International Journal of Wavelets, Multiresolution and Information Processing

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.

Recent advances in intelligent surveillance to boost public security have increased interest in anomaly location and identification among computer vision researchers in congested situations. Unrestricted video monitoring is required due to its extensive use in private and public spheres. Particularly, research on finding anomalies in surveillance videos has drawn much interest. Video condensation is an efficient method for quickly scanning and retrieving lengthy surveillance films. Reordering the video events in the spatial or temporal domain seeks to condense large video sequences into their equivalent compact video representation. Additionally, if a delay occurs in anomaly detection, it leads to time consumption for rectifying it. Therefore, the core aim of this task is to reduce the time consumption of detecting the instance of video anomaly detection faster by introducing the optimal object stitching through the deep learning-based video condensation concept. The steps include video condensation and deep learning-based anomaly detection. Initially, the necessary video for anomaly detection is gathered from the datasets. The gathered video is converted into frames and is used for object detection in each frame using Improved YOLOv5 (I-YOLOv5). Then, the optimal frame selection is performed using the hybrid Fitness of Wild Geese and Path Finder (FWGPF) for stitching the detected objects into the selected optimal frames, thus compressing the relevant frames. In the second phase, the condensed (compressed) frames are utilized for determining the anomaly frames with the support of Parameter Tuning in Dilated MobileNet (PTDM), and further, the anomaly objects are detected on the classified condensed frames based on the I-YOLOv5. Here, the tuning of constraint is done in the anomaly detection phase by the same hybrid FWGPF to reduce the time consumption. The experimental analysis of the developed model is performed with baseline algorithms and detection techniques to confirm the developed model’s efficiency.

We consider bounded linear operators from the view of functional reproducing property. For some bounded linear operators associated with orthogonal polynomials we define an inner product space associated with a kernel constructed with orthogonal polynomials, show that it is a functional reproducing kernel Hilbert space (FRKHS) associated with these bounded linear operators and give decay rate for the best FRKHS approximation with a $K$-functional associated with the FRKHS. On this basis, we provide a learning rate for kernel regularized regression whose hypothesis space is the defined FRKHS. As applications, we define some concrete FRKHSs associated with polynomial operators such as the Bernstein–Durrmeyer operators, the de la Vallée Poussin operators on both the unit sphere $S^{d-1}$ and the unit ball $B^d$. We show that these polynomial operators have reproducing property with respect to the corresponding concrete FRKHSs and show the learning rate for the kernel regularized regression. In short, we provide a way of constructing FRKHS operators with Fourier multipliers and show a learning framework from the view of operator approximation.

In this paper, we introduce the concept of trend function made from adaptive Fourier decomposition. Through applying a data preprocessing method, we achieve trend functions of the rational function type. The trend functions are divided into different levels to describe the tendency of the signal or time series in question. They are, in particular, smooth, and are free from the Gibbs phenomenon as usually introduced by the Fourier type methods. To justify the role of the trend function concept, an interpolation result is proved. An effective application of trend function in predicting stochastic time series is presented based on real COVID-19 outbreak data of China. The algorithm aspect is fully discussed.

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.

This paper examines the stability of the à trous algorithm under arbitrary iteration in the context of a more general study of shift-invariant filter banks. The main results describe sufficient conditions on the associated filters under which an infinitely iterated shift-invariant filter bank is stable. Moreover, it is shown that the stability of an infinitely iterated shift-invariant filter bank guarantees that of any associated finitely iterated shift-invariant filter bank, with uniform bounds. The reverse implication is shown to hold under an additional assumption on the low-pass filter. Finally, it is also shown that the separable product of stable one-dimensional shift-invariant filter banks produces a stable two-dimensional shift-invariant filter bank.

This paper introduces a nonconvex ${\ell }_{1-2}$-analysis model:

Noting that the gap between individual communication abilities is amplified in the network era, we classify spreaders into super-spreaders and ordinary spreaders by the Pareto principle. In addition, when facing negative information, individuals with higher knowledge levels will recognize it. Based on these, in this study, an improved Ignorants-Hesitant-Super-spreaders-Ordinary spreaders-Wise-Removers (IEASWR) information propagation model was developed. Meanwhile, in view of the gradual saturation, density dependence and nonlinear relationship of the propagation process, the Holling-type II functional response function is introduced to information propagation modeling for the first time making it more realistic. First, the basic reproduction number ${{ℛ}}_0$ is deduced. Then, the global asymptotic stability of the information-free/prevailing equilibria is proved by constructing the Lyapunov function. Furthermore, using the Pontryagin maximum principle, a real-time optimization guidance measure is proposed to achieve the correct guidance of negative information within the expected time. Finally, the validity of the theory is verified through numerical simulation.

