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25 pages, 9749 KB  
Article
An Integrated Path Planning Algorithm Based on Vector Jump Point Search and Ant Colony Optimization for Quay Crane Inspection
by Haoye Zhang, Zihan Lei, Mingxiao Wang, Zhipeng Hou, Hongren Zhao, Christophe Claramunt, Gang Tang and Weidong Zhu
Machines 2026, 14(7), 750; https://doi.org/10.3390/machines14070750 - 3 Jul 2026
Viewed by 153
Abstract
Unmanned aerial vehicles have become a promising platform for inspecting large port machinery; however, quay cranes contain sparse but complex steel-frame structures, multiple inspection points, and narrow collision-constrained spaces, which make efficient inspection path planning difficult. Existing approaches often focus either on global [...] Read more.
Unmanned aerial vehicles have become a promising platform for inspecting large port machinery; however, quay cranes contain sparse but complex steel-frame structures, multiple inspection points, and narrow collision-constrained spaces, which make efficient inspection path planning difficult. Existing approaches often focus either on global point sequencing or local collision-free search, and conventional global optimizers usually use straight-line distances that do not reflect obstacle-constrained flight costs. This paper proposes an integrated path planning method for quay crane inspection based on vector jump point search and ant colony optimization. In the local path-searching stage, vector-guided preprocessing and path simplification are used to calculate collision-free paths between mission points and construct a path cost matrix. In the global optimization stage, ant colony optimization determines the inspection sequence using the collision-free cost matrix rather than Euclidean distances. Simulation experiments were conducted on a simplified quay crane model of 132 m × 22 m × 70 m with 25 mission points. The results show that the proposed method reduced the average local path-searching time from 5.3392 s to 4.2907 s, corresponding to a 19.6% improvement over jump point search, while reducing the average local path length by 5.1%. The final global inspection path obtained in the experimental case was 516.1 m, which was shorter than those obtained by simulated annealing, genetic algorithm, particle swarm optimization, and the previous method. These results indicate that the proposed method can improve local planning efficiency and provide an effective inspection route for unmanned aerial vehicle-based quay crane inspection. Full article
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21 pages, 449 KB  
Article
Gridless DOA Estimator for 1.5-Bit Sparse Massive MIMO Systems Based on Covariance Matrix Estimation
by Yuan Peng, Xiongbo Zheng and Zhiyong Cheng
Entropy 2026, 28(6), 605; https://doi.org/10.3390/e28060605 - 28 May 2026
Viewed by 227
Abstract
To reduce the hardware cost of massive multiple-input multiple-output (MIMO) systems, low-bit analog-to-digital converters (ADCs) and sparse arrays are widely used. Compared with traditional 1-bit and 2-bit quantization techniques, 1.5-bit quantization uses two symmetric non-zero thresholds to quantize signal power into three levels, [...] Read more.
To reduce the hardware cost of massive multiple-input multiple-output (MIMO) systems, low-bit analog-to-digital converters (ADCs) and sparse arrays are widely used. Compared with traditional 1-bit and 2-bit quantization techniques, 1.5-bit quantization uses two symmetric non-zero thresholds to quantize signal power into three levels, thereby balancing quantization complexity against system performance. However, the quantization loss introduced by 1.5-bit quantization is still significant and leads to degradation in DOA estimation performance. To improve the DOA estimation accuracy of 1.5-bit sparse massive MIMO systems, a covariance matrix estimation method is proposed. This method exploits the Toeplitz property of the covariance matrix of sparse arrays and the relationship between 1.5-bit quantized signals and their unquantized counterparts to transform the covariance matrix estimation problem for 1.5-bit sparse arrays into a non-convex optimization problem with equality constraints. We then further exploit the properties of 1.5-bit quantized signals to relax this problem into a convex problem and solve it via semidefinite programming. Once the covariance is estimated, the DOAs can be recovered by subspace-based methods. Numerical results show that the proposed method achieves higher estimation accuracy than 1.5B-MUSIC and 1-bit covariance-fitting baselines on 1.5-bit sparse arrays, and is competitive with structured covariance-fitting baselines applied to unquantized data, especially on coprime arrays in low-snapshot scenarios. Full article
(This article belongs to the Special Issue Wireless Communications: Signal Processing Perspectives, 2nd Edition)
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29 pages, 1911 KB  
Article
A Leakage-Resistant Digital Inheritance Distribution Scheme Based on Sparse-Matrix Secret Sharing
by Yucong Ma, Huiying Hou, Xuerui Gan and Zisu Zhao
Algorithms 2026, 19(5), 410; https://doi.org/10.3390/a19050410 - 19 May 2026
Viewed by 242
Abstract
With digital assets increasingly comprising a significant portion of personal wealth, the secure management and transfer of digital legacies have emerged as a pressing concern. Secret sharing offers a solution to this problem. However, distributing shares containing the unique private key for digital [...] Read more.
