Search Results (110)

Compressed sensing (CS) and matrix completion algorithms (MCA) have each introduced sparse and low-rank priors into synthetic aperture radar (SAR) imaging. However, their combined use reveals a fundamental zero-sum trade-off: enhancing spatial continuity tends to obscure weak targets, while strengthening sparse recovery amplifies off-grid artifacts. This inherent conflict is further exacerbated by static regularization, which imposes a rigid global compromise and prevents genuine synergy between the two priors. To overcome this limitation, this paper proposes a Spatio-Temporal Adaptive Synergistic Constraint Imaging (STASCI) algorithm, which dynamically balances the two priors in a scene-aware manner. The core of STASCI is a unified regularization framework. The low-rank constraint models’ spatial continuity in the background to suppress off-grid artifacts. The sparse constraint, enhanced by a non-convex Geman-McClure function, is employed to detect weak targets and compensate for detail loss. A key innovation is a spatio-temporal dual-dimensional regularization mechanism that employs Sobel operators to probe local spatial gradients and dynamically adjusts the strength of each prior according to regional scene characteristics. This enables adaptive synergy rather than a fixed trade-off. The optimization is solved via the alternating direction method of multipliers (ADMM), with the low-rank subproblem accelerated by randomized singular value decomposition (RSVD). Final imaging is performed using the Range Migration Algorithm (RMA). Experiments on real measurements and public datasets demonstrate that STASCI breaks the conventional detail-background trade-off. It effectively suppresses off-grid artifacts while retaining weak targets, leading to significant improvements in imaging accuracy and robustness across complex scenarios. Full article

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

Low-rank sparse decomposition models have become the mainstream optimization framework for multiframe infrared small target detection. Existing low-rank matrix decomposition approximations typically pre-decompose infrared videos into the product of two low-rank matrices to capture the background’s low-rank characteristics. However, such approximations are not optimal and often result in suboptimal background recovery. To achieve more accurate low-rank recovery, we exploit the intrinsic relationship between low-rank matrices and their generalized inverse matrices, thereby improving conventional decomposition approximations. Moreover, to address the high computational cost of applying low-rank and sparse decomposition models to multi-frame infrared videos, we introduce a robust column-row (CUR) decomposition to accelerate the iterative process, thereby significantly improving computational efficiency. The experimental results show that the proposed method achieves fast detection of small targets in infrared videos while maintaining competitive detection performance. Full article

Infrared small target detection (IRSTD) task is vital in practical applications. It is still a challenge when the target size is very small and the local signal-to-noise ratio is particularly low. This paper proposed an Infrared Tall Patch-Matrix (ITPM) model, which takes a novel perspective to construct a lower-rank patch matrix structure to improve the detection performance of low-contrast small targets. Specifically, we use a sliding split window to reconstruct the original image into a suitable low-rank structure called Tall Patch-Matrix, which can increase the detection rate of low-contrast small targets and suppress most noise. Second, the High Local Variance Low-Rank and Sparse Decomposition (ITPM-HiLV-LRSD) method is used to perform low-rank and sparse decomposition of the Infrared Tall Patch-Matrix, and a Thin Singular Value Decomposition (Thin SVD) optimization strategy is proposed to further reduce the computational complexity. Given the absence of open literature datasets for detecting infrared targets in low-contrast small scenarios, we created a Low-contrast Small Target Detection Dataset (LSTDD) comprising 600 infrared target detection images with varied sky backgrounds. This dataset simulates low-contrast small targets across different signal-to-noise ratios. To demonstrate the generalizability of our method, we also conducted experiments on a representative low-contrast subset of real-world images from the SIRST dataset. Compared with six state-of-the-art methods, our proposed method excels in detecting low-contrast small targets with superior performance. Full article

