Tensor data, often acquired under physical constraints, is frequently degraded by corruption or missing entries, posing significant challenges in multidimensional signal processing. While recent coupled-prior frameworks aim to unify low-rank and sparse regularizers, they fall short of effectively reconciling these priors in the gradient domain. To overcome this limitation, we propose a novel Tensor Robust Gradient Norm (TRGN) framework, which introduces an explicit decomposition of the tensor gradient into distinct low-rank and sparse components, different from existing methods that apply holistic constraints. Theoretically, we prove that TRGN guarantees exact recovery of both components under mild incoherence conditions and uniformly distributed sparse support. By integrating TRGN into tensor completion and robust PCA models, we develop efficient ADMM-based optimization algorithms with provable convergence. Comprehensive experiments demonstrate that TRGN consistently outperforms state-of-the-art methods in recovery quality and robustness, especially under extreme sampling rates and high-intensity noise, while remaining computationally efficient on large-scale hyperspectral and video data. Notably, TRGN achieves PSNR gains of 0.87-1.30 dB at a 0.5% sampling rate, and improves denoising performance by 0.70-1.58 dB under noise level 0.5 in TRPCA tasks. This work bridges low-rank and sparse priors in gradient domains, offering a theoretically sound and versatile solution for tensor recovery.

Accurate and efficient Video Polyp Segmentation (VPS) is vital for the early detection of colorectal cancer and the effectivetreatment of polyps. However, achieving this remains highly challenging due to the inherent difficulty in modeling the spatial-temporal relationships within colonoscopy videos. Existing methods that directly associate video frames frequently fail to account for variations in polyp or background motion, leading to excessive noise and reduced segmentation accuracy. Conversely, approaches that rely on optical flow models to estimate motion and align frames incur significant computational overhead. To address these limitations, we propose a novel VPS framework, termed Deformable Alignment and Local Attention (DALA). In this framework, we first construct a shared encoder to jointly encode the feature representations of paired video frames. Subsequently, we introduce a Multi-Scale Frame Alignment (MSFA) module based on deformable convolution to estimate the motion between reference and anchor frames. The multi-scale architecture is designed to accommodate the scale variations of polyps arising from differing viewing angles and speeds during colonoscopy. Furthermore, Local Attention (LA) is employed to selectively aggregate the aligned features, yielding more precise spatial-temporal feature representations. Extensive experiments conducted on the challenging SUN-SEG dataset and PolypGen dataset demonstrate that DALA achieves superior performance compared to state-of-the-art models.

Radar target detection remains a critically important research area. This paper models the radar echo data within each range cell as a stationary linear process driven by reversible, independent and identically distributed innovations. Exploiting the distinct inter-pulse correlation structures present under target absent and target present conditions, we propose the sample autocovariance as the detection statistic. Under appropriate theoretical conditions, we establish the validity of the autoregressive (AR) sieve bootstrap for approximating the distribution of this statistic. Adopting a single-sample hypothesis testing framework, we develop an adaptive constant false alarm rate (CFAR) detector, termed the Sample Autocovariance Trimmed CFAR (SACT-CFAR). Specifically, this method operates as follows: the numerical distribution of the sample autocovariance statistic is derived using the AR-sieve bootstrap method. The detection threshold for the cell under test is then determined based on a predefined false alarm probability. Through comprehensive numerical experiments on both simulated and real-world radar data, we benchmark the SACT-CFAR against established target detection methods. Key advantages of our approach include: 1. Superior Performance: Demonstrates higher detection probability, particularly in challenging low signal-to-clutter ratio regimes; 2. Model-Free Practicality: Eliminates the need for explicit derivation of theoretical detection thresholds and explicit statistical clutter modeling; 3. Robust Generality: Exhibits significant adaptability across diverse clutter environment distributions, overcoming the limitations of detectors reliant on specific clutter assumptions.

Graph neural networks (GNNs) have shown strong capability in learning from graph-structured data, yet they often lack explicit structural priors and face difficulties in modeling cross-layer semantic dependencies in multiplex heterogeneous graphs. To address these limitations, we propose MTP-GNN, a structure-aware representation learning framework that integrates multiplex topological potential modeling with multi-layer GNN architectures. Unlike conventional GNNs that mainly rely on local message passing, the proposed method introduces a continuous and interpretable structural prior through Gaussian-based topological potential fields, enabling the joint modeling of intra-layer and inter-layer dependencies. Node-level topological potentials are further encoded as structural embeddings and incorporated into graph convolution, allowing the model to combine global topological awareness with local semantic aggregation. A learnable potential entropy regularization term is introduced to enhance structural discriminability and a two-stage attention mechanism effectively fuses complementary semantics across heterogeneous layers. Extensive experiments on benchmark datasets demonstrate that the proposed framework consistently outperforms strong baselines in node classification and clustering tasks, highlighting the effectiveness of incorporating multiplex topological structures for interpretable and structure-aware graph representation learning.

