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This paper introduces a nonconvex ℓ 1 − 2 -analysis model: min x (∥ D ∗ x ∥ 1 − ∥ D ∗ x ∥ 2) s.t.  A x = y , where A is a measurement matrix and D is a tight frame. Our main motivation is to generalize the sparse recovery via ℓ 1 − ℓ 2 minimization to this new model. As a nonconvex model, it is well known that its global minimizer and local minimizer are usually inconsistent. This paper provides a type of null space property (NSP) characterization which are necessary and sufficient conditions for the measurement matrix A such that a vector x can be recovered from A x with a tight frame D via ℓ 1 − 2 -analysis local minimization, or any vector x can be uniformly recovered from A x with a tight frame D via ℓ 1 − 2 -analysis minimization locally and globally. [ABSTRACT FROM AUTHOR]

The null space property (NSP), which relies merely on the null space of the sensing matrix column space, has drawn numerous interests in sparse signal recovery. This paper studies NSP of the weighted ℓ r − ℓ 1 (r ∈ (0 , 1 ]) minimization. Several versions of NSP of the weighted ℓ r − ℓ 1 minimization including the weighted ℓ r − ℓ 1 NSP, the weighted ℓ r − ℓ 1 stable NSP, the weighted ℓ r − ℓ 1 robust NSP and the ℓ q weighted ℓ r − ℓ 1 robust NSP for 1 ≤ q ≤ 2 , are proposed, as well as the associating considerable results are derived. Under these NSPs, sufficient conditions for the recovery of (sparse) signals with the weighted ℓ r − ℓ 1 minimization are established. Furthermore, we show that to some extent, the weighted ℓ r − ℓ 1 stable NSP is weaker than the restricted isometric property (RIP). And the RIP condition we obtained is better than that of Zhou (2022). [ABSTRACT FROM AUTHOR]

When constructing multivariate framelets, it is often unavoidable to work with matrices of multivariate trigonometric polynomials and complicated matrix decomposition problems. These problems become even harder when good properties such as high-order vanishing moments are required on the framelets. In this paper, we establish a new method for constructing multivariate dual framelets with high-order vanishing moments. The underlying scheme of our algorithm is the famous Mixed Extension Principle that allows us to derive the high-pass filters (or framelet generators) from a given pair of refinable filters with high-order linear-phase moments. Our method only involves two steps: (1) directly constructing the first few pairs of high-pass filters by using the linear-phase moment conditions of the refinement filters; (2) solving a system of linear equations to obtain the rest of the high-pass filters. Both are easy to implement for scientific computation, regardless of what dimension or dilation matrix we work with. Apart from high-order vanishing moments, we will see that if the refinement filters take coefficients from some subfield of ℂ that is closed under complex conjugation, so do the high-pass filters. Furthermore, our algorithm gives the upper bounds for the number of high-pass filters in arbitrary dimensions. At the end of the paper, we will give several illustrative examples, from which we can also see that the support sizes of the high-pass filters are comparable with those of the refinement filters. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the continuous and discrete version of the linear canonical shearlet transform (LCST). The authors begin with the definition of the LCST and then establish a relationship between the linear canonical transform (LCT) and the LCST. Next, the paper derives several basic properties like Parseval's Formula, inversion formula, and the characterization of the transform's range. In addition to the continuous version of the transform, the authors also present a discrete version of the LCST. This discrete version allows for practical implementation and efficient computation of the transform in digital signal processing systems. Lastly, the paper establishes a frame condition for the discrete LCST, which thereby helps in establishing the reconstruction formula for the discrete LCST. The paper ends with a conclusion. [ABSTRACT FROM AUTHOR]

The goal of the paper is to establish quadrature formulas on combinatorial graphs. Three types of quadrature formulas are developed. Quadrature formulas of the first type are obtained through interpolation by variational splines. This set of formulas is exact on spaces of variational splines on graphs. Since bandlimited functions can be obtained as limits of variational splines we obtain quadrature formulas which are approximately exact on spaces of bandlimited functions. Accuracy of this type of quadrature formulas is given in terms of geometry of the set of nodes of splines and in terms of smoothness of functions which is measured by means of the combinatorial Laplace operator. Quadrature formulas of the second type are obtained through point-wise sampling for bandlimited functions and based on existence of certain frames in appropriate subspaces of bandlimited functions. The third type quadrature formulas are based on the average sampling over subgraphs. Our quadrature formulas which are based on sampling are exact on a relevant subspaces of bandlimited functions. The results of the paper have potential applications to problems that arise in data mining. [ABSTRACT FROM AUTHOR]

