Search Results (68)

To address the poor computational efficiency of traditional fixed-stratification methods in very low frequency (VLF) ionospheric propagation modeling, this paper proposes a dynamic stratification algorithm. First, filtering optimization is applied to the electron density, and dynamic adaptive stratification is implemented in the vertical direction. By establishing a nonlinear mapping relationship between the electron density gradient and the stratification thickness, the algorithm integrates dynamic ionospheric stratification with a hybrid regularization algorithm for the transmission matrix. Specifically, Singular Value Decomposition (SVD) and dynamic truncation techniques are employed to process the transmission matrix, effectively resolving the numerical ill-posedness in regions with abrupt ionospheric changes. This enables high-precision calculation of reflection coefficients in the 3–30 kHz frequency band. By tuning parameters such as the reference stratification thickness and adjustment factors, an optimized stratification model and an algorithm quality evaluation coefficient are obtained. The simulation results demonstrate that, compared with fixed stratification, the proposed algorithm achieves an average relative error of 4.7% for the reflection coefficient in the VLF range while improving computational efficiency by more than 50%. This provides a promising approach for efficient and high-precision prediction of VLF wave propagation. Full article

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

This paper develops a robust numerical scheme based on a frame collocation method for solving multi-term fractional ordinary differential equations (FODEs) whose solutions exhibit multiple singularities at the origin. To adaptively capture the singular behavior, we construct a hybrid basis-function frame by combining shifted fractional Legendre polynomials. An efficient computational formula for the Caputo fractional derivative is derived, which transforms the original problem into a nonlinear algebraic system at the collocation points. Due to the over-completeness of the fractional polynomial frame, the resulting linear system becomes rank-deficient, with only a small subset of singular components carrying meaningful solution information. To eliminate the adverse effects of numerical null-space components, we employ truncated singular value decomposition (TSVD) regularization, thereby enabling stable and high-precision solutions. Extensive numerical experiments on several benchmark problems, including the fractional Bagley–Torvik equation, linear multi-term FODEs, and nonlinear cases, demonstrate that the proposed method achieves exponential convergence rates. Notably, when the singular exponent of the solution matches a tunable parameter ($\delta$) in the basis functions, superconvergence is observed, significantly outperforming standard spectral methods. Compared with traditional spectral approaches, the proposed frame collocation framework retains spectral accuracy while exhibiting superior capability in handling complex singular structures, providing a powerful and reliable tool for high-precision simulations of multi-term fractional differential equations. Full article

This paper explores the relationship between random matrix theory (RMT) and the use of weight conditioning for training deep neural networks by employing an integrated framework. It has been shown that trained neural networks produce singular value distributions that follow universal distributions prescribed by RMT; however, the presence of non-universal outliers in the distribution can contain significant information particular to the task being performed. In addition, this research investigates how the application of diagonal row equilibration as a form of conditioning affects spectral behavior and optimization stability within deep neural networks. The results show that through conditioning, the random bulk of the singular value decomposition (SVD) spectrum is effectively compressed into a narrow band about the value 1, significantly reducing the Marchenko–Pastur bounds. The results also support the claim that weight conditioning retains the informative nature of the spectral outliers. The experimental results show that weight condition numbers (κ(W)) decreased from extremely ill-conditioned regimes of approximately 10³ to 10⁴ to almost 1.0, producing smoother training landscapes, a quicker convergence rate, and an improved ability for gradients to propagate. These results suggest that conditioning weights can be thought of as an implicit spectral regularize linking RMT evidence and concepts to the practical optimization of deep learning methods. Full article

Deep learning systems deployed in regulated settings require explanations that are accurate and stable under nuisance transformations, yet classical post hoc transition matrices rely on fidelity-only fitting that fails to guarantee consistent explanations under spatial rotations or other group actions. In this work, we propose Equivariant Transition Matrices, a post hoc approach that augments transition matrices with Lie-group-aware structural constraints to bridge this research gap. Our method estimates infinitesimal generators in the formal and mental feature spaces, enforces an approximate intertwining relation at the Lie algebra level, and solves the resulting convex Least-Squares problem via singular value decomposition for small networks or implicit operators for large systems. We introduce diagnostics for symmetry validation and an unsupervised strategy for regularization weight selection. On a controlled synthetic benchmark, our approach reduces the symmetry defect from 13,100 to 0.0425 while increasing the mean squared error marginally from 0.00367 to 0.00524. On the MNIST dataset, the symmetry defect decreases by 72.6 percent (141.19 to 38.65) with changes in structural similarity and peak signal-to-noise ratio below 0.03 percent and 0.06 percent, respectively. These results demonstrate that explanation-level equivariance can be reliably imposed post-training, providing geometrically consistent interpretations for fixed deep models. Full article