With digital assets increasingly comprising a significant portion of personal wealth, the secure management and transfer of digital legacies have emerged as a pressing concern. Secret sharing offers a solution to this problem. However, distributing shares containing the unique private key for digital assets poses significant risks of theft or tampering, potentially leading to the illegal appropriation of user assets. This paper presents a leakage-resistant digital inheritance distribution scheme based on sparse-matrix secret sharing. It employs an efficient thresholding scheme that uses sparse matrices, achieving near-linear complexity for share reconstruction via a random striped matrix. Reconstruction time is significantly reduced compared to traditional polynomial interpolation methods. To address the realistic scenario where an asset owner holds multiple independent digital accounts, we propose a multi-account blinding and aggregation mechanism. This mechanism allows the dealer to establish isolated group keys for each account in a single round of communication, while preventing adversaries from linking different accounts to the same owner. A key-derivation and encrypted-transmission mechanism is then designed based on the aggregated group keys. Group keys are established by consensus among heirs, from which each heir derives a unique session key. Authenticated encryption ensures the confidentiality, integrity, and identity-bound transmission of shares. Through security proofs and experimental performance evaluation, it is demonstrated that the proposed scheme satisfies adaptive security requirements with the hash function H modeled as a random oracle, while all other cryptographic primitives (PRF, AES-GCM, HMAC) are assumed to be secure under standard computational assumptions. Full article
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19 pages, 14058 KB  
Article
Robust Beamforming for Improved FDA-MIMO Radar Based on INCM Reconstruction and Joint Objective Function-Oriented Steering Vector Correction
by Qinlin Li, Yuming Lu, Ningbo Xie, Kefei Liao, Peiqin Tang, Xianglai Liao, Hanbo Chen and Jie Lang
Appl. Sci. 2026, 16(9), 4156; https://doi.org/10.3390/app16094156 - 23 Apr 2026
Viewed by 315
Abstract
Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar offers significant advantages in mainlobe deceptive interference suppression, as its transmit steering vector contains both angle and range information, providing additional degrees of freedom beyond the angular dimension. However, conventional FDA-MIMO radar suffers from insufficient angle-range [...] Read more.
Frequency diverse array multiple-input multiple-output (FDA-MIMO) radar offers significant advantages in mainlobe deceptive interference suppression, as its transmit steering vector contains both angle and range information, providing additional degrees of freedom beyond the angular dimension. However, conventional FDA-MIMO radar suffers from insufficient angle-range resolution, which limits its ability to suppress interferences located close to the target. Moreover, it lacks robustness under limited snapshots and parameter mismatch conditions. To address these issues, this paper proposes a robust beamforming method based on the FDA-MIMO radar model. A collocated sparse array with a sinusoidal element spacing offset and a logarithmic frequency offset is adopted to enhance beam resolution and resolve the periodic angle-range ambiguity problem. Based on this model, the interference-plus-noise covariance matrix is reconstructed using two-dimensional Capon spatial spectrum, and the steering vector is corrected via a joint objective function that combines MUSIC orthogonality and the flatness of the covariance residual spectrum. Simulation results demonstrate that, under conditions of near-target interferences, random range-angle errors, and frequency offset errors, the proposed method achieves a signal-to-interference-plus-noise ratio (SINR) close to the ideal value, exhibiting excellent mainlobe interference suppression performance and robustness. Full article
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22 pages, 4038 KB  
Article
Mainlobe Interference Suppression Based on POL-SPICE and Covariance Matrix Reconstruction for Polarization-Sensitive Arrays
by Buma Xiao, Huafeng He, Liyuan Wang and Tao Zhou
Sensors 2026, 26(9), 2604; https://doi.org/10.3390/s26092604 - 23 Apr 2026
Viewed by 263
Abstract
Adaptive beamforming based on polarization-sensitive arrays enables joint spatial–polarization filtering for mainlobe interference suppression, but mainlobe distortion and performance degradation occur when the received data include the desired signal or multiple mainlobe interferences. Accordingly, this paper proposes a mainlobe interference suppression method based [...] Read more.
