International Journal of Wavelets, Multiresolution and Information Processing

In this paper, we show that B-spline quarks and the associated quarklets fit into the theory of biorthogonal multiwavelets. Quark vectors are used to define sequences of subspaces $V_{p,j}$ of $L_2(ℝ)$ which fulfill almost all conditions of a multiresolution analysis. Under some special conditions on the parameters, they even satisfy all those properties. Moreover, we prove that quarks and quarklets possess modulation matrices which fulfill the perfect reconstruction condition. Furthermore, we show the existence of generalized dual quarks and quarklets which are known to be at least compactly supported tempered distributions from ${\mathrm{\text{S}}}^{\prime }(ℝ)$. Finally, we also verify that quarks and quarklets can be used to define sequences of subspaces $W_{p,j}$ of $L_2(ℝ)$ that yield non-orthogonal decompositions of $L_2(ℝ)$.

The accuracy of feature-based vision algorithms, including the self-calibration of binocular camera extrinsic parameters used in autonomous driving environment perception techniques relies heavily on the quality of the features extracted from the images. This study investigates the influence of the depth distance between objects and the camera, the feature points in different object regions, and the feature points in dynamic object regions on the self-calibration of binocular camera extrinsic parameters. To achieve this, the study first filters out different types of objects in the image through semantic segmentation. Then, it identifies the areas of dynamic objects and extracts the feature points in the static object region for the self-calibration of binocular camera extrinsic parameters. By calculating the baseline error of the binocular camera and the row alignment error of the matching feature points, this study evaluates the influence of feature points in dynamic object regions, feature points in different object regions, and feature points at different distances on the self-calibration algorithm. The experimental results demonstrate that feature points at static objects close to the camera are beneficial for the self-calibration of extrinsic parameters of binocular camera.

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.

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.

In today’s era, video analysis is immensely involved in recognizing the sport-related movement that has become a significant part of human’s life. The intent of this approach is to know about the player’s activities with prior information of tracking objects. It also analyzes the player potential or capacity to lead the winning team. When the player frequently changes their location, object tracking and action recognition will become a quite challenging task. Over the game, various athletes or different objects are considered to assist the system to easily recognize the respective actions of the player. Most of the previous models have been implemented, yet, it faces such consequences to provide promising performance. To meet the pre-requisite, a new multi-athlete tracking model for action recognition in soccer sports is designed with deep learning approaches. Initially, the multi-object tracking video is offered as the input to pre-processing phase. Here, occlusion and background clutter removal and contrast enhancement techniques are utilized to perform pre-processing in the videos. Then, the pre-processed video is offered to the multi-object tracking phase, where the jersey number is observed during multi-object tracking to avoid the identity switch problem. Then, effective multi-object tracking is performed by adaptive YOLOv5. The parameters presented in the improved adaptive YOLOv5 are tuned by proposing a new algorithm as the Random-based Cheetah Red Deer Algorithm (RCRDA). Next, in the action recognition phase, the tracked object from the video is taken based on the Region of Interest (ROI) that is subjected to an action recognition model named Optimized Transformer-based Residual Network with Deep Convolutional Network (OTRN-DCN). At first, ROI is offered as the input to TRN for attaining the feature vectors. Then, the optimal weighted vector extraction is performed, where the weight is tuned by the developed RCRDA. Finally, the attained optimally weighted vectors are given to the DCN phase for attaining recognized action as output. Hence, the developed multi-object tracking and action recognition model will secure an improved recognition rate than the traditional framework.

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.

This study gives a kind of sharp Wirtinger inequalities (Pizone inequalities)

Pan-sharpening is a procedure to fuse the spatial detail of high-resolution multispectral images (HR-MSI) and low-resolution hyperspectral images (LR-HSI) to produce HR-MSI. Due to increase in high-resolution satellites, methods based on pan-sharpening are increasingly utilized all over the world. However, the majority of techniques consider pan-sharpening as a major issue, which hinders the discriminative ability. This work proposes an optimization-based deep model for pan-sharpening using LR-HSI and HR-MSI. Initially, the LR-HSI is input into an up-sampling mode, and the resulting image is fed into weighted linear regression. Concurrently, HR-MSI is supplied into weighted linear regression. Weighted linear regression is used to combine the upsampled LR-HSI and HR-MSI. The HR-MSI is then sent into the Deep Maxout network (DMN), which learns the priors via residual learning. Furthermore, the suggested Competitive Multi-Verse Feedback Artificial Tree (CMVFTA) strategy is used for DMN training, which is constructed by combining the Competitive Multi-Verse Optimizer (CMVO) and Feedback Artificial Tree (FAT) approaches. Finally, the DMN, LR-HSI, and HR-MSI outputs are merged together to provide a pan-sharpening image. The proposed CMVFTA-based DMN offered enhanced performance with Degree of Distortion (DD) of 0.0402 dB, Peak signal-to-noise ratio (PSNR) of 49.60 dB, Root Mean Squared Error (RMSE) of 0.330, Relative Average Spectral Error (RASE) of 0.322, Filtered Correlation Coefficients (FCC) of 0.874, Quality with no reference (QNR) of 76.19.

Positive instances are often significantly less than negative instances in real-world classification problems. However, positive categories are typically more relevant to the primary focus of categorization tasks. Moreover, obtaining labeled data is often expensive, and the majority of real-life data is unlabeled. Therefore, semi-supervised learning has become a popular approach for addressing imbalanced problems. Traditional support vector machines (SVMs) treat all samples equally and are not suitable for semi-supervised learning. To address this issue, a semi-supervised model called the fuzzy semi-supervised SVM (FS³VM) has been proposed. The FS³VM model uses the degree of entropy-based fuzzy membership to ensure the materiality of positive classes by assigning positive instances to relatively large degrees of fuzzy membership. After introducing the mainstream FS³VM model, the fundamental theory and methods of the model are discussed and expanded upon, including the FS³VM algorithm, which applies the Sequential Minimal Optimization (SMO) algorithm to the dual problem. The proposed FS³VM model is a smooth and continuous optimization problem, and its dual is a standard quadratic programming. Experimental results demonstrate that the proposed FS³VM model outperforms other compared learning algorithms.

Partially linear additive models (PLAMs) have attracted much attention in the statistical machine learning community due to their interpretability and flexibility in data-driven prediction and inference. Since the performance of PLAMs is closely related to the structure information of linear and nonlinear components, several approaches have been proposed for regression estimation and data-driven structure discovery. However, the existing automatic discovery strategy is limited to the mean regression framework and is usually sensitive to non-Gaussian noises, e.g. skewed noise and heavy-tailed noise. To further improve the robustness of PLAMs, this paper proposes a Robust Partially Linear Trend Filtering (RPLTF) for regression estimation and structure discovery by integrating the mode-induced error metric and the trend filtering-based nonlinear approximation into regularized PLAMs. Besides the computing algorithm of RPLTF, we establish its upper bound on generalization error in theory. Empirical examples are provided to validate the effectiveness of the proposed method.