Spatio-temporal action detection (STAD) aims to classify the actions present in a video and localize them in space and time. It has become a particularly active area of research in computer vision because of its explosively emerging real-world applications, such as autonomous driving, visual surveillance and entertainment. Many efforts have been devoted in recent years to build a robust and effective framework for STAD. This paper provides a comprehensive review of the state-of-the-art deep learning-based methods for STAD. First, a taxonomy is developed to organize these methods. Next, the linking algorithms, which aim to associate the frame- or clip-level detection results together to form action tubes, are reviewed. Then, the commonly used benchmark datasets and evaluation metrics are introduced, and the performance of state-of-the-art models is compared. At last, this paper is concluded, and a set of potential research directions of STAD are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we combine the benefits of the well-known special affine Fourier and Stockwell transforms into a novel integral transform dubbed as special affine Stockwell transform and investigate the associated constant Q-property in the joint time–frequency domain. We do this by using the convolution structure of the special affine Fourier transform. The derivation of the basic properties, Rayleigh's energy theorem, the inversion formula and the range theorem are all included in the preliminary analysis. Besides, we also derive a direct relationship between the recently introduced special affine scaled Wigner distribution and the proposed SAST. Furthermore, we establish Heisenberg's uncertainty principle, logarithmic uncertainty principle and Nazarov's uncertainty principle associated with the proposed SAST. Towards the culmination of this paper, some potential applications with simulation are presented. [ABSTRACT FROM AUTHOR]

High-dimensional data that often lie in low-dimensional subspaces are ubiquitous in many fields of signal and image processing, pattern recognition, machine learning, etc. Finding sparse representations of data points in a dictionary built by using the collection of data helps to study low-dimensional subspaces. In this paper, we consider the problem of subspace-sparse representation for data composed of two distinct features. Applying different measures to the coefficients of the two distinct features under different dictionaries makes the model used in this paper more general. We present theoretical guarantee for subspace-sparse representation under conditions on the subspaces and data. The program used in this paper can handle data with structured corruption, missing entries, sparse outliers and random bounded noise well. [ABSTRACT FROM AUTHOR]

The function of pseudoknots cannot be ignored in the RNA secondary structure. Existing methods for analyzing RNA secondary structures with pseudoknots exhibit many shortcomings. This paper presents a novel RNA secondary structure visualization method in the case of a joint analysis of RNA primary structures and secondary structures. The way is based on the page number representation of the RNA secondary structure. It innovatively uses five vectors to represent bases, which are sequentially connected to outline the characteristics of the RNA secondary structure. The method covers almost all the constituent elements of the RNA secondary structure and extracts features completely. Experiments are based on the available techniques for large-scale annotation of RNA secondary structures, using a combination method of discrete wavelet transform and fractal dimension. The classification effect is compared with the previous RNA secondary structure representation methods. Experimental results show that the RNA secondary structure visualization method proposed in this paper has good application prospects in RNA secondary structure classification. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the effects of principal component analysis (PCA) on hyperspectral imagery denoising. Our previous work combined PCA with wavelet shrinkage and particularly good denoising results has been achieved. We debate that any denoising methods can be used to replace wavelet shrinkage in our PCA+wavelet shrinkage algorithm. The major difference between this work and our previous PCA-based denoising method is that we consider a mixture of Gaussian and shot noise in this work whereas our previous methods studied Gaussian white noise alone. In addition, we retain k 1 (k 1 < D) PCA output components in our forward PCA transform in this paper whereas we keep all PCA output components (k 1 = D) in our previous works. The D above is the number of spectral bands in the original hyperspectral imagery data cube. In addition, PCA is much better than nonlinear PCA for hyperspectral imagery denoising when Gaussian white noise and shot noise are introduced as demonstrated in this paper. Extensive experiments demonstrate that the method proposed in this paper outperforms the existing methods significantly in terms of signal-to-noise ratio for two testing hyperspectral imagery data cubes. [ABSTRACT FROM AUTHOR]

