Search Results (220)

This paper focuses on two-dimensional (2-D) direction-of-arrival (DOA) estimation for an L-shaped array. While recent studies have explored sparse methods for this problem, most exploit only the cross-correlation matrix, neglecting self-correlation information and resulting accuracy degradation. We propose a multidimensional matrix completion method that employs joint sparsity and redundant correlation information embedded in the covariance matrix to reconstruct a structured matrix compactly coupling the two DOA parameters. A semidefinite program problem formulated via covariance fitting criteria is proved equivalent to the atomic norm minimization framework. The alternating direction method of multipliers is designed to reduce computational costs. Numerical results corroborate the analysis and demonstrate the superior estimation accuracy, identifiability, and resolution of the proposed method. Full article

The growing importance of social networks has led to increased research into trust estimation and interpretation among network entities. It is important to predict the trust score between users in order to minimize the risks in user interactions. This article enables the identification of the most reliable and least reliable entities in a network by expressing trust scores numerically. In this paper, the social network is modeled as a graph, and trust scores are calculated by taking the powers of the ratio matrix between entities and summing them. Taking the power of the proportion matrix based on the number of entities in the network requires a lot of arithmetic load. After taking the powers of the eigenvalues of the ratio matrix, these are multiplied by the eigenvector matrix to obtain the power of the ratio matrix. In this way, the arithmetic cost required for calculating trust between entities is reduced. This paper calculates the trust score between entities using linear algebra techniques to reduce the arithmetic load. Trust detection algorithms use shortest paths and similar methods to eliminate paths that are deemed unimportant, which makes the result questionable because of the loss of data. The novelty of this method is that it calculates the trust score without the need for explicit path numbering and without any data loss. Full article

Recently, a growing number of researchers have focused on multi-view subspace clustering (MSC) due to its potential for integrating heterogeneous data. However, current MSC methods remain challenged by limited robustness and insufficient exploitation of cross-view high-order latent information for clustering advancement. To address these challenges, we develop a novel MSC framework termed TMSC-TNNBDR, a tensorized MSC framework that leverages t-SVD based tensor nuclear norm (TNN) regularization and block diagonal representation (BDR) learning to unify view consistency and structural sparsity. Specifically, each subspace representation matrix is constrained by a block diagonal regularizer to enforce cluster structure, while all matrices are aggregated into a tensor to capture high-order interactions. To efficiently optimize the model, we developed an optimization algorithm based on the inexact augmented Lagrange multiplier (ALM). The TMSC-TNNBDR exhibits both optimized block-diagonal structure and low-rank properties, thereby enabling enhanced mining of latent higher-order inter-view correlations while demonstrating greater resilience to noise. To investigate the capability of TMSC-TNNBDR, we conducted several experiments on certain datasets. Benchmarking on circumscribed datasets demonstrates our method’s superior clustering performance over comparative algorithms while maintaining competitive computational overhead. Full article

Current depth map sensing technologies capture depth maps at low spatial resolution, rendering serious problems in various applications. In this paper, we propose a single depth map super-resolution method that combines the advantages of model-based methods and deep learning approaches. Specifically, we formulate a linear inverse problem which we solve by introducing a graph Laplacian regularizer. The regularization approach promotes smoothness and preserves the structural details of the observed depth map. We construct the graph Laplacian matrix by deploying latent features obtained from a pretrained deep learning model. The problem is solved with the Alternating Direction Method of Multipliers (ADMM). Experimental results show that the proposed approach outperforms existing optimization-based and deep learning solutions. Full article

