEM-DNN is compared to that of other imputation approaches, such as traditional imputation techniques and deep learning methods without data discretization. Our findings show that data discretization significantly enhances imputation accuracy. In terms of imputation accuracy and prediction performance on downstream tasks, the EEM-DNN method regularly performs better than alternative methods. It also examines if various discretization techniques affect the overall imputation process. They find that the trade-off between bias and variance in imputed data depends on the discretization method selected. This highlights the significance of choosing a suitable discretization approach depending on the unique properties of the dataset.

The aim of this paper is to establish several versions of Paley–Wiener-type theorems for the canonical Fourier–Bessel transform, which is a Bessel type of linear canonical transform indexed by a matrix parameter m [Formula: see text].

In this paper we define, using the Stirling numbers of the second kind, the Gompertz wavelets and show their basic properties. In particular, we prove that the admissibility condition holds for them. We also compute the normalizing factors in the space of the square-integrable functions [Formula: see text] and present an explicit formula for them in terms of the Bernoulli numbers. Then, after implementing the second-order Gompertz wavelets in the Matlab Wavelet Toolbox, we perform numerical experiments demonstrating the practical applicability and effectiveness of the wavelets.

This paper addresses the problem of Bayesian wavelet estimating the mean vector of multivariate normal distribution under a multivariate normal prior distribution based on linear and nonlinear exponential balanced loss functions. The covariance matrix of multivariate normal distribution is considered known. Bayes estimators of mean vector parameter of multivariate normal distribution are achieved. Then two soft shrinkage wavelet threshold estimators based on Stein’s unbiased risk estimate (SURE) and Bayes estimators are provided. Finally, the performance of the soft shrinkage wavelet estimators was checked through simulation study and Electrical Grid Stability Simulated data set. Simulation and real data results showed the better performance of SURE thresholds based on linear and nonlinear exponential balanced loss functions compared to other classical wavelet methods. Also, they showed better performance for SURE threshold based on nonlinear exponential balanced loss function in multivariate normal distribution with small dimensions.

Let [Formula: see text] be a positive, Lebesgue integrable and exponential decay function defined on an infinite interval [Formula: see text] and let [Formula: see text] be the space of weighted Lebesgue integrable functions on [Formula: see text]. In this paper, we give the relations of the best one-sided approximation and the optimal Hermite–Fejér interpolation by the set of algebraic polynomials of degree not exceeding a given number for the smooth function classes [Formula: see text], [Formula: see text], in the metric of the space [Formula: see text] and prove that the Hermite–Fejér interpolation based on the set of the zeros of some orthogonal polynomials is optimal in [Formula: see text]. In addition, we show that the approximation error of the optimal Hermite–Fejér interpolation and quadrature errors of the weighted Gaussian quadrature formula are equal, and give the exact constant of the errors.

This paper designs a preview repetitive control (PRC) policy for a class of Takagi–Sugeno (T–S) fuzzy systems with time-varying delay and external disturbances. First, the T–S fuzzy model is employed to represent a nonlinear plant, once the nonlinear plant is represented by a T–S fuzzy model, a fuzzy improved-equivalent-input-disturbance (IEID)-based PRC law can be designed to achieve better tracking performance and disturbance rejection. Next, based on a new equality constraint, we derive a continuous-discrete two-dimensional (2D) system that paves the way to solve the design problem of the IEID-based PRC law using linear matrix inequality (LMI) approach. Then, by solving LMIs, the gains of the controller and state observer can be obtained. Finally, a numerical example is included to show the effectiveness of the proposed method.

In this study, we introduce a novel approach to speech enhancement through the design of a complex temporal convolutional network (Complex-TCN). This model leverages the power of complex networks, enabling the simultaneous capture of both magnitude and phase information inherent in speech signals. By employing a temporal convolutional network, the Complex-TCN excels at extracting contextual information within the time domain of speech. Our findings underscore the substantial performance improvements achieved through the synergistic use of the temporal convolutional network and the incorporation of complex representations.

Dropping the ambient noise from microseismic signals is very important for disaster monitoring such as a rockburst and early warning system using microseismic monitoring techniques in the mine and coal mines. Currently, it is still a challenge to remove high and low-frequency noise simultaneously without losing the useful information of microseismic signal. The aim of this paper is to remove the low-frequency noise contained in microseismic signal effectively, while preserving the useful signal information by using a stochastic approach. We first statistically model the wavelet coefficients in the approximation subband of noisy microseismic signal. In addition, we evaluate qualitatively and quantitatively the fitness of Gauss–Laplace mixture distribution and the statistical modeling of data. Then, we propose a novel denoising algorithm to remove the ambient noise effectively from the noisy microseismic signals in wavelet domain. This algorithm removes the low-frequency noise by using a stochastic approach and the high-frequency noise by using a traditional wavelet thresholding method. The low-frequency noise is removed by using a closed-form shrinkage function based on Gauss–Laplace mixture distribution, while the high-frequency noise is removed by using a threshold function combined with Garrote and hyperbolic threshold functions. Next, we evaluated the ambient denoising performance of our novel denoising algorithm by comparing it with various denoising methods with different test signals. Experimental results show that the ambient denoising performance of the proposed method is better than the other seven existing methods.

In this paper, we improve the broad learning system (BLS) by speeding up the incremental learning for added inputs. We propose an efficient implementation for a step that is in the pseudoinverse computation of a partitioned matrix, to reduce the computational complexity. The proposed efficient implementation has two different forms for the cases of [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] and [Formula: see text] denote the number of additional training samples and the total number of nodes, respectively. The proposed implementation for [Formula: see text] utilizes the inverse of a sum of matrices to compute only a [Formula: see text] matrix inverse, instead of a [Formula: see text] matrix inverse in the original implementation, and the corresponding speedup for the matrix inversion operation in the number of floating-point operations is [Formula: see text]. Moreover, it also speeds up two relevant matrix multiplication operations in the original implementation. On the other hand, the proposed implementation for [Formula: see text] speeds up one matrix multiplication operation in the original implementation. The numerical simulations show that both the proposed and original implementations always achieve the same testing accuracy. On the Modified National Institute of Standards and Technology dataset, the speedups of the proposed efficient BLS implementation over the original BLS implementation in total training time are 1.35–1.57 when [Formula: see text] and 1.09–1.13 when [Formula: see text], while on the NYU object recognition benchmark dataset, the speedups are 1.10–1.35 when [Formula: see text] and 1.07–1.09 when [Formula: see text].

In this paper, we propose a new image denoising technique which consists in applying a stationary wavelet transform (SWT)-based image denoising technique, in the domain of 2D dual-tree discrete wavelet transform (DWT). In fact, this proposed technique consists first of applying the 2D dual-tree DWT to the noisy image. Then, the noisy wavelet coefficients obtained from this application are denoised by applying to each of them, a SWT-based image denoising technique. Finally, the denoised image is reconstructed by applying the inverse of the 2D dual-tree DWT to the obtained denoised wavelet coefficients. For applying this SWT-based image denoising technique, we use the soft thresholding, the Daubechies 4 as the mother wavelet, and the decomposition level is equal to 5. The performance of this image denoising technique proposed in this work is proven by its comparison to three other denoising techniques existing in the literature. These three techniques are the denoising technique based on the soft thresholding in the SWT domain, the image denoising technique based on soft thresholding in the domain of 2D dual-tree DWT and the image denoising approach using deep neural network. All the previously mentioned techniques, including our proposed denoising approach, are applied to a number of noisy images, and the obtained results are in terms of peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). Those results show that this proposed denoising technique outperforms the other three denoising techniques used in this evaluation.