Speech-driven portrait animation generation models have made significant progress in generating realistic and dynamic portrait animations. The class of end-to-end latent diffusion paradigms represented by Hallo achieves impressive results in terms of alignment accuracy between audio inputs and visual outputs, encompassing lip movements, expressions and head poses. However, constrained by the suboptimal interaction design between reference portrait information and the denoising U-Net in such architectures, certain frames in the output video sequences suffer from inconsistencies in identity and background preservation. Moreover, the temporal attention within the temporal module operates by incorporating information across frames within each generation unit to capture overall motion trends, but ignoring shorter frame subsequences within the generation unit, consequently losing fine-grained details between adjacent frames. In order to solve the above problems, we take the end-to-end latent diffusion paradigm Hallo as the backbone, and construct a Multi-Source Self Attention (MSSA) to optimize the interaction between reference portrait identity information and denoising U-Net. In addition, we also propose a plug-and-play, training-free method known as Unit-wise Spectral-Blend Temporal Attention (U-SBTA), which enables simultaneously capture local high-frequency facial details from shorter frame subsequences within each generation unit, thereby improving facial fidelity in synthesized portrait videos. Our method is comprehensively evaluated on public dataset and our collected datasets from qualitative and quantitative analysis. The results demonstrate that the portrait animation videos generated by our method are better able to preserve identity and background consistency with the reference portrait, as well as exhibiting superior facial detail fidelity.

Reconstructing network connections and dynamics simultaneously is essential for understanding complex systems and developing appropriate strategies. Graph neural networks (GNNs) and Transformers are frequently employed to model dynamics. These models depend on MultiLayer Perceptrons (MLPs) with linear weights and predetermined activation functions to integrate information, which somewhat limits their expressive capability. Additionally, the inferred structure may be inaccurate, as the dynamics and correlations within the complex system are interdependent. As a result, its forecasting ability may be limited. To enhance fitting accuracy of both structure and dynamics, we introduce the Kolmogorov-Arnold Networks (KANs) and Gumbel-softmax technique for modeling continuous and discrete dynamics via spline-parameterized univariate functions and explicit network structure, respectively. Experiments conducted on both simulated data and a real dataset demonstrate that two novel approaches, GGNKAN and more efficient GKAN, can effectively capture the complex and nonlinear functions of the nodes and their interactions, outperforming the Gumbel Graph Networks (GGNs), the state-of-the-art method, in terms of interactions recovery and/or prediction error.

Aiming at the problems of information loss and the relationship between features and target tasks in multimodal medical image segmentation, a multimodal medical image segmentation algorithm based on feature decoupling and information bottleneck theory is proposed in this paper. Based on the reversible network, the bottom-up learning method for different modal information is constructed, which enhances the features' expression ability and the network's learning ability. The feature fusion module is designed to balance multi-directional information flow. To retain the information relevant to the target task to the maximum extent and suppress the information irrelevant to the target task, the feature decoupling module is designed to ensure a strong correlation between the feature and the target task. A loss function based on information bottleneck theory was intended to improve information quality and remove redundant information. Based on BraTs2021, BraTs2023-MET and ANNLIB datasets, the proposed algorithm is analyzed qualitatively and quantitatively in this paper. In the quantitative experiment, the Dice coefficient of the proposed algorithm was increased by 0.110 on average compared with other methods, and the HD95 was decreased by 28.568 on average compared with other methods. In qualitative analysis, the proposed algorithm can effectively segment the incoherent region between the lesion and the lesion boundary and achieve accurate segmentation of the lesion.

Following the proposition of the original AWENO (Alternative Formulation of Weighted Essentially Non-Oscillatory) FD (Finite Difference) scheme, we construct the new AMDCD FD scheme, an Alternative formulation of the linear FD scheme with Minimized Dispersion and Controllable Dissipation, in this article. Spectral analysis shows that the proposed AMDCD FD scheme can be more efficient in resolving smooth solutions due to the flexibility in controlling dissipation. To efficiently solve compressible flows with discontinuities, we further combined the proposed AMDCD FD scheme with the original AWENO FD scheme using a hybrid interpolation scheme, in which the optimized linear MDCD (Minimized Dispersion and Controllable Dissipation) interpolation scheme would be switched to the nonlinear WENO (Weighted Essentially Non-Oscillatory) type interpolation scheme gradually as the flow structures are in transition from smooth region towards the vicinity of discontinuities. Therefore, the resulting hybrid AWENO-AMDCD FD scheme is suitable for solving compressible flows with broad-scale flow structures and/or shock waves. A series of one-, two-, and three-dimensional compressible flow problems are numerically tested to demonstrate the accuracy, superior resolution, as well as the robustness of the proposed hybrid AWENO-AMDCD FD scheme.

