International Journal of Wavelets, Multiresolution and Information Processing

In this paper, we bring forward a completely perturbed nuclear norm minimization method to tackle a formulation of completely perturbed low-rank matrices recovery. In view of the matrix version of the restricted isometry property (RIP) and the Frobenius-robust rank null space property (FRNSP), this paper extends the investigation to a completely perturbed model taking into consideration not only noise but also perturbation, derives sufficient conditions guaranteeing that low-rank matrices can be robustly and stably reconstructed under the completely perturbed scenario, as well as finally presents an upper bound estimation of recovery error. The upper bound estimation can be described by two terms, one concerning the total noise, and another regarding the best $r$-approximation error. Specially, we not only improve the condition corresponding with RIP, but also ameliorate the upper bound estimation in case the results reduce to the general case. Furthermore, in the case of ${ℰ}=0$, the obtained conditions are optimal.

The detection and classification of underwater targets such as fish are one of the major tasks of the underwater acoustic signal processing and are very important for scientific, fisheries and ocean engineering and economic fields. The convolutional neural network (CNN) combined with the discrete wavelet transform (DWT) (namely CNN_DWT) not only reduces the data processing dimension of signals and the computational costs of the signal analysis, but also improves the performance of target detection and classification. This paper proposes a new CNN to classify the images that reflected the underwater acoustic signal in the database that is made up of the scalogram of underwater acoustic signals. Also, in order to attain greater accuracy and comparable efficiency to the spatial domain processing, we convert the data to the wavelet domain. Also, we propose a deep learning method for the classification of underwater acoustic signals using the new CNN combined with DWT. Next, through the simulation experiment, we evaluate our new method for underwater acoustic signal classification using the CNN combined with DWT, by comparing with classical methods. Comparing the proposed method to spatial domain CNN and classical methods, the experimental results reveal a substantial increment in classification accuracy and noise robustness. And the learning curves show that the proposed CNN_DWT does not generate the overfitting problem and its generalization ability is high. The proposed CNN_DWT improves the classification accuracy and convergence of underwater acoustic signals than the classical CNNs. The noise robustness of the proposed CNN_DWT is higher than those of classical CNNs and back-propagation neural networks (BPNNs) for the classification of underwater acoustic signals. Experimental results show that the classification performance of new CNN combined with DWT is higher than those of classical CNNs and BPNNs for the classification of underwater acoustic signals.

With the advent of the Internet of Things (IoT), the security of the network layer in IoT is getting more attention in recent decades. Various intrusion detection methods were developed in the existing research works, but the capability to detect malicious and intrusion activities in the complex Internet environment poses a challenging task in IoT. Hence, an effective and optimal intrusion detection mechanism, named Harmony Search Hawks Optimization-based Deep Reinforcement Learning (HSHO-based Deep RL), is proposed in this research to detect malicious network activities. The proposed Harmony Search Hawks Optimization (HSHO) algorithm is designed by integrating Harmony Search (HS) with the Harris Hawks Optimization (HHO) algorithm. However, the optimal detection result that is effectively achieved through the fitness measures such that the minimum fitness value is only declared as the optimal solution. The Deep Reinforcement Learning (Deep RL) classifier effectively detects the malicious or intruder behaviors and generates a satisfactory result. By reducing the dimensionality of data using nonnegative matrix factorization, the data is optimally fit to perform intrusion detection process in the IoT environment. The proposed HSHO-based Deep RL obtained better performance in terms of the metrics like accuracy (96.925%), True Positive Rate (TPR; 96.90%), and True Negative Rate (TNR; 97.920%) with respect to $K$-fold.

This paper deals with the study of the localization operators associated with the $q$-Bessel wavelet transform. First, we develop the notion of two $q$-Bessel wavelets. Second, motivated by Wong’s approach, we present in our setting, the general theory on the Schatten–von Neumann class, including the boundedness and compactness and Schatten class properties. Next, we prove under suitable conditions on the symbols and two $q$-Bessel wavelets, the boundedness and compactness of these localization operators on $L_{\nu ,q}^p({ℝ}_q^{+})$, $1\le p\le \infty$. We culminate our study by formulating typical examples of localization operators.

We study the efficiency of the Weak Rescaled Pure Greedy Algorithm (WRPGA) with respect to a dictionary in a Hilbert space or more generally a Banach space. We obtain the sufficient and necessary conditions for the convergence of WRPGA for any element and any dictionary. This condition is weaker than the sufficient conditions for convergence of the Weak Pure Greedy Algorithm (WPGA). In addition, we establish the noisy version of the error estimate for the WRPGA, which implies the results on sparse classes obtained in [G. Petrova, Rescaled pure greedy algorithm for Hlibert and Banach spaces, Appl. Comput. Harmon. Anal. 41(3) (2016) 852–866].