Tempered fractional diffusion equations constitute a critical class of partial differential equations with broad applications across multiple physical domains. In this paper, the Crank–Nicolson method and the tempered weighted and shifted Grünwald formula are used to discretize the tempered fractional diffusion equations. The discretized system has the structure of the sum of the identity matrix and a diagonal matrix multiplied by a symmetric positive definite (SPD) Toeplitz matrix. For the discretized system, we propose a structure approximation-based preconditioning method. The structure approximation lies in two aspects: the inverse approximation based on the row-by-row strategy and the SPD Toeplitz approximation by the $\tau$ matrix. The proposed preconditioning method can be efficiently implemented using the discrete sine transform (DST). In spectral analysis, it is found that the eigenvalues of the preconditioned coefficient matrix are clustered around 1, ensuring fast convergence of Krylov subspace methods with the new preconditioner. Numerical experiments demonstrate the effectiveness of the proposed preconditioner. Full article

Frequency agile radar (FAR) exhibits robust anti-jamming capabilities and a superior low probability of intercept performance due to its randomized carrier frequency (CF) and pulse repetition frequency (PRF) hopping sequences. The advent of compressed sensing (CS) theory has effectively addressed the coherent processing challenges of frequency agile signals. Nonetheless, the reconstructed results often suffer from elevated sidelobe levels, which lead to significant sparse recovery errors. The performance of sparse reconstruction is greatly influenced by the correlation between the dictionary matrix columns. Specifically, weaker correlation usually means better target detection performance and lower false alarm probability. Consequently, this paper adopts the maximum coherence coefficient (MCC) between the dictionary matrix columns as the cost function. In addition, in order to reduce the correlation of the dictionary matrix and improve the target detection performance, a genetic algorithm (GA) is employed to jointly optimize the CF hopping coefficients and PRFs of the FAR. The echo of optimized signals is subsequently reconstructed using the alternating direction method of multipliers (ADMM) algorithm. Simulation results demonstrate the effectiveness of the proposal. Full article

Existing forest height estimation methods based on polarimetric interferometric synthetic aperture radar (PolInSAR) typically process each pixel independently, potentially introducing inconsistent estimates and additional decorrelation in the covariance matrix estimation. To address these limitations and effectively exploit the spatial context information, this paper proposes the first patch-based inversion method named joint pixel optimization inversion (JPO). By leveraging the smoothness and regularity of homogeneous pixels, a joint-pixel optimization problem is constructed, incorporating a first-order regularization on the ground phase. To solve the non-parallelizable problem of the alternating direction method of multipliers (ADMM), we devise a new parallelizable ADMM algorithm and prove its sublinear convergence. With the contextual information of neighboring pixels, JPO can provide more reliable forest height estimation and reduce the overestimation caused by additional decorrelation. The effectiveness of the proposed method is verified using spaceborne L-band repeat-pass SAOCOM acquisitions and LiDAR heights obtained from ICESat-2. Quantitative evaluations in forest height estimation show that the proposed method achieves a lower mean error (1.23 m) and RMSE (3.67 m) than the existing method (mean error: 3.09 m; RMSE: 4.70 m), demonstrating its improved reliability. Full article

In the Moon–Earth elliptic restricted three-body problem, near-polar and near-circular lunar-type periodic orbits are numerically continued from Keplerian circular orbits using Broyden’s method with line search. The Hamiltonian system, expressed in Cartesian coordinates, is treated via the symplectic scaling method. The radii of the initial Keplerian circular orbits are then scaled and normalized. For cases in which the integer ratios $\{j/k\}$ of the mean motions between the inner and outer orbits are within the range $[9,150]$, some periodic orbits of the elliptic restricted three-body problem are investigated. For the middle-altitude cases with $j/k\in [38,70]$, the perturbations due to $J_2$ and $C_{22}$ are incorporated, and some new near-polar periodic orbits are computed. The orbital dynamics of these near-polar, near-circular periodic orbits are well characterized by the first-order double-averaged system in the Poincaré–Delaunay elements. Linear stability is assessed through characteristic multipliers derived from the fundamental solution matrix of the linear varational system. Stability indices are computed for both the near-polar and planar near-circular periodic orbits across the range $j/k\in [9,50]$. Full article

