Hyperspectral image super-resolution (HSI-SR) aims to reconstruct a high-resolution HSI (HR-HSI) by fusing a low-resolution HSI (LR-HSI) with a high-resolution multispectral image (HR-MSI). Tensor Nuclear Norm (TNN) regularization exploits transform domains to capture the low-rank structure of HSIs. However, existing methods face a fundamental rigidity-flexibility trade-off: fixed transforms offer stability but lack adaptability, while data-driven transforms provide flexibility but suffer from optimization instability. To address this, we propose a novel HSI-SR model based on a Log-sum-based full-scale Learnable TNN (LLTNN) regularizer. The core of our framework is the Hierarchical Progressive Transform (HPT) operator, which establishes a principled dual-layer scheme. The explicit layer employs fixed multi-domain transforms to provide a robust structural anchor, while the implicit layer introduces a data-driven adaptive transform that captures scene-specific correlations which fixed bases cannot model. This explicit-to-implicit design yields more compact low-rank representations than single-domain or simple cascade methods. The full-scale framework imposes low-rankness jointly across all three tensor modes with a non-convex log-sum penalty to preserve essential features while suppressing noise. Extensive experiments on simulated and real-world datasets demonstrate that our method achieves state-of-the-art performance compared with existing approaches. The code is available at https://github.com/Tuzhihui/LLTNN_code.

Images acquired in real-world applications such as medical imaging, remote sensing and hyperspectral imaging are frequently degraded by mixed noise, where Gaussian perturbations, impulsive outliers, and structured artifacts coexist. Conventional restoration methods, typically developed and evaluated on grayscale or RGB images with only one or three channels, often struggle to handle such heterogeneous degradations. In this work, we propose a denoising framework that integrates fractal priors and Deep Image Prior (DIP) for mixed-noise image restoration, which can be naturally applied to multi-channel data such as Hyper Spectral Images (HSI). Specifically, the noisy observation is decomposed into four components: the clean image, Gaussian noise, sparse impulsive noise, and structured stripe noise. Each component is penalized with tailored regularizations, including a Frobenius norm for Gaussian noise, an & ell;(1) norm for impulsive noise, and a mixed & ell;(2,1,1) norm for structured noise. By combining the complementary capabilities of DIP and fractal modeling, a fractal regularization term enforces nonlocal self-similarity, whereas DIP provides a strong implicit prior that captures global image structure for faithful reconstruction. The overall problem is formulated as a constrained variational optimization and efficiently solved using the Alternating Direction Method of Multipliers (ADMM). Extensive experiments on grayscale, RGB and hyperspectral datasets demonstrate that the proposed framework effectively suppresses diverse noise types while preserving fine structural details, achieving superior robustness compared with existing approaches.

Subspace clustering is a fundamental problem in machine learning that has attracted considerable attention in recent years. Most existing methods focus on designing effective models to regularize the coefficient matrix, often neglecting the impact of noise on subspace structures. However, real-world data are typically corrupted by noise, which can distort the underlying subspace structure. Additionally, for sequential data, a key challenge is the effective exploitation of temporal information. To address these issues, we propose a novel and robust sequential subspace clustering method, termed joint capped $ℓ_2$ and $ℓ_{2,p}$ norm minimization (JCLLM). The capped $ℓ_2$ norm-based loss function mitigates the influence of noise and outliers in regression, while the $ℓ_{2,p}$ norm regularization captures the temporal dependencies inherent in sequential data. We develop an iteratively reweighted optimization algorithm to solve the JCLLM model and prove its convergence to a stationary point. Extensive experiments on both synthetic and real-world datasets demonstrate that our method consistently outperforms several state-of-the-art subspace clustering approaches.

Remote sensing has become indispensable in applications such as urban planning, maritime surveillance, and disaster management, yet accurate object detection remains challenging due to arbitrary orientations, dense layouts, and large intra-class variations. Existing oriented detectors have made progress through rotation-sensitive heads and featurealignment mechanisms, but they still handle rotation primarily in an implicit manner, lacking explicit geometric priors and often exhibiting inconsistency between feature representations and final predictions. To address these limitations, we design a parameter-efficient modular adaptor readily applicable to diverse detectors with only a small learnable-parameter overhead. Specifically, we introduce a Rotation-Aware Multi-branch Module with Consistency Regularization (RAMMC), which explicitly embeds rotation as a structural inductive bias: a multi-branch adaptor enhances rotation-aware feature construction, while two complementary regularization terms enforce feature-level equivariance and prediction-level consistency, ensuring coherent and geometry-aligned detection behavior. The design is inspired by rotation equivariance and invariance theory. We provide a conditional theoretical analysis showing that the group-pooling branch of RAMMC realizes a Reynolds averaging operator over the discrete rotation group, and we derive an implementation-aware equivariance-defect bound that accounts for finite kernel rotation, spatial gating, and orientation-attention residuals. Extensive experiments on diverse detectors, such as Faster R-CNN, RoI Transformer, and Oriented R-CNN implemented in the MMRotate toolbox, as well as YOLO models implemented under the Ultralytics framework, confirm that our adaptor consistently improves performance. Notably, it achieves 84.32 mAP on DOTA-v1.0, 47.31 mAP on FAIR1M-v1, and 52.28 mAP on FAIR1M-v2.0, surpassing strong baselines. These results demonstrate that explicitly modeling rotation consistency through a parameter-efficient adaptor with mathematically grounded rotation priors and consistency constraints provides an effective and general solution for remote sensing object detection.