Measuring image visual quality is extremely important for many image processing tasks. In the past, several metrics have been proposed for measuring image visual quality such as structural similarity index (SSIM) and visual information fidelity (VIF). Nevertheless, these metrics are not robust to image spatial shifts when the reference and distorted images are misaligned by a few pixels. These metrics generate extremely low metric scores which is undesirable. It is well known that shifting the image by a few pixels does not affect the perceived image quality significantly. In this paper, we modify the SSIM metric to make it more robust to spatial shifts by pre-processing the input images with two-dimensional (2D) Fast Fourier Transform (FFT2). We then use the magnitudes of the Fourier coefficients in the existing metrics since these coefficients are shift-invariant. Experiments show that our proposed novel method is particularly good at measuring the visual quality of 2D images because it is far less complex than the existing methods and it offers better accuracy. Our new method is better than SSIM even when no spatial shifts are introduced to the images. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method to realize single image super resolution using a network composed of residual blocks with a cross architecture and wavelet transform. For the high quality of the reconstructed high resolution image, the brightness change must be sharp at the edge and gentle at the flat region. In single image super resolution, it is important to accurately predict the high-frequency components of the image. Hence, we propose a method to realize single image super resolution by estimating the high-frequency component in the wavelet domain using neural network composed of residual blocks with two crossing skip connections. [ABSTRACT FROM AUTHOR]

The phase retrieval (PR) problem is to reconstruct real/complex functions from the magnitudes of their Fourier/frame measurements in classical computational imaging. In this paper, we consider phase retrieval of complex vectors/images from the magnitudes of short-time fractional Fourier transform (STFrFT). In our setting, the above problem is solved by minimizing a least square ReLu loss function and a novel algorithm by alternating direction method of multipliers (ADMM) is presented. As shown in the numerical simulations on complex signals/images, our proposed PR-ADMM algorithm from STFrFT has a better recovery performance with flexible window functions and appropriate fractional orders. It demonstrates to have satisfactory performance from mixed phaseless STFrFT measurements. Compared with several six other main algorithms, the proposed algorithm explicitly recovers the phase of image with higher the peak signal-to-noise ratio. Meanwhile, the proposed algorithm is robust to noise. These also generalize some of about phase retrievals with Fourier measurements. [ABSTRACT FROM AUTHOR]

A new version of ambiguity function (AF) associated with the offset linear canonical transform (OLCT) is considered in this paper. This new version of AF coined as the k -AF associated with the OLCT (k -AFOL) is defined based on the OLCT and the fractional instantaneous auto-correlation. A natural magnification effect characterized by the extra degrees of freedom of the OLCT and by a factor k on the frequency axis enables the k -AFOL to have flexibility to be used in cross-term reduction. Firstly, we defined the k -AF associated with the OLCT (k -AFOL), and establish its relationship with the k -Wigner distribution in OLCT domain. Later on, we define the basic properties including the scaling, conjugate-symmetry, shifting, marginal and Moyal's formulae of k -AFOL in depth. The results show that k -AFOL can be viewed as one of the generalizations of the classical AF which has elegance, simplicity and flexibility in the frequency marginal property. The novelty of our paper lies in applications part, where we have shown how the proposed transform is used for the detection of single-component and bi-component linear frequency-modulated (LFM) signals. [ABSTRACT FROM AUTHOR]

In this paper, we propose an applicable algorithm of the so-called adaptive Fourier decomposition in H 2 (ℂ +) the Hardy H 2 space on the upper half-plane ℂ + , which provides a new method for decomposing real-valued signals and analytic signals on the real line. As a by-product, a new approach for computing the Hilbert transform on the real line is also given. Numerical experiments are used to demonstrate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Hyperspectral image (HSI) classification methods based on deep learning have demonstrated excellent performance, while these deep learning methods take a lot of time to train the parameters. In this paper, we propose a deep sparse representation (SR) network (DSRNet) without spending a lot of time training network parameters in the feature extraction stage. The contributions of this paper are three-fold. First, we introduce random dictionary into HSI classification, and solve sparse representation model under this dictionary. Second, we extend the shallow sparse representation model to the deep sparse representation model, where the SR model needs to be solved for each layer and used to extract the deep features of HSI. Finally, we investigate the classification performance of different classifiers on the deep features extracted by using DSRNet. Experimental results show that the proposed method can achieve better classification results compared with some closely related HSI classification methods and the other state-of-the-art deep learning methods. [ABSTRACT FROM AUTHOR]

