Search Results (398)

The rapid development of the low-altitude economy demands comprehensive electromagnetic spectrum awareness. However, constructing a comprehensive radio environment map (REM) in this scenario is challenging, as spectrum sensing data collected by unmanned aerial vehicles (UAVs) in complex low-altitude environments is typically sparse, fragmented, and non-uniformly distributed across the high-dimensional space of time, frequency, and 3D space. To address these issues, this study proposes a rank-adaptive Bayesian tensor ring completion (Ra-BTRC) framework. The method models the low-altitude electromagnetic environment as a unified five-dimensional (5D) spectrum tensor. It then employs tensor ring (TR) decomposition to capture latent high-order correlations across all dimensions. To overcome the sensitivity of conventional TR methods to predefined ranks, Ra-BTRC introduces sparsity-inducing priors on the TR core factors, enabling variational Bayesian inference to learn observation uncertainty and infer effective TR ranks from sparse measurements without manually fixing the TR rank. Simulations demonstrate that Ra-BTRC significantly outperforms existing TR-based baselines, achieving more than 10 dB MMSE improvement at a 5% sampling rate while accurately recovering local spectrum structures and temporal dynamics. The proposed approach provides a robust and scalable solution for reliable global low-altitude spectrum cognition under stringent sensing budgets. Full article

Spectral fidelity is critical for accurate hyperspectral image (HSI) processing. A key characteristic of HSI data is the strong correlation between spectral bands, which manifests as structured symmetry in spectral covariance matrices. While global low-rank tensor decompositions leverage this spectral structure, they often neglect the significant spatial heterogeneity present in real-world scenes. To address this limitation, we propose a Region-Aware 3D Tensor Decomposition (RA-3DTD) framework that balances global spectral consistency with local spatial adaptation. Our approach first performs residual energy-based region detection to identify complex regions within the hyperspectral cube, and then applies localized Higher-Order Orthogonal Iteration (HOOI) specifically to those regions requiring enhanced detail preservation. This two-phase design incorporates global low-rank constraints with local spatial processing, improving denoising accuracy. Extensive experiments on four benchmark datasets (Pavia_80, Indian Pines, Salinas, and Pavia University) demonstrate the effectiveness of our method compared to five leading model-based baselines including BM3D, LRMR, NLR, LRTD, and FastHyDe. Our approach achieves a 1.33 dB increase in PSNR over a leading model-based competitor (FastHyDe) in complex urban scenes while maintaining strong structure fidelity as measured by SSIM and SAM metrics. Full article

The solution theory of Sylvester-type equations finds wide applications in control theory, robotics, and image processing. This paper systematically surveys, classifies and summarizes the existing research results of three classes of Sylvester-type equations: matrix equations, tensor equations, and operator equations. It extracts nine mainstream research methods and clarifies the internal correlations among these methods, as well as their applicable equation types. Combined with four prior review articles focusing on special cases of Sylvester-type equations, this work establishes a comprehensive framework for solving such equations. It not only provides a systematic theoretical foundation and a clear research thread for subsequent researchers but also offers valuable methodological insights for further investigations in related fields. Full article

Accurate prediction of traffic flow is the key to highways control. However, traditional time series forecasting methods cannot meet the accuracy requirements of long-term forecasting. This paper proposes a multi-channel univariate long-term highway inbound traffic flow forecasting framework with multidimensional signal feature decomposition of time series and a patch time series depth-separable convolutional neural network. Firstly, we propose a multidimensional decomposition block consisting of a principal feature decomposition block based on the Fourier transform, a backbone and noise decomposition block based on the Stationary Wavelet Transform, a cyclic signal enhancer based on threshold comparator, and a trend extraction block based on average pooling. Secondly, we propose to change the depth-separable convolution layer mode and stack multiple depth-separable convolution layers so as to capture the developmental characteristics of the time series signal. Furthermore, a feed-forward neural network layer is set up between the depth-separable convolution layers. Then, true time series decomposition is used in the training phase to compute the multidimensional feature loss, with the aim of improving the shortcoming of the tensor decomposition that does not allow for gradient propagation. Finally, weight aggregation is used to transform the multidimensional data into univariate time series data. Experimental results on real highway inbound traffic flow datasets show that the proposed method achieves better performance than the baseline model and effectively improves the prediction accuracy. Full article