Adaptive beamforming based on polarization-sensitive arrays enables joint spatial–polarization filtering for mainlobe interference suppression, but mainlobe distortion and performance degradation occur when the received data include the desired signal or multiple mainlobe interferences. Accordingly, this paper proposes a mainlobe interference suppression method based on Polarimetric Sparse Iterative Covariance-based Estimation (POL-SPICE) and covariance matrix reconstruction. This method utilizes the POL-SPICE algorithm to accurately estimate the direction of arrival (DOA), polarization, and power parameters. It reconstructs the covariance matrix by nulling the corresponding source power and constructs a feature projection matrix to preprocess the received signal. These eliminate the impact of the desired signal and mainlobe interference components on subsequent joint spatial–polarization domain beamforming, ultimately achieving interference suppression and mainlobe shape preservation. Simulation results illustrate that the proposed method is applicable to scenarios with the coexistence of the desired signal and multiple mainlobe interferences, and its superiority over existing methods is verified. Full article
(This article belongs to the Section Electronic Sensors)
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15 pages, 58473 KB  
Article
Aw-DuNet: Adaptive-Weight Deep Unfolding Network for High Precision Infrared Weak Target Segmentation
by Xu Yang, Aoxiang Li, Hancui Zhang, Long Wu, Zhen Yang, Yong Zhang and Jianlong Zhang
Appl. Sci. 2026, 16(8), 3767; https://doi.org/10.3390/app16083767 - 12 Apr 2026
Viewed by 388
Abstract
Deep learning (DL) methods have achieved promising performance in infrared weak target segmentation. However, their interpretability and robustness against cluttered backgrounds and noise remain limited. We propose an adaptive-weighted deep unfolding network (AwDuNet) that unfolds alternating direction method of multipliers (ADMM) iterations for [...] Read more.
Deep learning (DL) methods have achieved promising performance in infrared weak target segmentation. However, their interpretability and robustness against cluttered backgrounds and noise remain limited. We propose an adaptive-weighted deep unfolding network (AwDuNet) that unfolds alternating direction method of multipliers (ADMM) iterations for adaptive sparse–low-rank decomposition into multi-stage interpretable modules for end-to-end training. An adaptive weight matrix is jointly estimated from a local structural-difference matrix and a sparse-enhancement matrix, thereby strengthening target–background separation while preserving fine target details. To suppress background clutter, we design a dual-path complementary attention (DCA) mechanism for the low-rank background reconstruction module (LBRM), which improves low-rank background modeling by jointly leveraging spatial and channel attention. By extracting local details and global context in parallel, DCA enhances weak-target responses and mitigates interference from complex backgrounds. We also build a real-scene infrared dataset with 632 images for out-of-domain evaluation. The model is tested without fine-tuning after training on public datasets to assess practical robustness. Experiments on multiple public datasets validate the effectiveness and generalization of AwDuNet. Full article
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24 pages, 4186 KB  
Article
Progressive Spatiotemporal Graph Modeling for Spacecraft Anomaly Detection
by Zihan Chen, Zewen Li, Yuge Cao, Yue Wang and Hsi Chang
Entropy 2026, 28(4), 426; https://doi.org/10.3390/e28040426 - 10 Apr 2026
Viewed by 827
Abstract
The growing number of on-orbit spacecraft and the increasing volume of telemetry data have made intelligent anomaly detection in multi-channel telemetry essential for mission operations. Current spacecraft anomaly detection methods primarily rely on statistical models or time-series deep learning approaches, which often fail [...] Read more.