A Riesz basis for a separable Hilbert space $H$ is the image of an orthonormal basis under a bounded, linear and bijective operator acting on $H$. Equivalently, it is an exact frame that shares the properties of a basis for $H$. Let $G$ be a $\sigma$-compact and metrizable locally compact abelian group, and $s$ and $r$ be positive integers. It is illustrated that the image of a matrix-valued orthonormal basis under a bijective, bounded and linear operator acting on the matrix-valued signal space $L^2(G,{ℂ}^{s\times r})$ may not be a frame, hence not a basis of the space $L^2(G,{ℂ}^{s\times r})$. We introduce a notion of matrix-valued Riesz basis in the space $L^2(G,{ℂ}^{s\times r})$, where the adjointability of a bounded linear operator in the definition of Riesz basis with respect to the matrix-valued inner product plays a crucial role. We establish the existence of matrix-valued Riesz bases of the space $L^2(G,{ℂ}^{s\times r})$. Extending results for standard Riesz bases of separable Hilbert spaces, we give necessary and sufficient conditions, and a characterization of matrix-valued Riesz bases of the space $L^2(G,{ℂ}^{s\times r})$.

Graves’ disease is a common condition that is diagnosed clinically by determining the smoothness of the thyroid texture and its morphology in ultrasound images. Currently, the most widely used approach for the automated diagnosis of Graves’ disease utilizes Convolutional Neural Networks (CNNs) for both feature extraction and classification. However, these methods demonstrate limited efficacy in capturing texture features. Given the high capacity of wavelets in describing texture features, this research integrates learnable wavelet modules utilizing the Lifting Scheme into CNNs and incorporates a parallel wavelet branch into the ResNet18 model to enhance texture feature extraction. Our model can analyze texture features in spatial and frequency domains simultaneously, leading to optimized classification accuracy. We conducted experiments on collected ultrasound datasets and publicly available natural image texture datasets, our proposed network achieved 97.27% accuracy and 95.60% recall on ultrasound datasets, 60.765% accuracy on natural image texture datasets, surpassing the accuracy of ResNet and confirming the effectiveness of our approach.

In this paper, we construct a family of compactly supported dual wavelets associated to the Quincunx matrix on ${ℝ}^3$. Our family will have dual wavelets with any desired number of vanishing moments, any fixed degree of regularity and symmetry with respect to some point. Finally, we also present dual wavelets on $L^2({ℝ}^2)$ associated to some dilation matrices with determinant $2$.

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.

Tensor Robust Principal Component Analysis (TRPCA) has received much attention in many real-world applications which aims to recover a low-rank tensor corrupted by sparse noise. Most existing TRPCA methods usually regularize the low-rank component by minimizing its Tensor Nuclear Norm (TNN). However, the original TNN shrinks all of the singular values with the same penalty which generally leads to suboptimal results. The reason is that the large singular values should be less penalized since they usually correspond to salient information of the real-world tensor. In this work, we develop a Tensor Improved Huber Norm (TIHN) which considers the difference between the singular values of tensor. The TIHN can achieve better performance by recovering the large and significant singular values exactly. We also establish the Huber TRPCA (HTRPCA) method by utilizing the proposed TIHN. In addition, an efficient optimization algorithm based on the half-quadratic theory and Alternating Direction Method of Multipliers (ADMM) framework is designed to implement the HTRPCA. Finally, experiments on color image recovery and video recovery validate the effectiveness of the proposed method.

It is known that a smooth function of exponential decay at infinity cannot be an orthonormal wavelet. Dziubański and Hernández constructed smooth orthonormal wavelets of Gevrey-type subexponential decay. We weaken the Gevrey-type decay and construct orthonormal wavelets of subexponential decay related to the so-called extended Gevrey classes. The virtue of our construction is that precise asymptotics of functions from such classes can be given in terms of the Lambert $W$-function.