Detecting weak radar targets in complex cluttered environments remains a significant challenge, particularly when attempting to effectively detect low signal-to-clutter ratio (SCR) targets while maintaining a constant false alarm rate (CFAR). We propose novel CFAR detectors based on time series analysis and statistical foundations. We model radar echo data within a coherent processing interval as stationary time series governed by linear random processes, enabling the application of a time series resampling approach to establish the autoregressive sieve bootstrap consistency of the banded sample autocovariance matrix (SACM) in the spectral norm. Leveraging this, we derive the numerical distribution of statistics related to the largest eigenvalue of the banded SACM. We introduce two improved CFAR detectors: one based on the banded SACM spectral norm (BSN detector) and another based on the likelihood ratio test in banded SACM eigenvalues (BLR detector). Additionally, we propose an adaptive CFAR detector, the maximum eigenvalue trimmed (MET) detector, developed using single-sample hypothesis testing. Our analysis demonstrates that detection probabilities stabilize as the number of bands exceeds a certain threshold, with robust performance under varying SCRs and false alarm probabilities. Simulations and real data experiments validate that all three detectors significantly outperform traditional radar target detection methods in terms of both detection performance and computational efficiency. Notably, the MET detector offers unique advantages by eliminating the need for non-target reference data and exhibiting strong adaptive characteristics. Experimental results confirm its remarkable robustness in scenarios with other targets present in reference cells, achieving over 80% detection probability when the SCR is set to -5 dB with appropriate parameter adjustments. This work provides a comprehensive framework for enhancing radar target detection performance through advanced statistical methods and innovative detector designs.

Artificial intelligence-based models for global weather forecasting have advanced rapidly, but research on high-resolution data-driven limited area models remains scarce. Here we introduce a limited area artificial intelligence-based weather forecasting model with 3 km and 1 h resolutions, utilizing parallel global-local structures to capture multiscale meteorological features. The model is trained on high-resolution regional analysis data, and utilizes the global artificial intelligence-based model forecasts for the lateral boundary condition during prediction, and operates much faster than the dynamical forecast model. In two selected limited areas, it outperforms dynamical forecast models in surface wind speed forecasting but underperforms in surface temperature and pressure. Skills in surface temperature and pressure can be further improved comparable to the dynamical forecast model by providing better lateral boundary conditions. Issues related to lateral boundary conditions, such as selecting width of lateral boundary regions and combining finer and coarser resolution predictions in the regions, are also studied.

In the context of pulse compression radar target detection, this letter assumes that the echo data from each range cell within a coherent processing interval is derived from a stationary random process. We utilize the temporal correlation differences between pulses to determine if a target is present in the cell to be detected. This difference is represented by the quadratic sum of sample autocovariances. We demonstrate the autoregressive-sieve bootstrap validity of this statistic and subsequently design an ordered statistic adaptive constant false alarm rate (CFAR) detector based on this theory. Notably, the proposed detector exhibits a certain degree of generalization to clutter backgrounds, eliminating the need for complex clutter modeling and removing the convoluted process of deriving theoretical threshold. Detection results from measured data indicate that our detector outperforms several matrix CFAR and traditional CFAR methods. Additionally, the detector is not easily affected by the multi-target environment, and can detect the target well.

In this paper, we are interested in the study of finding robust efficient solutions in vector rational optimization problems with SOS-convex polynomials under data uncertainty. In order to solve such a class of vector rational optimization problems, we provide a mixed-type method consisting of the ε -constraint method for vector optimization, the parameter-free approach for rational optimization, and the exact SDP-based relaxation method for SOS-convex polynomial programs. We also give a procedure (with a detailed computed example) to show how our method works.

In this paper, we study a class of vector polynomial optimization over a linear matrix inequality (LMI in short) constraint. We show that the weakly efficient solution set can be characterized as the zero level set of a type of merit function, which admits polynomial approximations from above with coefficients computed via semidefinite programming (SDP) problems. An example is given to illustrate our method.