To address the issue of missing position in flight trajectory data collected by Automatic Dependent Surveillance-Broadcast (ADS-B) systems, a flight trajectory tensor completion model based on truncated Schatten p-norm minimization is proposed. First, the low-rank characteristics of the trajectory set are validated using Singular Value Decomposition (SVD); based on this, the data is transformed into a three-dimensional tensor structure. Next, a regularization strategy combining the Schatten p-norm with a singular value truncation mechanism is introduced to construct the trajectory tensor completion model, which suppresses noise and interference from minor components while preserving the main variation patterns of the trajectories. Finally, the model is optimized and solved using the Alternating Direction Method of Multipliers (ADMM) to obtain the completed trajectories. Taking historical ADS-B trajectory data from Orly Airport to Toulouse Airport as an example, the completion results of the proposed model under different missing patterns, missing rates, and flight phases are analyzed from both qualitative and quantitative perspectives. Experimental results show that compared with other representative models, the proposed model achieves the best completion performance under different missing patterns and missing rates; the completion performance during the cruise phase is better than during the ascent and descent phases. The proposed model can serve as a preprocessing technique for flight trajectory data in air traffic, providing more complete and reliable data support for various downstream applications. Full article

We propose a low-complexity hybrid beamforming method for massive Multiple-Input Multiple-Output (MIMO) systems that is robust to Channel State Information (CSI) estimation errors. These errors stem from hardware impairments, pilot contamination, limited training, and fast fading, causing spectral-efficiency loss. However, existing hybrid beamforming solutions typically either assume near-perfect CSI or rely on greedy/black-box designs without an explicit mechanism to regularize the error-distorted singular modes, leaving a gap in unified, low-complexity, and theoretically grounded robustness. We unfold the Alternating Direction Method of Multipliers (ADMM) into a trainable Deep Learning (DL) network, termed DL-ADMM, to jointly optimize Radio-Frequency (RF) and baseband precoders and combiners. In DL-ADMM, the ADMM update mappings are learned (layer-wise parameters and projections) to amortize the joint RF/baseband optimization, whereas Regularized Singular Value Decomposition (RSVD) acts as an analytical regularizer that reshapes the observed channel’s singular values to suppress noise amplification under imperfect CSI. RSVD is integrated to stabilize singular modes and curb noise amplification, yielding a unified and scalable design. For ${\sigma }_e^2=0.1$, the proposed DL-ADMM-Reg achieves approximately 8–11 bits/s/Hz higher spectral efficiency than Orthogonal Matching Pursuit (OMP) at Signal-to-Noise Ratio (SNR) $=20$–40 dB, while remaining within <1 bit/s/Hz of the digital-optimal benchmark across both $(N_t,N_r)=(32,32)$ and $(64,64)$ settings. Simulations confirm higher spectral efficiency and robustness than OMP and Adaptive Phase Shifters (APSs). Full article

Five-axis precision dispensing machines are employed for semiconductor packaging. The dispensing accuracy is significantly affected by multiple geometric errors among the five axes. This paper proposes a vision-based measurement (VBM) system for identifying geometric errors and calibrating kinematics. The VBM system is also employed to complete the detection of the workpiece. A kinematic model of the machine was established using a local product-of-exponential formulation of screw theory. A geometric error identification algorithm was designed. Eight position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) were involved. The system of overdetermined equations was solved. Combining the singular value decomposition and regularization, eight PIGEs in the A and C axes were identified. Comprehensive error measurement results verified the proposed approach. The VBM system measured a mean spatial position error of approximately 59.9 μm and a mean orientation error of about 160 arcsec for the end-effector, reflecting the geometric error level of the prototype machine. The proposed approach provides a feasible and automated calibration solution for five-axis precision dispensing machines. Full article