The growing number of on-orbit spacecraft and the increasing volume of telemetry data have made intelligent anomaly detection in multi-channel telemetry essential for mission operations. Current spacecraft anomaly detection methods primarily rely on statistical models or time-series deep learning approaches, which often fail to explicitly model spatiotemporal dependencies across multiple telemetry channels. This shortcoming limits their ability to capture the dynamically evolving and intricately coupled relationships between variables. To overcome this limitation, a Progressive Spatiotemporal Graph (PSTG) model is proposed for anomaly detection in multi-channel spacecraft telemetry. PSTG employs a multi-scale patch embedding module to extract hierarchical semantic features from multi-channel time series, effectively reducing the dimensionality of the spatiotemporal graph. It constructs a sparse adjacency matrix using a multi-head attention mechanism that integrates intra-channel temporal dynamics, inter-channel spatial correlations, and cross-channel spatiotemporal interactions. An improved multi-head graph attention network then captures pairwise dependencies among nodes within the adjacency matrix. As a result, PSTG encodes rich spatiotemporal representations derived from intricate variable interactions, enabling accurate, real-time prediction of multi-channel telemetry. Furthermore, a dynamic thresholding mechanism is incorporated into PSTG to perform online anomaly detection based on prediction residuals. Extensive experiments on real-world spacecraft telemetry data collected over 84 months show that PSTG outperforms eleven state-of-the-art benchmark methods in almost all cases across multiple evaluation metrics. Finally, visualizations of the learned adjacency and attention matrices are presented to interpret the spatiotemporal modeling process, providing operators with actionable insights into the detected anomalies and facilitating root cause analysis. Full article
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14 pages, 401 KB  
Article
Adaptive LASSO-MGARCH for Multivariate Volatility Forecasting
by Yongdeng Xu, Juyi Lyu and Wenna Lu
Mathematics 2026, 14(6), 1053; https://doi.org/10.3390/math14061053 - 20 Mar 2026
Viewed by 470
Abstract
This paper evaluates an Adaptive LASSO-MGARCH model for multivariate volatility forecasting, with applications in green and conventional bonds, equities, energy commodities, and EU carbon allowances. By introducing coefficient-specific adaptive penalisation directly into the multivariate GARCH variance equations, the model delivers a sparse and [...] Read more.
This paper evaluates an Adaptive LASSO-MGARCH model for multivariate volatility forecasting, with applications in green and conventional bonds, equities, energy commodities, and EU carbon allowances. By introducing coefficient-specific adaptive penalisation directly into the multivariate GARCH variance equations, the model delivers a sparse and data-driven volatility spillover structure while preserving the positive definiteness of the conditional covariance matrix. Using daily data on green and conventional bonds, equities, energy commodities, and carbon allowances, we show that adaptive regularisation substantially reduces model complexity and improves economic interpretability relative to an unpenalised MGARCH benchmark. Out-of-sample forecasting experiments at multiple horizons demonstrate that the Adaptive LASSO-MGARCH model consistently achieves lower covariance forecast losses, and statistical tests based on the White reality check confirm that these improvements are significant across alternative loss functions. Full article
(This article belongs to the Special Issue Time Series Forecasting for Green Finance and Sustainable Economics)
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23 pages, 531 KB  
Article
Beacon-Aided Self-Calibration and Robust MVDR Beamforming for UAV Swarm Virtual Arrays Under Formation Drift and Low Snapshots
by Siming Chen, Xin Zhang, Shujie Li, Zichun Wang and Weibo Deng
Drones 2026, 10(3), 157; https://doi.org/10.3390/drones10030157 - 26 Feb 2026
Viewed by 640
Abstract
Unmanned aerial vehicle (UAV) swarms can form sparse virtual antenna arrays (VAAs) for airborne sensing and communications, but their beamforming performance is highly vulnerable to quasi-static formation drift and the limited number of snapshots available within each coherent processing interval. This paper proposes [...] Read more.