Three-dimensional reconstruction based on optical satellite images has always been a research hotspot in the field of photogrammetry. In particular, the 3D reconstruction of building areas has provided great help for urban planning, change detection and emergency response. The results of 3D reconstruction of satellite images are greatly affected by the input images, and this paper proposes an improvement method for 3D reconstruction of satellite images based on the generative adversarial network (GAN) image enhancement. In this method, the perceptual loss function is used to optimize the network, so that it can output high-definition satellite images for 3D reconstruction, so as to improve the completeness and accuracy of the reconstructed 3D model. We use the public benchmark dataset of satellite images to test the feasibility and effectiveness of the proposed method. The experiments show that compared with the satellite stereo pipeline (S2P) method and the bundle adjustment (BA) method, the proposed method can automatically reconstruct high-quality 3D point clouds.

Gliomas have the highest mortality rate of all brain tumors. Correctly classifying the glioma risk period can help doctors make reasonable treatment plans and improve patients’ survival rates. This paper proposes a hierarchical multi-scale attention feature fusion medical image classification network (HMAC-Net), which effectively combines global features and local features. The network framework consists of three parallel layers: The global feature extraction layer, the local feature extraction layer, and the multi-scale feature fusion layer. A linear sparse attention mechanism is designed in the global feature extraction layer to reduce information redundancy. In the local feature extraction layer, a bilateral local attention mechanism is introduced to improve the extraction of relevant information between adjacent slices. In the multi-scale feature fusion layer, a channel fusion block combining convolutional attention mechanism and residual inverse multi-layer perceptron is proposed to prevent gradient disappearance and network degradation and improve feature representation capability. The double-branch iterative multi-scale classification block is used to improve the classification performance. On the brain glioma risk grading dataset, the results of the ablation experiment and comparison experiment show that the proposed HMAC-Net has the best performance in both qualitative analysis of heat maps and quantitative analysis of evaluation indicators. On the dataset of skin cancer classification, the generalization experiment results show that the proposed HMAC-Net has a good generalization effect.

Epilepsy, as a serious neurological disorder, can be detected by analyzing the brain signals produced by neurons. Electroencephalogram (EEG) signals are the most important data source for monitoring these brain signals. However, these complex, noisy, nonlinear and nonstationary signals make detecting seizures become a challenging task. Feature-based seizure detection algorithms have become a dominant approach for automatic seizure detection. This study presents an algorithm for automatic seizure detection based on novel features with clinical and statistical significance. Our algorithms achieved the best results on two benchmark datasets, outperforming traditional feature-based methods and state-of-the-art deep learning algorithms. Accuracy exceeded 99.99% on both benchmark public datasets, with the 100% correct detection of all seizures on the second one. Due to the interpretability and robustness of our algorithm, combined with its minimal computational resource requirements and time consumption, it exhibited substantial potential value in the realm of clinical application. The coefficients of variation of datasets proposed by us makes the algorithm data-specific and can give theoretical guidance on the selection of appropriate random spectral features for different datasets. This will broaden the applicability scenario of our feature-based approach.

The autoregressive sieve (ARS) bootstrap method can capture the correlation of time series and expand the original data set to the required volume. In this study, we introduce the ARS bootstrap into the matrix constant false alarm rate (CFAR) method to counter the inability of the Monte Carlo methods to extract the detection threshold due to the limited number of pulses under a certain false alarm probability. We assume the echo data of each range cell in a coherent processing interval (CPI) to be a stationary time series, and regard target detection as a two-sample hypothesis testing problem. We propose a statistic to test the equivalence of the autocovariance corresponding to two potential time series by using the correlation between pulses in a short pulse dataset, and analyze the validity of the ARS bootstrap for this statistic. The statistic distribution is obtained according to the bootstrap procedure and the threshold is obtained under fixed false alarm probabilities. Numerical experiments on the simulated and real sea clutter data were conducted to compare the detection results of the partial matrix CFAR detectors for the short and long pulse cases. With the introduction of the bootstrap method, we do not need to model the clutter amplitude distribution and the related statistical characteristics during target detection. To improve the detection probability with low signal-to-clutter ratio (SCR), we propose the two-sample autocovariance vector (ACV) detector based on the proposed statistic and use the correlation properties between pulses. We observed a 28% increase in detection probability when the SCR was 0 dB compared to other matrix CFAR methods, such as detectors based on Logarithmic Euclidean (LE) distance, Kernel Function-based Symmetric Kullback-Leibler (KSKL) divergence, and Total Bregman divergence (TBD) for the short pulse case.