Satellite videos are widely applied for large-scale surveillance. Existing low-rank matrix decomposition-based methods produce promising results under simple and stationary backgrounds. However, these methods suffer a severe performance drop on satellite videos with complex and dynamic backgrounds. To address these challenges, we propose a matrix-based total variation regularized robust PCA (TV-RPCA) approach for moving-vehicle detection. Specifically, our TV-RPCA uses the partial sum of singular values to model the low-rank background. Moreover, a ${\mathit{\ell }}_p$ norm and a spatial–temporal TV regularization are adopted to encourage the spatial–temporal continuity of foregrounds. The optimization of our TV-RPCA is carried out using the augmented Lagrangian multiplier framework combined with the alternating direction minimization approach. Comprehensive experiments conducted on SkySat and Jilin-1 video data verify the effectiveness of the proposed approach. Full article

Background: Current fMRI (functional magnetic resonance imaging)-driven brain information decoding for visual image reconstruction techniques faces issues such as poor structural fidelity, inadequate model generalization, and unnatural visual image reconstruction in complex scenarios. Methods: To address these challenges, this study proposes a Dynamic Confidence Bayesian Adaptive Network (DCBAN). In this network model, deep nested Singular Value Decomposition is introduced to embed low-rank constraints into the deep learning model layers for fine-grained feature extraction, thus improving structural fidelity. The proposed Bayesian Adaptive Fractional Ridge Regression module, based on singular value space, dynamically adjusts the regularization parameters, significantly enhancing the decoder’s generalization ability under complex stimulus conditions. The constructed Dynamic Confidence Adaptive Diffusion Model module incorporates a confidence network and time decay strategy, dynamically adjusting the semantic injection strength during the generation phase, further enhancing the details and naturalness of the generated images. Results: The proposed DCBAN method is applied to the NSD, outperforming state-of-the-art methods by 8.41%, 0.6%, and 4.8% in PixCorr (0.361), Incep (96.0%), and CLIP (97.8%), respectively, achieving the current best performance in both structural and semantic fMRI visual image reconstruction. Conclusions: The DCBAN proposed in this thesis offers a novel solution for reconstructing visual images from fMRI signals, significantly enhancing the robustness and generative quality of the reconstructed images. Full article

Voice biometric systems play a critical role in numerous security applications, including electronic device authentication, banking transaction verification, and confidential communications. Despite their widespread utility, these systems are increasingly targeted by sophisticated spoofing attacks that leverage advanced artificial intelligence techniques to generate realistic synthetic speech. Addressing the vulnerabilities inherent to voice-based authentication systems has thus become both urgent and essential. This study proposes a novel experimental analysis that extensively explores various dimensionality reduction strategies in conjunction with supervised machine learning models to effectively identify spoofed voice signals. Our framework involves extracting multicepstral features followed by the application of diverse dimensionality reduction methods, such as Principal Component Analysis (PCA), Truncated Singular Value Decomposition (SVD), statistical feature selection (ANOVA F-value, Mutual Information), Recursive Feature Elimination (RFE), regularization-based LASSO selection, Random Forest feature importance, and Permutation Importance techniques. Empirical evaluation using the ASVSpoof 2017 v2.0 dataset measures the classification performance with the Equal Error Rate (EER) metric, achieving values of approximately 10%. Our comparative analysis demonstrates significant performance gains when dimensionality reduction methods are applied, underscoring their value in enhancing the security and effectiveness of voice biometric verification systems against emerging spoofing threats. Full article