Unmanned aerial vehicle (UAV) swarms can form sparse virtual antenna arrays (VAAs) for airborne sensing and communications, but their beamforming performance is highly vulnerable to quasi-static formation drift and the limited number of snapshots available within each coherent processing interval. This paper proposes a beacon-aided self-calibration and robust beamforming framework for narrowband UAV-swarm uplinks in strong-interference, low-snapshot regimes. We consider one signal of interest (SOI) and multiple co-channel interferers characterized by their coarse direction-of-arrival (DOA) information. The key idea is to exploit a single dominant non-SOI emitter as a strong calibration source (beacon) to learn the quasi-static geometry drift from data. First, the beacon spatial signature is extracted from the sample covariance matrix via eigenvector–steering-vector alignment, and a correlation-based gate is used to decide whether geometry calibration is reliable. When the gate is passed, the inter-UAV position drift is estimated from element-wise steering ratios to build a calibrated array manifold. Second, using the calibrated steering vectors and coarse DOA information, the interference-plus-noise covariance matrix (INCM) is reconstructed through a low-dimensional non-negative power fitting with mild diagonal loading. Finally, a geometry-aware minimum-variance distortionless response (MVDR) beamformer is designed based on the reconstructed INCM. Simulations on coprime-inspired UAV formations with a single dominant interferer show that the proposed scheme recovers most of the SINR loss caused by geometry mismatch and consistently outperforms baseline MVDR, worst-case MVDR, a recent covariance-reconstruction baseline, and URGLQ in the low-snapshot regime. For example, in a representative setting with Nuav=7, σp=0.10, INRc=30 dB, and L=10, the proposed method achieves approximately 14 dB output SINR at SNRin=10 dB, outperforming nominal SCM-MVDR by about 13 dB and approaching a genie-aided MVDR bound within a few dB, while retaining a computational complexity comparable to standard MVDR. Full article
(This article belongs to the Special Issue Optimizing MIMO Systems for UAV Communication Networks)
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21 pages, 7919 KB  
Article
Design of a Four-Dimensional Discrete Chaotic Image Encryption Algorithm Based on Dynamic Adjacency Matrix
by Hua Cai, Wenxia Xu, Ziwei Zhou and Guodong Li
Mathematics 2026, 14(4), 616; https://doi.org/10.3390/math14040616 - 10 Feb 2026
Viewed by 627
Abstract
Chaotic systems, with their characteristics of high sensitivity to initial conditions, pseudo-randomness, and ergodicity, provide high-quality pseudo-random sequences. Graph theory, through mechanisms such as vertex mapping, path traversal, and graph partitioning, can enhance data confusion and diffusion capabilities. This research designs an image [...] Read more.
Chaotic systems, with their characteristics of high sensitivity to initial conditions, pseudo-randomness, and ergodicity, provide high-quality pseudo-random sequences. Graph theory, through mechanisms such as vertex mapping, path traversal, and graph partitioning, can enhance data confusion and diffusion capabilities. This research designs an image encryption method that combines graph theory and chaotic systems. Firstly, a four-dimensional discrete chaotic system is constructed based on the Hénon map, and its chaotic characteristics and high complexity over a wide range of parameters and initial values are verified using Lyapunov exponents and permutation entropy. Secondly, an encryption framework based on a dynamic adjacency matrix from graph theory is proposed: image pixels are mapped to a dynamic graph structure, and sparse adjacency matrices are generated using chaotic sequences to achieve pixel scrambling based on graph traversal; then, chaotic sequences are used for feedback diffusion with pixel values to enhance the confusion effect. Multiple sets of experiments verify its effectiveness and robustness in terms of key sensitivity, statistical analysis, resistance to differential attacks, and resistance to cropping attacks. Full article
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19 pages, 3020 KB  
Article
Channel Estimation for RIS-Assisted Multi-User mmWave MIMO Systems via Joint Correlation
by Nanqing Zhou, Honggui Deng and Ni Li
Electronics 2026, 15(3), 594; https://doi.org/10.3390/electronics15030594 - 29 Jan 2026
Viewed by 1115
Abstract
Reconfigurable intelligent surface (RIS) demonstrates significant potential in millimeter-wave (mmWave) multiple-input multiple-output (MIMO) wireless communication systems. However, the introduction of RIS leads to a substantial number of parameters in the channel matrix, making channel estimation highly challenging. By exploiting the sparsity of mmWave [...] Read more.