Toom–Cook-n multiplication is an efficient large-width multiplication algorithm based on a divide-and-conquer strategy, widely used in modular multiplication operations for cryptographic algorithms. Theoretically, as the degree n increases, Toom–Cook-n can split the multiplicands into more sub-terms to further enhance the performance of the multiplier. However, constrained by the computational burden brought by the growing size of the interpolation matrix as the degree increases, current research predominantly focuses on Toom–Cook-4 and Toom–Cook-3. This paper proposes a Montgomery modular multiplication design based on Toom–Cook-5, which alleviates the computational difficulty of the interpolation step by introducing an interpolation matrix pre-simplification strategy. Additionally, the design incorporates and optimizes carry–save adder and Karatsuba multiplication, enabling Toom–Cook-5 multiplication to be applied in practical and efficient hardware implementation. This paper presents the ASIC implementation results of the hardware architecture under a 90nm process, demonstrating superior performance compared to previous works. Full article

Vector–matrix multiplication (VMM), which dominates the computational workload in neural networks, accounts for over 99% of all operations, particularly in Convolutional Neural Networks (CNNs). These operations, consisting of multiply-and-accumulate (MAC) functions, are straightforward but demand massive parallelism, often involving billions of operations per layer. This computational demand negatively affects processing time, energy consumption, and memory bandwidth due to frequent external memory access. To efficiently address these challenges, this paper investigates the implementation of a full neural network for image classification, using TensorFlow as a software baseline, and compares it with a hardware counterpart mapped onto resistive RAM-based crossbar arrays, a practical implementation of the memristor concept. By leveraging the inherent ability of RRAM crossbars to perform VMMs in a single step, we demonstrate how RRAM-based neural networks can achieve efficient in-memory analog computing. To ensure realistic and practical results, the hardware implemented utilizes RRAM memory cells characterized through silicon measurements. Furthermore, the design exclusively considers positive weights and biases to minimize the area overhead, resulting in a lightweight hardware solution. This approach achieves an energy consumption of 190 fJ/MAC operation for the crossbar array, highlighting its efficiency in power-constrained applications despite a drop in the prediction confidence of 27.5% compared to the software approach. Full article

This study of risk assessment of gasoline station workers was performed by using the following three models: the occupational safety and health (OSH) risk assessment aligned with ISO 45001, the biomatrix of health risk, and the benzene risk matrix assessment for gasoline station workers. Levels of inhaled air benzene and urine tt-muconic acid (tt-MA) were measured using samples collected from 151 gasoline station workers. Opportunity levels of benzene exposure were obtained by multiplying the frequency of benzene exposure by the levels of tt-MA, the inhaled benzene concentration levels, or the likelihood levels from contributing risk factors at gasoline stations. The final risk scores were calculated by multiplying the opportunity levels by the severity based on the adverse symptoms of benzene toxicity experienced by workers. A checklist regarding risk factors contributing to benzene exposure was used to collect data on occupational safety performance. The potential health risk was at an unacceptable level for 66.23%, 75.50%, and 60.26% of workers according to the OSH risk, the biomatrix of health risk, and the benzene risk matrix model, respectively. There was a significant linear relationship between the risk levels indicated by the three matrix models (r > 0.6, p < 0.001). These findings demonstrate that alternative risk assessments can be provided and simply used for preventive action against health hazards from benzene exposure in risk management programs. Full article

Aiming at the high-precision trajectory tracking problem of the new surface and underwater joint observation system (SUJOS) in the ocean remote sensing monitoring mission under complex sea conditions, especially at the problem of excessive tracking errors and slow convergence of actual trajectory oscillations caused by the wide range of angular changes in the motion trajectory, a real-time optimization improved model predictive control (IMPC) trajectory tracking method based on fuzzy control is proposed. Initially, the novel observation platform has been designed, and its mathematical model has been systematically established. In addition, this study optimizes the MPC trajectory tracking framework by integrating the least squares adaptive algorithm and the Extended Alternating Direction Method of Multipliers (EADMM). In addition, a fuzzy controller, optimized using a genetic algorithm, an output of real-time optimization coefficients, is employed to dynamically adjust and optimize the bias matrix within the objective function of the IMPC. Consequently, the real-time performance and accuracy of the system’s trajectory tracking are significantly enhanced. Ultimately, through comprehensive simulation and practical experimental verification, it is demonstrated that the real-time optimization IMPC algorithm exhibits commendable real-time and optimization performance, which markedly enhances the accuracy for trajectory tracking, and further validates the stability of the controller. Full article