The aim of this paper is to derive the uncertainty principle which has implications in signal analysis and in quantum mechanics. First, we derive the definition of the wavelet transform in $q$-calculus by using some weight function. Certain properties like linearity, scaling, translation, etc. were discussed. Later on, to illustrate this integral transform several results were derived for the effectiveness and performance of the proposed method. Also, this paper surveys recent applications to establish generalized uncertainty principle.

With the rapid development of computer technology, building pose estimation combined with Augmented Reality (AR) can play a crucial role in the field of urban planning and architectural design. For example, a virtual building model can be placed into a realistic scenario acquired by a Unmanned Aerial Vehicle (UAV)to visually observe whether the building can integrate well with its surroundings, thus optimizing the design of the building. In the work, we contribute a building dataset for pose estimation named BD3D. To obtain accurate building pose, we use a physical camera which can simulate realistic cameras in Unity3D to simulate UAVs perspective and use virtual building models as objects. We propose a novel neural network that combines MultiBin module with PoseNet architecture to estimate the building pose. Sometimes, the building is symmetry and ambiguity causes its different surfaces to have similar features, making it difficult for CNNs to learn the differential features between the different surfaces. We propose a generalized world coordinate system repositioning strategy to deal with it. We evaluate our network with the strategy on BD3D, and the angle error is reduced to $3^{\circ }$ from $45^{\circ }$. Code and dataset have been made available at: https://github.com/JellyFive/Building-pose-estimation-from-the-perspective-of-UAVs-based-on-CNNs.

In linear regression, outliers have a serious effect on the estimation of regression model parameters and the prediction of final results, so outlier detection is one of the key steps in data analysis. In this paper, we use a mean shift model and then we apply the penalty function to penalize the mean shift parameters, which is conducive to get a sparse parameter vector. We choose Sorted L1 regularization (SLOPE), which provides a convex loss function, and shows good statistical properties in parameter selection. We apply an iterative process which using gradient descent method and parameter selection at each step. Our algorithm has higher computational efficiency since the calculation of inverse matrix is avoided. Finally, we use Cross-Validation rules (CV) and Bayesian Information Criterion (BIC) criteria to fine tune the parameters, which helps our program identify outliers and obtain more robust regression coefficients. Compared with other methods, the experimental results show that our program has a fantastic performance in all aspects of outlier detection.

Digital signals are often modeled as functions in Banach spaces, such as the ubiquitous $Lp$ spaces. The frame theory in Banach spaces induces flexible representations of signals due to the robustness and redundancy of frames. Nevertheless, the lack of inner product in general Banach spaces limits the direct representations of signals in Banach spaces under a given basis or frame. In this paper, we introduce the concept of semi-inner product (SIP) $(p,q)$-Bessel multipliers to extend the flexibility of signal representations in separable Banach spaces, where $\frac{1}{p}+\frac{1}{q}=1,1<p<+\infty$. These multipliers are defined as composition of analysis operator of an SIP-I Bessel sequence, a multiplication with a fixed sequence and synthesis operator of an SIP-II Bessel sequence. The basic properties of the SIP $(p,q)$-Bessel multipliers are investigated. Moreover, as special cases, characterizations of $q$-Riesz bases related to signal representations are given, and the multipliers for $q$-Riesz bases are discussed. We show that SIP $(p,q)$-Bessel multipliers for $q$-Riesz bases are invertible. Finally, the continuity of SIP $(p,q)$-Bessel multipliers with respect to their parameters is investigated. The results theoretically show that the SIP $(p,q)$-Bessel multipliers offer a larger range of freedom than frames on signal representations in Banach spaces.

We show that for every nonzero vector $\varphi$ in ${ℂ}^N$, the discrete wave packet system ${\{D_a{M}_l{T}_k\varphi \}}_{a\in U(N),l,k\in {𝕀}_N}$ constitutes a frame for the unitary space ${ℂ}^N$. An application of this result is given, where frame conditions cannot be derived from discrete wavelet systems in ${ℂ}^{\mathbb{N}}$. The canonical dual of discrete wave packet frame is also discussed.

Domain adaption is a special transfer learning method, whose source domain and target domain generally have different data distribution, but need to complete the same task. There have been many significant types of research on domain adaptation in 2D images, but in 3D data processing, domain adaptation is still in its infancy. Therefore, we design a novel domain adaptive network to complete the unsupervised point cloud classification task. Specifically, we propose a multi-scale transform module to improve the feature extractor. Besides, a spatial-awareness attention module combined with channel attention to assign weights to each node is designed to represent hierarchically scaled features. We have validated the proposed method on the PointDA-10 dataset for domain adaption classification tasks. Empirically, it shows strong performance on par or even better than state-of-the-art.

In this paper, an efficient numerical method is proposed to handle two-dimensional fractional diffusion equations on a finite domain. The proposed method combines the product of Legendre wavelet bases for two spatial dimensions and a time direction. The operational matrix of the proposed method is obtained. Tikhonov regularization is employed to stabilize the system in cases where the final linear system of equations is large. The convergence analysis of the method is studied and some numerical examples are presented to investigate the efficiency and accuracy of the method.