Reconfigurable intelligent surface (RIS) demonstrates significant potential in millimeter-wave (mmWave) multiple-input multiple-output (MIMO) wireless communication systems. However, the introduction of RIS leads to a substantial number of parameters in the channel matrix, making channel estimation highly challenging. By exploiting the sparsity of mmWave channels, compressed sensing algorithms, such as the orthogonal matching pursuit (OMP) algorithm, can significantly reduce the pilot overhead. Nevertheless, traditional OMP algorithms typically require extensive prior knowledge about the number of effective paths, which is often difficult to obtain. To address this problem, we propose a novel multi-user joint correlation allocation (MUJCA) algorithm, which requires only minimal and easily measurable prior information. Our key idea is to divide the RIS coverage area into multiple sub-regions, each associated with a known number of scatterers, which is a pre-measured quantity, with users distributed within these sub-regions. Then, the MUJCA algorithm exploits joint correlation of multiple users to facilitate sparse channel recovery and transforms it back into the spatial channel. Simulation results show that the proposed MUJCA achieves higher channel estimation accuracy than existing benchmark algorithms. Full article
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28 pages, 3209 KB  
Article
Fast Computation for Square Matrix Factorization
by Artyom M. Grigoryan
Computers 2026, 15(1), 67; https://doi.org/10.3390/computers15010067 - 17 Jan 2026
Viewed by 706
Abstract
In this work, we discuss a method for the QR-factorization of N×N matrices where N3 which is based on transformations which are called discrete signal-induced heap transformations (DsiHTs). These transformations are generated by given signals and can be composed [...] Read more.
In this work, we discuss a method for the QR-factorization of N×N matrices where N3 which is based on transformations which are called discrete signal-induced heap transformations (DsiHTs). These transformations are generated by given signals and can be composed by elementary rotations. The data processing order, or the path of the transformations, is an important characteristic of it, and the correct choice of such paths can lead to a significant reduction in the operation when calculating the factorization for large matrices. Such paths are called fast paths of the N-point DsiHTs, and they define sparse matrices with more zero coefficients than when calculating QR-factorization in the traditional path, that is, when processing data in the natural order x0,x1,x2,. For example, in the first stage of the factorization of a 512 × 512 matrix, a matrix is used with 257,024 zero coefficients out of a total of 262,144 coefficients when using the fast paths. For comparison, the calculations in the natural order require a 512 × 512 matrix with only 130,305 zero coefficients at this stage. The Householder reflection matrix has no zero coefficients. The number of multiplication operations for the QR-factorization by the fast DsiHTs is more than 40 times smaller than when using the Householder reflections and 20 times smaller when using DsiHTs with the natural paths. Examples with the 4 × 4, 5 × 5, and 8 × 8 matrices are described in detail. The concept of complex DsiHT with fast paths is also described and applied in the QR-factorization of complex square matrices. An example of the QR-factorization of a 256 × 256 complex matrix is also described and compared with the method of Householder reflections which is used in programming language MATLAB R2024b. Full article
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29 pages, 73612 KB  
Article
DNMF-AG: A Sparse Deep NMF Model with Adversarial Graph Regularization for Hyperspectral Unmixing
by Kewen Qu, Xiaojuan Luo and Wenxing Bao
Remote Sens. 2026, 18(1), 155; https://doi.org/10.3390/rs18010155 - 3 Jan 2026
Viewed by 960
Abstract
Hyperspectral unmixing (HU) aims to extract constituent information from mixed pixels and is a fundamental task in hyperspectral remote sensing. Deep non-negative matrix factorization (DNMF) has recently attracted attention for HU due to its hierarchical representation capability. However, existing DNMF-based methods are often [...] Read more.