Advanced driver assistance systems improve driving safety and comfort by applying onboard sensors to collect environmental data, analyze environmental data and decision making. Therefore, advanced driver assistance systems have high requirements for distance perception of the environment. Perceptual sensors commonly used in traditional solutions include stereo vision sensors and the Light Detection and Ranging (LiDAR) sensors. This paper proposes a multi-sensing sensor fusion method for disparity estimation, which combines the perceptual data density characteristics of stereo vision sensors and the measurement accuracy characteristics of LiDAR sensors. The method enhances the sensing accuracy by ensuring high-density sense, which is suitable for distance sensing tasks in complex environments. This paper demonstrates with experimental results on real data that our proposed disparity estimation method performs well and is robust in different scenarios. [ABSTRACT FROM AUTHOR]

Lower bound estimation plays an important role for establishing the minimax risk. A key step in lower bound estimation is deriving a lower bound of the affinity between two probability measures. This paper provides a simple method to estimate the affinity between mixture probability measures. Then we apply the lower bound of the affinity to establish the minimax lower bound for a family of sparse covariance matrices, which contains Cai–Ren–Zhou's theorem in [T. Cai, Z. Ren and H. Zhou, Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation, Electron. J. Stat. 10(1) (2016) 1–59] as a special example. [ABSTRACT FROM AUTHOR]

When we wanted to further investigate the results of Bourgain–Pavlović, Koch–Tataru and Li–Xiao–Yang, we encountered the problem of stability of the parameter flow. For initial data in some space X , norm inflation implies that the solution does not belong to C (X). For BMO − 1 , Auscher–Dubois–Tchamitchian proved that Koch–Tataru's solution is stable in their defined space C 0 . In this paper, we consider Koch–Tataru's iteration space and construct a non-Gauss flow function to show that C 0 -stability may have meaning different to L ∞ (( BMO − 1) n) , which supports Chemin and Gallagher's point: well-posedness and norm inflation may have no conflict. [ABSTRACT FROM AUTHOR]

In this paper, the inversion formula and the continuity of the continuous Bessel wavelet transform of distributions in D L 2 ′ - type space are investigated. For the uniqueness of the inversion formula, the Bessel wavelet kernel of nonvanishing moments is considered. [ABSTRACT FROM AUTHOR]

The outbreak of the global COVID-19 pandemic has become a public crisis and is threatening human life in every country. Recently, researchers have developed testing methods via patients cough recordings. In order to improve the testing accuracy, in this paper, we establish a novel COVID-19 sound-based diagnosis framework, i.e. TFA-CLSTMNN, which integrates time-frequency domain features of the recorded cough with the Attention-Convolution Long Short-Term Memory Neural Network. Specifically, we calculate the Mel-frequency cepstrum coefficient (MFCC) of the cough data to extract the time-frequency domain features. We then apply the convolutional neural network and the attentional mechanism on the time-frequency features, which is followed by the long short-term memory neural network to analyze the MFCC features of the data. The recognition and classification can be then carried out to evaluate the positiveness or negativeness of the tested samples. Experimental results show that the proposed TFA-CLSTMNN framework outperforms the baseline neural networks in sound-based COVID-19 diagnosis and derives an accuracy over 0.95 on the public real-world datasets. [ABSTRACT FROM AUTHOR]

In this paper, we consider the online regularized pairwise learning (ORPL) algorithm with least squares loss function for non-independently and identically distribution (non-i.i.d.) observations. We first establish new Bennett's inequalities for α -mixing sequence, geometrically β -mixing sequence, V -geometrically ergodic Markov chain and uniformly ergodic Markov chain. Then we establish the convergence rates for the last iterate of the ORPL algorithm with the polynomially decaying step sizes and varying regularization parameters for non-i.i.d. observations. These established results in this paper extend the previously known results of ORPL from i.i.d. observations to the case of non-i.i.d. observations, and the established result of ORPL for α -mixing can be nearly optimal rate of ORPL for i.i.d. observations with L 2 -norm. [ABSTRACT FROM AUTHOR]

In recent years, the concepts of frame in n -Hilbert space and K -frames in n -Hilbert space have been introduced. The K -frames in the n -Hilbert space are more generalized than the ordinary frames. This paper deals with the problem of sum of K -frames in n -Hilbert space. First, the sufficient condition for the finite sum of K -frames and Bessel sequences in n -Hilbert space is given. Then, some results on the operator K and pre-frame operator are given, and some new results on the sum of K -frame are proved. We then discuss several results for the perturbation and stability of the K -frames in n -Hilbert space about the sum of the K -frames. [ABSTRACT FROM AUTHOR]