This paper aims to lay some groundwork for a systematic framework for quantum mereology based on the tensor product structures (TPSs) of Hilbert space. While previous work has suggested that such a TPS-based mereology might conform to classical extensional mereology, we demonstrate that the space of all possible tensor product structures for a given Hilbert space lacks the lattice-theoretic structure characteristic of classical partitions. Specifically, we show that this space admits no canonical meet operation, thus violating the global validity of a natural extension of the weak supplementation principle. These structural features suggest that quantum mereology, even when based on TPSs, should exhibit certain non-extensional behavior: what counts as a “part” is decomposition-relative in a stronger sense, with different decompositions allowed to be mutually incompatible. The resulting picture challenges extensional interpretations of quantum composition and underscores the need for a formally richer, genuinely non-classical mereology. Full article

In security and tactical surveillance applications, unmanned aerial vehicle (UAV) detection systems must provide both reliable recognition and stable real-time operation under communication-constrained conditions. However, remote server-based surveillance can suffer from unstable response times when the display or output path depends on a degraded network. This study formulates edge-based UAV surveillance under a network-denied operating condition as a stochastic latency-decomposition and constrained runtime-feasibility problem. The total system latency is decomposed into inference, processing, and display/I/O components, and an SSH X11-based lossless display-path proxy is used to examine how network-coupled output transmission can dominate the runtime path. In contrast, a Jetson AGX Orin-based edge implementation performs UAV detection, tracking, threat assessment, visualization, and output locally. A YOLO26-based reference detector accelerated with TensorRT and FP16 is evaluated using a high-resolution UAV dataset consisting of approximately 25,000 images from nine UAV classes. Five-fold cross-validation produced an mAP@0.5 of 0.7890 ± 0.0653. Runtime evaluation showed that the optimized edge system achieved 31.49 ± 2.49 FPS at SD resolution, satisfying the strict 30 FPS real-time condition, while HD resolution achieved 26.72 ± 1.31 FPS as a near-real-time high-detail mode. Under the SSH X11 proxy condition, the FHD runtime dropped to 4.85 ± 2.53 FPS with substantially increased display latency. These results indicate that real-time UAV surveillance depends not only on detector inference speed but also on execution architecture and display-path dependency, supporting the practical importance of network-independent edge deployment under communication-degraded conditions. Full article

The recursive least-squares (RLS) algorithm is an appealing choice in many adaptive filtering applications, especially due to its fast convergence rate. In the context of echo cancellation, the implementation of the conventional RLS algorithm is a challenging task, mainly due to the long length of the impulse response to be identified, which corresponds to the echo path. The computational complexity of this algorithm is proportional to the square of the filter length, which becomes prohibitive since the lengths of such impulse responses could be on the order of hundreds/thousands of coefficients. Recently, an efficient solution has been developed, which exploits a fourth-order (tensor-based) decomposition of the filter impulse response, using the nearest Kronecker product. This approach fits very well for low-rank impulse responses, like in echo cancellation. The resulting RLS-type algorithm designed in this context combines four (much shorter) adaptive filters, which work in parallel and are connected via their coefficients. Thus, the system owns an intrinsic symmetry-related structure. The overall behavior of this decomposition-based RLS algorithm is controlled by the forgetting factors associated to the four component filters. In order to achieve a proper balance between the main performance criteria (e.g., tracking versus accuracy), the current paper proposes a version of this algorithm with variable forgetting factors (VFFs). The design of these VFFs results in a practical manner, without requiring other additional control mechanisms or extra tuning parameters. Extensive simulation results obtained in the framework of echo cancellation support the performance features of the proposed decomposition-based RLS-type algorithm with VFFs. Full article

To address the problems of strong vertical heterogeneity in thin interbedded reservoirs of the N block in Daqing Oilfield, the complex coupling between porosity and permeability, and the difficulty of conventional single-parameter inversion methods in balancing local details with global geological background, a joint inversion method for porosity and permeability based on GeoFE-PPNet and logging imaging tensors is proposed. Using conventional logging curves, including GR, RT, RHOB, NPHI, DT, and PE, the method constructs a logging imaging tensor by integrating multi-channel responses with shale constraints and extracts intra-layer textural features through local encoding. Meanwhile, sequence decomposition and frequency enhancement are introduced to capture vertical trend variations and high-frequency non-stationary responses of the reservoir. On this basis, geological constraint fusion and dual-task collaborative prediction are employed to achieve joint inversion of porosity and permeability. Experimental results show that the proposed method achieves favorable inversion accuracy and cross-well generalization under complex reservoir conditions, with a porosity R² of 0.931, a permeability R² of 0.887, and an overall accuracy of 90.74%. Ablation and noise robustness experiments further demonstrate the effectiveness of the logging imaging tensor, frequency enhancement, geological constraints, and dual-task collaboration in improving model performance. The study indicates that the proposed method can more accurately characterize the vertical variation in reservoir physical properties and provides a new technical approach for fine reservoir evaluation and intelligent log interpretation. Full article