Sparse unmixing (SU) has become a research hotspot in hyperspectral image (HSI) analysis in recent years due to its interpretable physical mechanisms and engineering practicality. However, traditional SU methods are confronted with two core bottlenecks: Firstly, the high computational complexity of the abundance matrix inversion severely limits algorithmic efficiency. Secondly, the inherent challenges posed by large-scale highly coherent spectral libraries hinder improvement of unmixing accuracy. To overcome these limitations, this study proposes a novel sub-abundance map regularized sparse unmixing (SARSU) framework based on dynamic abundances subspace awareness. Specifically, first of all, we have developed an intelligent spectral atom selection strategy that employs a designed dynamic activity evaluation mechanism to quantify the participation contribution of spectral library atoms during the unmixing process in real time. This enables adaptive selection of critical subsets to construct active subspace abundance maps, effectively mitigating spectral redundancy interference. Secondly, we innovatively integrated weighted nuclear norm regularization based on sub-abundance maps into the model, deeply mining potential low-rank structures within spatial distribution patterns to significantly enhance the spatial fidelity of unmixing results. Additionally, a multi-directional neighborhood-aware dual total variation (DTV) regularizer was designed, which enforces spatial consistency constraints between adjacent pixels through a four directional (horizontal, vertical, diagonal, and back-diagonal) differential penalty mechanism, ensuring abundance distributions comply with physical diffusion laws of ground objects. Finally, to efficiently solve the proposed objective model, an optimization algorithm based on the Alternating Direction Method of Multipliers (ADMM) was developed. Comparative experiments conducted on two simulated datasets and four real hyperspectral benchmark datasets, alongside comparisons with state-of-the-art methods, validated the efficiency and superiority of the proposed approach. Full article

People are exposed to mixtures of metals, per- and polyfluoroalkyl substances (PFAS), phthalates, and polycyclic aromatic hydrocarbons (PAH) rather than single chemicals, yet mixture inference is hampered by high dimensionality, correlation, missingness, and left-censoring below limits of detection (LOD). We analyzed 2013–2014 National Health and Nutrition Examination Survey (NHANES) biomarkers (n = 4367) to (i) recover latent, interpretable co-exposure structures and (ii) quantify how these mixtures relate to liver health. To denoise and handle censoring, we applied Principal Component Pursuit with LOD adjustment (PCP-LOD), decomposing the exposure matrix into a non-negative low-rank component (population co-exposure profiles) and a sparse component (individual spikes), and then used Bayesian Kernel Machine Regression (BKMR) to estimate nonlinear and interactive associations with AST, ALT, GGT, ALP, total bilirubin, and the Fatty Liver Index (FLI), retaining analytes with ≥50% detection. PCP-LOD revealed coherent clusters (e.g., long-chain PFAS grouping; shared metal loadings), while the sparse layer highlighted episodic phthalate elevations. BKMR indicated outcome-specific mixture effects: PAHs and selected phthalates showed consistently positive associations with ALP, GGT, and FLI; PFAS (PFOS, PFNA, PFOA) exhibited modest associations with ALP and bilirubin; metals displayed mixed directions. A joint increase in the overall mixture from the 25th to 75th percentile corresponded to an upward shift in FLI and a smaller rise in ALT. This censoring-aware low-rank-plus-sparse framework coupled with flexible mixture modeling recovers actionable exposure architecture and reveals clinically relevant links to liver injury and steatosis, motivating longitudinal and mechanistic studies to strengthen causal interpretation. Full article

A long-standing challenge for the structural health monitoring (SHM) community is the masking effect of environmental variability, typically addressed by orthogonal projection (OP)-based data normalization to isolate the influence of environmental variability and enable structural anomaly detection. However, conventional OP techniques, such as principal component analysis, rely on clean and complete data, and their performance degrades in the presence of outliers or missing entries. To overcome this limitation, this paper proposes an integrated approach that combines OP with noisy low-rank matrix completion (NLRMC). The main advantage of NLRMC is its ability to couple low-rank and sparse decomposition with matrix completion, simultaneously handling data corruption and missingness to recover incomplete datasets and enable robust anomaly detection. By incorporating novelty-indicator extraction, a fully online, unsupervised anomaly-detection procedure is established. Validation on a vibration-based SHM dataset from the KW51 railway bridge confirms that the NLRMC-OP approach achieves reliable detection of operational state changes before and after retrofitting, even under both data corruption and missing scenarios. This study advances the usability of SHM data and facilitates efficient decision-making, while also highlighting the broader significance of leveraging the low-rank data structure in AI-enabled operation and maintenance of civil infra-structure. Full article