Feature extraction plays a vital role in pattern recognition and computer vision. In recent years, low-rank representation (LRR) has been widely used in feature extraction, due to its robustness against noise. However, existing methods often overlook the impact of a well-constructed low-rank coefficient matrix on projection learning. This paper introduces a novel feature extraction method, i.e., robust discriminative non-negative and symmetric low-rank projection learning (RDNSLRP), where a coefficient matrix with better properties, such as low-rank, non-negativity, symmetry and block-diagonal structure, is utilized as a graph matrix for learning the projection matrix. Additionally, a discriminant term is introduced to increase inter-class divergence while decreasing intra-class divergence, thereby extracting more discriminative features. An iterative algorithm for solving the proposed model was designed by using the augmented Lagrange multiplier method, and its convergence and computational complexity were analyzed. Our experimental results on multiple data sets demonstrate the effectiveness and superior image-recognition performance of the proposed method, particularly on data sets with complex intrinsic structures. Furthermore, by investigating the effects of noise corruption and feature dimension, the robustness against noise and the discrimination of the proposed model were further verified. Full article

Electricity consumption data form the foundation for the efficient and reliable operation of smart grids and are a critical component for ensuring effective data mining. However, due to factors such as meter failures and extreme weather conditions, anomalies frequently occur in the data, which adversely impact the performance of data-driven applications. Given the near full-rank nature of low-voltage distribution area electricity consumption data, this paper employs clustering to enhance the low-rank property of the data. Addressing common issues such as missing data, sparse noise, and Gaussian noise in electricity consumption data, this paper proposes a multi-norm optimization model based on low-rank matrix theory. Specifically, the truncated nuclear norm is used as an approximation of matrix rank, while the $L_1$-norm and F-norm are employed to constrain sparse noise and Gaussian noise, respectively. The model is solved using the Alternating Direction Method of Multipliers (ADMM), achieving a unified framework for handling missing data and noise processing within the model construction. Comparative experiments on both synthetic and real-world datasets demonstrate that the proposed method can accurately recover measurement data under various noise contamination scenarios and different distributions of missing data. Moreover, it effectively separates principal components of the data from noise contamination. Full article

In this paper, we extend the definition of tensor products from using an invertible matrix to utilising right-invertible matrices, exploring the algebraic properties of these new tensor products. Based on this novel definition, we define the concepts of tensor rank and tensor nuclear norm, ensuring consistency with their matrix counterparts, and derive a singular value thresholding (${\ast }_{L,R}$ SVT) formula to approximately solve the subproblems in the alternating direction method of multipliers (ADMM), which is integral to our proposed tensor robust principal component analysis (${\ast }_{LR}$ TRPCA) algorithm. The computational complexity of the ${\ast }_{LR}$ TRPCA algorithm is $O(k·(n_1{n}_2{n}_3+p·\min (n_1^2{n}_2,n_1{n}_2^2)))$ for k iterations. According to this complexity analysis, by using a right-invertible matrix that selects p rows from the $n_3$ rows of the invertible matrix used in the tensor product with an invertible matrix, the computational load is approximately reduced to $p/n_3$ of what it would be with an invertible matrix, highlighting the efficiency gain in terms of computational resources. We apply this efficient algorithm to grayscale video denoising and motion detection problems, where it demonstrates significant improvements in processing speed while maintaining comparable quality levels to existing methods, thereby providing a promising approach for handling multi-linear data and offering valuable insights for advanced data analysis tasks. Full article