Inpainting noisy remote-sensing images can reduce the cost of acquiring remote-sensing images (RSIs). Since RSIs contain complex land structure features and concentrated obscured areas, existing inpainting methods often produce color inconsistency and structural smoothing when applied to RSIs with a high missing ratio. To address these problems, inspired by tensor recovery, a lightweight image Inpainting Generative Adversarial Network (GAN) method combining low-rankness and local-smoothness (IGLL) is proposed. IGLL utilizes the low-rankness and local-smoothness characteristics of RSIs to guide the deep-learning inpainting. Based on the strong low rankness characteristic of the RSIs, IGLL fully utilizes the background information for foreground inpainting and constrains the consistency of the key ranks. Based on the low smoothness characteristic of the RSIs, learnable edges and structure priors are designed to enhance the non-smoothness of the results. Specifically, the generator of IGLL consists of a pixel-level reconstruction net (PIRN) and a perception-level reconstruction net (PERN). In PIRN, the proposed global attention module (GAM) establishes long-range pixel dependencies. GAM performs precise normalization and avoids overfitting. In PERN, the proposed flexible feature similarity module (FFSM) computes the similarity between background and foreground features and selects a reasonable feature for recovery. Compared with existing works, FFSM improves the fineness of feature matching. To avoid the problem of local-smoothness in the results, both the generator and discriminator utilize the structure priors and learnable edges to regularize large concentrated missing regions. Additionally, IGLL incorporates mathematical constraints into deep-learning models. A singular value decomposition (SVD) loss item is proposed to model the low-rankness characteristic, and it constrains feature consistency. Extensive experiments demonstrate that the proposed IGLL performs favorably against state-of-the-art methods in terms of the reconstruction quality and computation costs, especially on RSIs with high mask ratios. Moreover, our ablation studies reveal the effectiveness of GAM, FFSM, and SVD loss. Source code is publicly available on GitHub. Full article

Compared to conventional single-aperture infrared cameras, the bio-inspired infrared compound eye camera integrates the advantages of infrared imaging technology with the benefits of multi-aperture systems, enabling simultaneous information acquisition from multiple perspectives. This enhanced detection capability demonstrates unique performance in applications such as autonomous driving, surveillance, and unmanned aerial vehicle reconnaissance. Current single-aperture small target detection algorithms fail to exploit the spatial relationships among compound eye apertures, thereby underutilizing the inherent advantages of compound eye imaging systems. This paper proposes a low-rank and sparse decomposition method based on bio-inspired infrared compound eye image features for small target detection. Initially, a compound eye structural weighting operator is designed according to image characteristics, which enhances the sparsity of target points when combined with the reweighted $l_1$-norm. Furthermore, to improve detection speed, the structural tensor of the effective imaging region in infrared compound eye images is reconstructed, and the Representative Coefficient Total Variation method is employed to avoid complex singular value decomposition and regularization optimization computations. Our model is efficiently solved using the Alternating Direction Method of Multipliers (ADMM). Experimental results demonstrate that the proposed model can rapidly and accurately detect small infrared targets in bio-inspired compound eye image sequences, outperforming other comparative algorithms. Full article

Temporal random noise (TRN) in uncooled infrared detectors significantly degrades image quality. Existing denoising techniques primarily address fixed-pattern noise (FPN) and do not effectively mitigate TRN. Therefore, a novel TRN denoising approach based on total variation regularization and low-rank tensor decomposition is proposed. This method effectively suppresses temporal noise by introducing twisted tensors in both horizontal and vertical directions while preserving spatial information in diverse orientations to protect image details and textures. Additionally, the Laplacian operator-based bidirectional twisted tensor truncated nuclear norm (bt-LPTNN), is proposed, which is a norm that automatically assigns weights to different singular values based on their importance. Furthermore, a weighted spatiotemporal total variation regularization method for nonconvex tensor approximation is employed to preserve scene details. To recover spatial domain information lost during tensor estimation, robust principal component analysis is employed, and spatial information is extracted from the noise tensor. The proposed model, bt-LPTVTD, is solved using an augmented Lagrange multiplier algorithm, which outperforms several state-of-the-art algorithms. Compared to some of the latest algorithms, bt-LPTVTD demonstrates improvements across all evaluation metrics. Extensive experiments conducted using complex scenes underscore the strong adaptability and robustness of our algorithm. Full article

In the context of hybrid twins, a data-driven enrichment is added to the physics-based solution to represent with higher accuracy the reference solution assumed to be known at different points in the physical domain. Such an approach enables better predictions. However, the data-driven enrichment is usually represented by a regression, whose main drawbacks are (i) the difficulty of understanding the subjacent physics and (ii) the risks induced by the data-driven model extrapolation. This paper proposes a procedure enabling the extraction of a differential operator associated with the enrichment provided by the data-driven regression. For that purpose, a sparse Singular Value Decomposition, SVD, is introduced. It is then employed, first, in a full operator representation regularized optimization problem, where sparsity is promoted, leading to a linear programming problem, and then in a tensor decomposition of the operator’s identification procedure. The results show the ability of the method to identify the exact missing operators from the model. The regularized optimization problem was also able to identify the weights of the missing terms with a relative error of about 10% on average, depending on the selected use case. Full article