Accurate node localization is essential for many Internet of Things (IoT) applications. However, incomplete and noisy distance measurements often degrade the reliability of the Euclidean Distance Matrix (EDM), which is critical for range-based localization. To address this issue, a Low-Rank Matrix Completion approach based on nonconvex rank approximation (LRMCN) is proposed to recover the true EDM. First, the observed EDM is decomposed into a low-rank matrix representing the true distances and a sparse matrix capturing noise. Second, a nonconvex surrogate function is used to approximate the matrix rank, while the $l_1$-norm is utilized to model the sparsity of the noise component. Third, the resulting optimization problem is solved using the Alternating Direction Method of Multipliers (ADMMs). This enables accurate recovery of a complete and denoised EDM from incomplete and corrupted measurements. Finally, relative node locations are estimated using classical multi-dimensional scaling, and absolute coordinates are determined based on a small set of anchor nodes with known locations. The experimental results show that the proposed method achieves superior performance in both matrix completion and localization accuracy, even in the presence of missing and corrupted data. Full article

Thoracic electrical impedance tomography (EIT) provides real-time, bedside imaging of pulmonary function and has demonstrated significant clinical value in guiding treatment strategies for critically ill patients. However, the practical application of EIT remains challenging due to its susceptibility to measurement disturbances, such as electrode contact problems and patient movement. These disturbances often manifest as spike-like noise that can severely degrade EIT image quality. To address this issue, we propose a robust Principal Component Analysis (RPCA)-based approach that models EIT data as the sum of a low-rank matrix and a sparse matrix. The low-rank matrix captures the underlying physiological signals, while the sparse matrix contains spike-like noise components. In simulation studies considering different spike magnitudes, widths and channels, all the image correlation coefficients between RPCA-processed images and the ground truth exceeded 0.99, and the image error of the original fEIT image with spike-like noise was much larger than that after RPCA processing. In eight patient cases, RPCA significantly improved the image quality (image error: p < 0.001; image correlation coefficient: p < 0.001) and enhanced the clinical EIT-based indexes accuracy (p < 0.001). Therefore, we conclude that RPCA is a promising technique for reducing spike-like noise in clinical EIT data, thereby improving data quality and potentially facilitating broader clinical application of EIT. Full article

Conventional acoustic velocity-independent direction of arrival (DOA) estimation models have limited measurement ranges and low degrees of freedom. This paper proposes an omnidirectional DOA estimation model based on improved Toeplitz matrix reconstruction to address these issues. The proposed method focuses on the Toeplitz matrix reconstruction method for sparse arrays to enhance the degree of freedom of the arrays. The method employs an expanding coprime array with a larger aperture, eliminating the acoustic velocity factor through geometric relationships and constructing a larger-size Toeplitz matrix. In addition, the concept of “low-rank matrix reconstruction” is introduced to fill the vacant terms in the Toeplitz matrix. Finally, the simulation experiments demonstrate the effectiveness of the proposed algorithm in improving the estimation accuracy. 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

By leveraging the high correlation between multi-ping echo data, low-rank and sparse decomposition methods are applied for reverberation suppression. Previous methods typically perform decomposition on the vectorized multi-ping echograph, which is obtained by stacking beamforming outputs from all directions in the same column. However, when the multi-ping correlation of beamforming outputs from different directions varies significantly due to the time-varying nature of the underwater acoustic channel, it becomes challenging to precisely capture the variations of the reverberation background. As a result, the performance of reverberation suppression is degraded. To alleviate this issue, we attempt to decompose the matrix formed by multi-ping beamforming outputs in different directions individually. The accelerated alternating projections method is used to estimate the steady reverberation for moving target detection. By exploiting the differences in spatio-temporal dimensions between moving targets and reverberation fluctuations, a weighted spatio-temporal density method with adaptive thresholding is used to further extract the target echoes. Field data were utilized to validate the effectiveness of the proposed method, and the experimental results demonstrated its superior robustness in an unstable reverberation-limited environment, maintaining an accurate estimation of steady reverberation. Full article