Dynamically grasping the scope of the caving zone and fractured zone in overlying strata is crucial for ground pressure control in sublevel caving mining. Taking Dahongshan Iron Mine as the research object, this study systematically analyzed the evolutionary characteristics of overlying strata caving during sublevel caving mining from 2009 to 2013. Microseismic monitoring was employed as the main method to monitor and locate rock mass fracturing, while roadway monitoring and borehole monitoring were used as auxiliary means to determine the caving boundary and fractured zone scope of overlying strata. Comprehensive analysis of the monitoring data showed that the elevation of the overlying strata caving zone expanded from 930 m to 1215 m, and the width of the fractured zone varied from 50 m to 75 m in different periods. To clarify the rock mass fracture mechanism, P-wave first-motion moment tensor inversion and the Ohtsu moment tensor decomposition method were adopted to classify fracture types. The results indicated that tensile fracturing-related microseismic events accounted for 76.2–80.2% of all events in different periods, demonstrating that tensile failure dominated the fracturing of overlying strata. After December 2012, the caving scope extended to the surface, and a surface collapse area of 290,000 m² was formed by December 2013, which effectively eliminated the threat of sudden overlying strata caving disasters to the mine. The research results provide reliable technical support for ensuring mine safety production and can serve as a reference for similar sublevel caving mining projects. Full article

The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions, the Lorentz-invariant coefficient functions of which encode the physics of the process. For growing n, the complexity of these objects may increase considerably and make it challenging to deal with them. Here, we give a pedagogical introduction to the topic and provide some tools to manage this complexity, and we will show how symmetries can be used as organizing principles. Full article

Being capable of high-resolution imaging and non-contact measurement, Ground Penetrating Radar (GPR) is a promising technology for the detection of unexploded ordnance (UXO). However, UXO detection is severely hindered by clutter, particularly in environments with significant surface roughness where conventional suppression methods prove ineffective. To address this, we propose a polarimetric GPR clutter suppression method based on an improved non-convex Tensor Robust Principal Component Analysis (TRPCA) framework. Specifically, a polarization-aware tensor construction scheme is designed by stacking the HH and VV channel data. This approach exploits the strong inter-channel correlation of clutter to enhance its low-rank property, while highlighting the distinct sparse signatures of targets derived from their polarimetric responses. To further optimize tensor decomposition, we introduce a non-convex Tensor Adjustable Logarithmic Norm (TALN) to overcome the estimation bias inherent in the conventional Tensor Nuclear Norm (TNN). Serving as a tighter surrogate for tensor rank, the proposed TALN regularizer improves the approximation accuracy of the low-rank component, thereby ensuring a clearer separation between clutter and targets. The resulting non-convex optimization problem is efficiently solved using Alternating Direction Method of Multipliers (ADMM). Numerical simulations and laboratory experiments demonstrate that the proposed method suppresses strong clutter stemming from rough-surface reflections more effectively than existing methods, achieving a Signal-to-Clutter Ratio (SCR) improvement of over 20 dB. Full article

This paper extends the theory of equivalence canonical forms from quaternion matrices to quaternion tensors under the Einstein product. Motivated by recent results on the simultaneous decomposition of two specific configurations of five quaternion matrices, we establish a comprehensive framework for the corresponding configurations of five quaternion tensors. The core approach leverages bijective transformation maps that establish isomorphisms between quaternion tensor spaces and matrix spaces, allowing us to systematically construct invertible transformation tensors that simultaneously reduce the given tensor quintuples to canonical forms consisting solely of binary entries (0 and 1). A detailed structural analysis of the resulting canonical tensor forms is provided, including explicit dimension formulas for all identity blocks derived from precise rank conditions. To demonstrate practical utility, we integrate the proposed tensor decomposition with the discrete wavelet transform to construct a color video encryption and decryption system. Experimental results confirm perfect reconstruction (PSNR exceeding 300 dB, SSIM equal to 1) and strong security performance: NPCR of 49.8%, UACI of 49.6%, information entropy of 0.9986 bits per pixel, adjacent pixel correlation below 0.03 in absolute value, and a key space exceeding 2⁵¹². The developed theory significantly extends the existing literature on quaternion tensor decompositions and provides powerful tools for multidimensional signal processing. Full article