In recent years, the field of speech enhancement has greatly benefited from the rapid development of neural networks. However, the requirement for large amounts of noisy and clean speech pairs for training limits the widespread use of these models. Wavelet network-based speech enhancement typically relies on clean speech signals as a training target. This paper presents a new method that combines a neural network with the wavelet theory for speech enhancement without the need for clean speech signals as targets in training mode. Five wide evaluation criteria, namely short-time objective intelligibility (STOI), signal-to-noise ratio (SNR), segmental signal-to-noise ratio (SNRseg), weighted spectral slope (WSS) and logarithmic spectral distance (LSD), have been used to confirm the effectiveness of the proposed method. The results show that the proposed method performs similar to a wavelet neural network (WNN) trained with clean signals, or even superior to those obtained from the clean target-based strategies. [ABSTRACT FROM AUTHOR]

In recent years, there has been an increasing interest in multi-view subspace clustering (MSC). However, existing MSC methods fail to take full advantage of the local geometric structure in each manifold throughout the data flow, which is essential for clustering. To remedy this drawback, in this paper, a novel Double Graphs Regularized Multi-view Subspace Clustering (DGRMSC) method is proposed, which aims to harness both global and local structural information of multi-view data in a unified framework. Specifically, DGRMSC first learns a latent representation to exploit the global complementary information of multiple views. Based on the learned latent representation, we learn a self-representation to explore its global cluster structure. Further, Double Graphs Regularization (DGR) is performed on both latent representation and self-representation to take advantage of their local manifold structures simultaneously. Then, we design an iterative algorithm to solve the optimization problem effectively. Comprehensive experiments on several popular multi-view datasets demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

As we know, feedforward neural networks (FNNs) with sigmoidal activation function are universal approximators. Theoretically, for any continuous function defined on a compact set, there exists an FNN such that the FNN can approximate the function with arbitrary accuracy, which constitutes a theoretical guarantee that FNN can be used as an efficient learning machine. This paper addresses the construction and approximation for FNNs. We construct an FNN with sigmoidal activation function and estimate its approximation error. In particular, an inverse theorem of the approximation is established, which implies the equivalence characterization theorem of the approximation and reveals the relationship between the topological structure of the FNN and its approximation ability. As keys in this study, the concepts of modulus of continuity of function, K-functional, and their relationship are utilized, and two Bernstein-type inequalities are established. [ABSTRACT FROM AUTHOR]

Federated learning (FL) is an important approach to cooperate with multiple devices for learning without exchanging data between devices and central server. However, due to bandwidth and other reasons, the communication efficiency should be considered when the volume of information transmitted is limited. In this paper, we utilize the tool of lattice quantization form quantization theory and the variable intercommunication interval to improve communication efficiency. Meanwhile, to make strong privacy guarantee, we incorporate the notion of differential privacy (DP) to the FL framework with local SGD algorithm. By adding calibrated noises, we propose a universal lattice quantization for differentially private federated averaging algorithm (ULQ-DP-FedAvg). We provide tight privacy bound by using some privacy techniques. We also analyze the convergence bound of ULQ-DP-FedAvg based on bits rate constraints and the growing inter-communication interval as well as the data are non-independent identically distribution (Non-IID). It turns out that the algorithm converges and preserves that the privacy has scarcely influenced on the convergence rate. The effectiveness of our algorithm is demonstrated by synthetic and real datasets. [ABSTRACT FROM AUTHOR]

Aquila optimizer (AO) is an efficient meta-heuristic optimization method, which mimics the hunting style of Aquila in nature. However, the AO algorithm may suffer from immature convergence during the exploitation stage. In this paper, two strategies are elegantly employed into conventional AO, such as random opposition-based learning and nonlinear flexible jumping factor, which can efficiently enhance the performance of conventional AO. Experiments on 1 7 benchmark functions and image segmentation demonstrate the effectiveness of the proposed algorithm. Comparison with several state-of-the-art meta-heuristic optimization techniques indicates the efficacy of the developed method. [ABSTRACT FROM AUTHOR]