Traditional underwater polarization imaging methods can only provide clear degree of polarization (DOP) and intensity images of the object but cannot provide images of the polarization state of the object. This paper proposes a method to extract clear object information from turbid water in all four Stokes parameter (I, Q, U, and V) channels by using the full Stokes camera, enabling clear polarization state image reconstruction. The method utilizes multiple images from different angles to construct a low-rank and sparse matrix. Then, by decomposing this matrix into sparse and low-rank components, clear Q, U, and V images (i.e., the full polarization state) can be obtained. Unlike traditional methods that assume the circularly polarized component (V component) to be zero, this method retains V channel information, allowing for circular polarization component measurement. The study successfully reconstructed clear underwater images of samples with inhomogeneous DOP distribution and obtained the clear polarization states of polarizers and fish in the turbid water. The results show that the proposed method can visualize and analyze the object’s polarization state quantitatively with high accuracy in turbid water for the first time, potentially extending the applicability of polarization underwater imaging in ocean exploration. Full article

Hyperspectral compressed imaging is a novel imaging detection technology based on compressed sensing theory that can quickly acquire spectral information of terrestrial objects in a single exposure. It combines reconstruction algorithms to recover hyperspectral data from low-dimensional measurement images. However, hyperspectral images from different scenes often exhibit high-frequency data sparsity and existing deep reconstruction algorithms struggle to establish accurate mapping models, leading to issues with detail loss in the reconstruction results. To address this issue, we propose a hyperspectral reconstruction method based on global gradient information and local low-rank priors. First, to improve the prior model’s efficiency in utilizing information of different frequencies, we design a gradient sampling strategy and training framework based on decision trees, leveraging changes in the loss function gradient information to enhance the model’s predictive capability for data of varying frequencies. Second, utilizing the local low-rank prior characteristics of the representative coefficient matrix, we develop a sparse sensing denoising module to effectively improve the local smoothness of point predictions. Finally, by establishing a regularization term for the reconstruction process based on the semantic similarity between the denoised results and prior spectral data, we ensure spatial consistency and spectral fidelity in the reconstruction results. Experimental results indicate that the proposed method achieves better detail recovery across different scenes, demonstrates improved generalization performance for reconstructing information of various frequencies, and yields higher reconstruction quality. Full article

As an extension of non-negative matrix factorization (NMF), graph-regularized non-negative matrix factorization (GNMF) has been widely applied in data mining and machine learning, particularly for tasks such as clustering and feature selection. Traditional GNMF methods typically rely on predefined graph structures to guide the decomposition process, using fixed data graphs and feature graphs to capture relationships between data points and features. However, these fixed graphs may limit the model’s expressiveness. Additionally, many NMF variants face challenges when dealing with complex data distributions and are vulnerable to noise and outliers. To overcome these challenges, we propose a novel method called sparse feature-weighted double Laplacian rank constraint non-negative matrix factorization (SFLRNMF), along with its extended version, SFLRNMTF. These methods adaptively construct more accurate data similarity and feature similarity graphs, while imposing rank constraints on the Laplacian matrices of these graphs. This rank constraint ensures that the resulting matrix ranks reflect the true number of clusters, thereby improving clustering performance. Moreover, we introduce a feature weighting matrix into the original data matrix to reduce the influence of irrelevant features and apply an $L_{\mathrm{2,1}/2}$ norm sparsity constraint in the basis matrix to encourage sparse representations. An orthogonal constraint is also enforced on the coefficient matrix to ensure interpretability of the dimensionality reduction results. In the extended model (SFLRNMTF), we introduce a double orthogonal constraint on the basis matrix and coefficient matrix to enhance the uniqueness and interpretability of the decomposition, thereby facilitating clearer clustering results for both rows and columns. However, enforcing double orthogonal constraints can reduce approximation accuracy, especially with low-rank matrices, as it restricts the model’s flexibility. To address this limitation, we introduce an additional factor matrix R, which acts as an adaptive component that balances the trade-off between constraint enforcement and approximation accuracy. This adjustment allows the model to achieve greater representational flexibility, improving reconstruction accuracy while preserving the interpretability and clustering clarity provided by the double orthogonality constraints. Consequently, the SFLRNMTF approach becomes more robust in capturing data patterns and achieving high-quality clustering results in complex datasets. We also propose an efficient alternating iterative update algorithm to optimize the proposed model and provide a theoretical analysis of its performance. Clustering results on four benchmark datasets demonstrate that our method outperforms competing approaches. Full article