Hyperspectral unmixing (HU) aims to extract constituent information from mixed pixels and is a fundamental task in hyperspectral remote sensing. Deep non-negative matrix factorization (DNMF) has recently attracted attention for HU due to its hierarchical representation capability. However, existing DNMF-based methods are often sensitive to noise and outliers, and face limitations in incorporating prior knowledge, modeling feature structures, and enforcing sparsity constraints, which restrict their robustness, accuracy, and interpretability. To address these challenges, we propose a sparse deep NMF model with adversarial graph regularization for hyperspectral unmixing, termed DNMF-AG. Specifically, we design an adversarial graph regularizer that integrates local similarity and dissimilarity graphs to promote intraclass consistency and interclass separability in the spatial domain, thereby enhancing structural modeling and robustness. In addition, a Gram-based sparsity constraint is introduced to encourage sparse abundance representations by penalizing inner product correlations. To further improve robustness and computational efficiency, a truncated activation function is incorporated into the iterative update process, suppressing low-amplitude components and promoting zero entries in the abundance matrix. The overall model is optimized using the alternating direction method of multipliers (ADMM). Experimental results on multiple synthetic and real datasets demonstrate that the proposed method outperforms state-of-the-art approaches in terms of estimation accuracy and robustness. Full article
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20 pages, 2814 KB  
Article
Application of the Q-Less QR Factorization to Resolve Sparse Linear Over-Constraints
by Jeong-Rae Cho, Keunhee Cho, Hyejin Yoon, Dong Sop Rhee and Jin Ho Lee
Appl. Sci. 2025, 15(24), 13059; https://doi.org/10.3390/app152413059 - 11 Dec 2025
Viewed by 591
Abstract
Over-constraint issues frequently arise in complex models with multiple constraints, such as those used in multibody systems and contact analyses. When over-constraints exist, commonly used constraint-handling methods, such as the transformation method, the Lagrange multiplier method, and the penalty method, can produce small [...] Read more.
Over-constraint issues frequently arise in complex models with multiple constraints, such as those used in multibody systems and contact analyses. When over-constraints exist, commonly used constraint-handling methods, such as the transformation method, the Lagrange multiplier method, and the penalty method, can produce small or zero pivot values in the system matrix. This may result in non-convergence, slow convergence, or incorrect solutions. Furthermore, in the transformation method, in which the slave degrees of freedom (DOFs) corresponding to each constraint equation are eliminated, most finite element software restricts the reuse of slave DOFs that have already been referenced in other constraint equations. This makes an already complex modeling process even more challenging. This paper first summarizes a systematic algorithm proposed by Cho for detecting and resolving over-constraints in linear constraint equations, highlighting its efficiency in less complex scenarios but also its limitations for large-scale models due to excessive computation time. To address these limitations, this paper introduces a new algorithm that leverages the sparsity of the constraint matrix and applies sparse QR factorization without generating a dense Q matrix. The effectiveness of this approach in handling complex, large-scale finite element (FE) models is demonstrated, confirming its applicability to complex engineering problems. Full article
(This article belongs to the Section Mechanical Engineering)
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15 pages, 3190 KB  
Article
Coded Aperture Optimization in X-Ray Computed Tomography via Sparse Covariance Matrix Estimation
by Yuqi Jiang, Tianyi Mao, Jianyong Zhou, Qile Zhao, Jun Yin, Xuedong Yi and Haiyou Wu
Sensors 2025, 25(24), 7479; https://doi.org/10.3390/s25247479 - 9 Dec 2025
Viewed by 659
Abstract
Coded aperture X-ray computed tomography (CAXCT) measures coded X-ray projections to reconstruct the inner structure of an object. Coded apertures, which determine the point spread function, can be designed to improve the reconstruction quality, but most approaches are computationally expensive, leading to very [...] Read more.
Coded aperture X-ray computed tomography (CAXCT) measures coded X-ray projections to reconstruct the inner structure of an object. Coded apertures, which determine the point spread function, can be designed to improve the reconstruction quality, but most approaches are computationally expensive, leading to very small images. In this paper, a sparse covariance matrix estimation approach is introduced to minimize the information loss sensed by projections corresponding to large tomographic images. The covariance matrix representing the map of the overlapping information of the projections is obtained by using block matrix multiplication and sparse estimation. A heuristic variant algorithm with a noise factor is presented to search the combinations of D projections leading to maximum non-overlapping information acquisition, where D is the number of unblocking elements on the coded apertures. Numerical experiments with simulated datasets show that the optimization performance of the proposed method is comparable to that of state-of-the-art methods with small images. Further, for the analyzed cases, coded aperture optimization was performed with 512 × 512 images by analyzing coefficients smaller than 0.02% in the covariance matrix. Full article
(This article belongs to the Special Issue Computational Optical Sensing and Imaging)
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