As multi-view datasets expand across diverse practical fields, feature selection (FS) has become an indispensable preparatory stage for machine learning models. Nevertheless, real-world multi-view data is often unlabeled and distributed among isolated clients, posing significant challenges to traditional centralized methods due to privacy concerns and communication constraints. Furthermore, existing centralized and federated approaches frequently suffer from entrapment in local optima and lack robust convergence guarantees. To address these issues, we propose Fed-MUFSHT, a federated framework for multi-view unsupervised FS (MUFS) that integrates tensor learning with a novel metaheuristic optimizer, Hierarchical-Cognitive Tianji’s Horse Racing Optimization (HC-THRO). Within the federated learning paradigm, Fed-MUFSHT follows a dual-stage local optimization process. Stage 1 applies HC-THRO, which integrates Hierarchical Competitive Learning and Adaptive Cognitive Mapping to simulate multi-level strategic competition and cognitive adaptation among individuals. This design enhances global exploration, adaptive learning, and fine-grained feature selection in high-dimensional spaces. Stage 2 employs a TL module based on canonical polyadic (CP) decomposition to perform missing-view imputation and refine latent representation learning. At the global level, a privacy-preserving aggregation strategy based on Normalized Mutual Information (NMI) and feature weights enables efficient model coordination without exposing raw data. Comparative experiments on several public benchmark datasets reveal that Fed-MUFSHT maintains clear advantages over strong competing methods, showing better optimization results together with more dependable convergence characteristics. The overall evidence suggests that the proposed approach is both robust and effective for distributed optimization tasks involving privacy protection. Full article

Reconfigurable intelligent surfaces (RISs) are regarded as a transformative technique for future wireless networks. Currently, the majority of research efforts have focused on channel estimation scenarios in communication systems assisted by a single passive RIS. However, single-RIS-assisted systems suffer from limited coverage performance, with significant performance degradation observed in dense obstacle environments. To mitigate the adverse impacts imposed by environmental factors, a dual-RIS-assisted communication system exhibits superior adaptability to practical scenarios. This work focuses on investigating such a system. It is worth noting that fully passive RISs lack the capability to process signals independently. Furthermore, when employing pilot-aided algorithms to acquire channel state information (CSI), wireless systems often encounter challenges arising from large channel matrix dimensions, thereby leading to substantial pilot overhead. To address the aforementioned issues, this paper proposes a novel semi-blind channel estimation method for multiple-input multiple-output (MIMO) systems aided by double reconfigurable intelligent surfaces (D-RISs). Specifically, we construct two tensor models, namely the Parallel Factor (PARAFAC) model and the Parallel Tucker2 model, for the received signal in two separate stages. By means of tensor decomposition, the joint channel estimation and symbol detection problem is reformulated as a least squares problem and solved using a two-stage algorithm. In the first stage, the ALS algorithm is adopted to estimate the transmitted symbols and provide initialization for the second stage. Then, in the second stage, the TALS algorithm is employed to obtain the final estimation results of the three sub-channels. Simulation results verify the effectiveness of the proposed receiver. Full article

This work introduces Structured 3D-SVD as a practical framework for the reconstruction, compression, and analysis of biological volumetric data. Inspired by the logic of matrix singular value decomposition (SVD), the proposed approach represents third-order volumetric data in the spatial domain and supports progressive reconstruction through ordered quasi-singular coefficients. The experimental evaluation was carried out on two biological volumetric datasets: one full-volume scan of a fish and another of a brain. The results show that Structured 3D-SVD achieves reconstruction quality close to that of Tucker decomposition while requiring shorter computation times and outperforms canonical polyadic decomposition (CPD) in both accuracy and runtime. In addition, a progressive reconstruction analysis shows that relatively low truncation levels are sufficient to preserve the main volumetric structures, while higher truncation levels lead to more detailed reconstructions. Full article