Glioma is a kind of brain disease with high incidence, high recurrence rate, high mortality, and low cure rate. To obtain accurate diagnosis results of brain glioma, doctors need to manually compare the imaging results of different modalities many times, which will increase the diagnosis time and reduce the diagnostic efficiency. Image fusion technology has been widely used in recent years to obtain information on multimodal medical images. This paper proposes a novel image fusion framework, target information enhanced image fusion network (TIEF), using cross-modal learning and information enhancement techniques. The framework consists of a multi-sequence feature extraction block, a feature selection block, and a fusion block. The multi-sequence feature extraction block consists of multiple sobel dense conv leaky ReLu block (SDCL-block). SDCL-block mainly realizes the extraction of edge features, shallow features, and deep features. The feature selection block identifies the feature channels with rich texture information and strong discrimination ability through the effective combination of global information entropy criterion and feature jump connection. The feature fusion block mainly comprises multi-head and spatial attention mechanisms, which can realize the fusion of intra-modality and inter-modality features. On this basis, considering the influence of tumor spatial location and structure information on the fusion results, a loss function is designed, which is a weighted combination of texture loss, structure loss, and saliency loss so that texture information from multimodal magnetic resonance imaging (MMRI) and saliency information from different anatomical structures of the brain can be fused at the same time to improve the expression ability of features. In this paper, the TIEF algorithm is trained and validated on the MMRI and (Single-Photon Emission Computed Tomography-MRI) SPECT-MRI datasets of glioma and generalized on the (Computed Tomography-MRI) CT-MRI dataset of meningioma to verify the performance of the TIEF algorithm. In the image fusion task, quantitative results showed that TIEF exhibited optimal or suboptimal performance in information entropy, spatial frequency, and average gradient metrics. Qualitative results indicate that the fused images can highlight tumor and edematous features. A downstream image segmentation task was used for evaluation to further verify TIEF’s effectiveness. TIEF achieved the best results in both (Dice similarity coefficient) Dice and (Hausdorff distance 95%) HD95 segmentation metrics. In the generalization task, quantitative results indicated that TIEF obtained more information in the meningioma dataset. In conclusion, TIEF can effectively achieve cross-domain information acquisition and fusion and has robustness and generalization ability.

Digital Surface Model (DSM) generation from high-resolution optical satellite images is an important topic of research in the remote sensing field. In optical satellite imaging systems, the attitude information of the cameras recorded by satellite sensors is often biased, which leads to errors in the Rational Polynomial Camera (RPC) model of satellite imaging. These errors in the RPC model can mislead the DSM generation. To solve the above problems, we propose an automatic DSM generation method from satellite images based on the Double-Penalty bundle adjustment (DPBA) optimization algorithm. In the proposed method, two penalty functions representing the camera’s attitude and the spatial 3D points, respectively, are added to the reprojection error model of the traditional bundle adjustment optimization algorithm. Instead of acting on images directly, the penalty functions are used to adjust the reprojection error model and improve the RPC parameters. We evaluate the performance of the proposed method using high-resolution satellite image pairs and multi-date satellite images. Through some experiments, we compare the accuracy and completeness of the DSM generated by the proposed method, the Satellite Stereo Pipeline (S2P) method, and the traditional bundle adjustment (BA) method. Compared to the S2P method, the experiment results of the satellite image pair indicate that the proposed method can significantly improve the accuracy and the completeness of the generated DSM by about 1–5 m and 20%–60% in most cases. Compared to the traditional BA method, the proposed method improves the accuracy and completeness of the generated DSM by about 0.01–0.05 m and 1%–3% in most cases. The experiment results can be a testament to the feasibility and effectiveness of the proposed method.

With the advent of the data era, medical image data plays an increasingly important role in diagnosing and treating diseases. This study combined deep learning, ensemble learning, and mathematical theory to construct a Stacking algorithm model based on the Naive Bayes method to achieve more accurate classification of medical images. In the Stacking algorithm, the results of the primary classifier are treated equally, and the performance of the primary classifier is ignored. The poor performance of the primary classifier will affect the final classification result. To solve this problem, a Stacking algorithm based on the Naive Bayes method is proposed in this paper. Firstly, the performance of the primary classifier is evaluated, and the output of the primary classifier is selected reasonably through the evaluation results. Secondly, the VGGNet, InceptionNet, and ResNet convolutional networks were used as primary classifiers to construct a complete Stacking algorithm based on the Naive Bayes method. Next, the algorithm was tested and validated using COVID-19 and NoCOVID-19 lung CT image data. Finally, it is compared with a single primary classifier and the traditional Stacking algorithm. The experimental results show that the Stacking algorithm based on the Naive Bayes method is suitable for the binary classification task of medical images and has better classification results than a single primary classifier and the traditional Stacking algorithm.