In Blind Hyperspectral Unmixing, the accuracy of the estimated number of endmembers affects the succeeding steps of extraction of endmember signatures and acquiring their fractional abundances. The characteristics of endmember signature depend on the nature of the material on the ground and share similar characteristics for variants of the same material. In this paper, we introduce a new concept of sub-endmembers to identify similar materials that are variants of a global endmember. Identifying the sub-endmembers will provide a meaningful interpretation of the endmember variability along with increased unmixing accuracy. This paper proposes a new algorithm exploiting both the spatial and spectral information present in hyperspectral data. The hyperspectral data are segmented into homogenous regions (superpixels) based on the Simple Linear Iterative Clustering (SLIC) algorithm, and the mean spectral of each region is accounted for in finding the global endmembers. The difference of eigenvalues-based thresholding method is used to find the number of global and sub-endmembers. The method has been tested on synthetic and real hyperspectral data and has successfully estimated the number of global endmembers as well as sub-endmembers. The method is also compared with other state-of-the-art methods, and better performances are obtained at a reasonably lower computational complexity. [ABSTRACT FROM AUTHOR]

In this paper, we will present several new results in finite and countable dimensional separable real Hilbert space phase retrieval and norm retrieval by fusion frames. We will characterize of norm retrieval for fusion frames similar norm retrieval for vectors and we will show that only one direction holds for fusion frames. In similar vector case, we will show that every tight fusion frame can do norm retrieval. Also we will show that the unitary operators preserve phase (norm) retrievability of fusion frames. We will make a detailed study of when hyperplanes do norm retrieval and show a general result about it. We will provide numerous examples to show that our results are best possible. [ABSTRACT FROM AUTHOR]

Explicitly using the block structure of the unknown signal can achieve better reconstruction performance in compressive sensing. An unknown signal with block structure can be accurately recovered from under-determined linear measurements provided that it is sufficiently block sparse. However, in practice, the block sparsity level is typically unknown. In this paper, we propose a soft measure of block sparsity k α (x) = (∥ x ∥ 2 , α / ∥ x ∥ 2 , 1) α 1 − α with α ∈ [ 0 , ∞ ] , and present a procedure to estimate it by using multivariate centered isotropic symmetric α -stable random projections. The limiting distribution of the estimator is given. Simulations are conducted to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study exponential tractability of multivariate approximation problem for Hermite spaces of analytic functions over ℝ d in the worst case setting. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. The considered algorithms based on tensor products of Gauss–Hermite rules for multivariate integration are constructive and use the class Λ std of only function evaluations. We give matching necessary and sufficient conditions for notions of EC-quasi-polynomial tractability and EC-uniform weak tractability in terms of two weight parameters of the problem. [ABSTRACT FROM AUTHOR]

Hyperspectral image (HSI) classification is an important topic in remote sensing. In this paper, we propose a new method for HSI classification by using minimum noise fraction (MNF), spatial filtering (SF) and support vector machine (SVM). We use MNF to reduce the dimensionality of a hyperspectral data cube before performing classification. We apply 2D SF to the DR output band images and then use SVM to classify the pixels of the data cube. In this way, both spatial information and spectral information are taken into consideration in the classification. Experimental results show that our MNF+SF method is extremely competitive when compared to several existing classification methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider a special relativistic space-time Fourier transform (SFT) in Clifford algebra Cl (3 , 1) , which was introduced recently from a mathematical point of view by E. Hitzer. Two versions of real Paley–Wiener theorems for the SFT are established. [ABSTRACT FROM AUTHOR]

This paper considers the minimax estimation of the high-dimensional sparse covariance matrices in the presence of missing observations. Based on random missing data, the upper bounds of convergence rate about the data-driven thresholding estimator are constructed over a large class of sparse covariance matrices under the l 1 norm and the Frobenius norm. In addition, we use Le Cam's lemma and the relation between the total variation affinity and the Kullback–Leibler divergence to establish the lower bounds which illustrate the desired upper bounds cannot be improved. It is worth mentioning that the approach we adopt to get the lower bounds is simpler than the existing ones. [ABSTRACT FROM AUTHOR]

The properties of activation functions profoundly affect the approximation performance of neural networks. It is always one of the most important tasks to find proper activation functions in approximation by neural networks for some specific purpose. In this paper, we introduce a new activation function which is generated by the Joukowski transformation, and construct some new neural network operators activated by the new activation function. We show that the new neural network operators can be used to approximate the continuous functions on some compact sets. In fact, we give the approximation rate by using the modulus of continuity of the objective function (see Theorem 1). Finally, we provide some specific numerical examples to verify the fitting effects of the neural network operators with different parameters for continuous functions. [ABSTRACT FROM AUTHOR]

In this paper, the boundedness and compactness of the Hankel wavelet multiplier associated with the unitary representation on Lp space for 1 ≤ p ≤∞, are obtained by using the Hankel transform technique. The application of Hankel wavelet multipliers in form of the Landau–Pollak–Slepian operator is given. With the help of the Hankel wavelet multiplier, the Sobolev space associated with the Hankel transform is constructed and its various properties are studied. [ABSTRACT FROM AUTHOR]

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 ∈ SL(2, ℝ). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 L2(ℝ) 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm is discussed for constructing the two-direction Armlet multiwavelet. First, the definition of two-direction Armlet multiwavelet is presented in this paper. A two-direction multiwavelet can be changed to a special multi-wavelet. By Two-scale Similar Transform (TST), a transform can be taken on the two-scale matrix symbols of a two-direction multi-wavelets. This transform keeps the orthogonality of the two-direction multi-wavelets. However, the condition is discussed which the two-direction multi-wavelet corresponding to a two-direction multi-scaling function is an Armlet with order n. An approach is given for constructing the transform matrix. Finally, an example is given for discussing the two-direction Armlet multi-wavelet with order 2. [ABSTRACT FROM AUTHOR]

The generalization is one of the main concerns of machine learning method. k-SVCR is an important multi-class classification algorithm, but there is no theoretical analysis on the generalization of k-SVCR algorithm up to now. Therefore, in this paper, we consider multi-class support vector classification and regression (MSVCR) algorithm. We first establish the generalization bounds of MSVCR based on uniformly ergodic Markovian chain (u.e.M.c.) samples, and obtain its fast learning rate of MSVCR. As applications, we estimate the generalization of MSVCR for independent and identically distributed (i.i.d.) observations and strongly mixing observations, respectively. We also propose a new MSVCR algorithm based on q-times Markovian resampling (MSVCR-Mar-q). The experimental studies indicate that compared to the classical k-SVCR and other multi-class SVM algorithms, the proposed algorithm not only has smaller misclassification rate, but also has less sampling and training total time. [ABSTRACT FROM AUTHOR]

Observing student body gesture has been widely used to assess teaching effectiveness over the past few decades. However, manual observation is not suitable for the automatic data analysis in the field of learning analytics. Consequently, a student body gesture recognition method based on Fisher Broad Learning System (FBLS) and Local Log-Euclidean Multivariate Gaussian (L2EMG) is proposed in this paper. FBLS is designed by introducing the discriminative information into the hidden layer of Broad Learning System (BLS) and reducing the dimensionality of hidden-layer representations. FBLS has superiorities in accuracy and speed. In addition, L2EMG, which is a highly distinctive descriptor, characterizes the local image with a multivariate Gaussian distribution. So L2EMG features are fed into the FBLS for recognition in this paper. Extensive experimental results on self-built dataset show that the proposed student body gesture recognition method obtains better results than other benchmarking methods. [ABSTRACT FROM AUTHOR]

Tremendous efficient optimization methods have been proposed for strongly convex objectives optimization in modern machine learning. For non-strongly convex objectives, a popular approach is to apply a reduction from non-strongly convex to a strongly convex case via regularization techniques. Reduction on objectives with adaptive decrease on regularization tightens the optimal convergence of algorithms to be independent on logarithm factor. However, the initialization of parameter of regularization has a great impact on the performance of the reduction. In this paper, we propose an aggressive reduction to reduce the complexity of optimization for non-strongly convex objectives, and our reduction eliminates the impact of the initialization of parameter on the convergent performances of algorithms. Aggressive reduction not only adaptively decreases the regularization parameter, but also modifies regularization term as the distance between current point and the approximate minimizer. Our aggressive reduction can also shave off the non-optimal logarithm term theoretically, and make the convergent performance of algorithm more compact practically. Experimental results on logistic regression and image deblurring confirm this success in practice. [ABSTRACT FROM AUTHOR]

Let v 1 , v 2 be vertices of a graph G with degree of the vertices being d (v 1) and d (v 2) , respectively. First, let us define the weight of the edge v 1 v 2 as twice the value of 1 d (v 1) + d (v 2) in G. Let us define H (G) , the harmonic index of the graph G , as the sum obtained by adding the weight assigned to every edge of G. In this paper, for the class of trees, we shall obtain an upper bound for the harmonic index H (G) in terms of the edge-vertex domination number and the order of G. Also, we shall ascertain that the equality is true by characterizing the collection of all extremal trees attaining this bound. [ABSTRACT FROM AUTHOR]