The removal of Salt-and-Pepper noise remains a persistent challenge in image restoration due to its sparse, non-Gaussian nature and the severe disruption it causes to fine structures. Traditional denoising algorithms often struggle to preserve image details under such extreme corruption. We propose a unified, unsupervised denoising framework that integrates Fractal Image Coding (FIC), Total Variation (TV) regularization, and the Deep Image Prior (DIP). FIC captures long-range self-similarity through affine transformations; TV enforces local smoothness and edge preservation; DIP exploits the inductive bias of untrained convolutional networks to reconstruct structured content without requiring external datasets. By jointly optimizing fractal codes, variational constraints, and implicit priors, our method effectively suppresses impulsive noise while maintaining structural fidelity. Experimental results demonstrate that the proposed approach outperforms classical and learning-based methods in both noise removal and perceptual quality. This work bridges model-based and learning-free paradigms, offering a robust and interpretable solution for impulsive noise removal.

Remote sensing images are currently crucial for applications in areas such as farmland monitoring, urban planning, and disaster assessment. However, cloud cover presents a significant challenge by degrading image quality and limiting its practical utility. Although many cloud removal methods have been proposed, existing approaches still exhibit two main limitations: ineffective utilization of local image information and high computational demands. To address these problems, a deep reinforcement learning-based framework for cloud removal is proposed, which adopts a two-stage approach: first, a patch-level cloud removal model is trained, and then the cloud removal task is formulated as a patch-wise Markov decision process. Deep reinforcement learning is subsequently employed to optimize the cloud removal trajectory. Experimental results on a Sentinel-2-based dataset demonstrate that the proposed framework not only substantially improves cloud removal performance but also enhances training efficiency by reducing the computational resources required.

Subspace clustering is a fundamental problem in machine learning that has attracted considerable attention in recent years. Most existing methods focus on designing effective models to regularize the coefficient matrix, often neglecting the impact of noise on subspace structures. However, real-world data are typically corrupted by noise, which can distort the underlying subspace structure. Additionally, for sequential data, a key challenge is the effective exploitation of temporal information. To address these issues, we propose a novel and robust sequential subspace clustering method, termed joint capped 2 pound and 2 pound,p norm minimization (JCLLM). The capped 2 pound norm-based loss function mitigates the influence of noise and outliers in regression, while the 2 pound,p norm regularization captures the temporal dependencies inherent in sequential data. We develop an iteratively reweighted optimization algorithm to solve the JCLLM model and prove its convergence to a stationary point. Extensive experiments on both synthetic and real-world datasets demonstrate that our method consistently outperforms several state-of-the-art subspace clustering approaches.

Point cloud registration is a fundamental task in 3D computer vision, with applications spanning robotics, autonomous driving, and augmented reality. While recent advances have improved the extraction of transformation-invariant (TI) features in point clouds, their potential in point registration remains underutilized due to the prevalence of high outlier correspondences. This paper introduces a novel two-channel model that leverages both transformation-variant (TV) and transformation-invariant (TI) features to enhance point cloud registration. Our approach employs a coarse-to-fine feature extraction framework, where a dual-feature attention module utilizes both TI and TV features to refine representations at the coarse level before projecting them to the fine level for accurate correspondence estimation. Extensive experiments on the 3DMatch and KITTI datasets demonstrate the effectiveness of our method, achieving an inlier ratio of 74.6 ^∘ and a relative translation error of 6.6 cm on KITTI. These results highlight the potential of our dual-feature approach in improving point cloud registration accuracy across diverse environments. Our code is available at http://www.github.com/saifabel/DualFeatAtt .

This paper introduces a unified nonconvex weighted tensor learning framework for multi-view subspace cluster ing. The model leverages a weighted tensor Schatten-p norm to accurately recover the global low-rank structure through adaptive singular value penalization. To enhance robustness against non-Gaussian noise, we integrate a logarithmic sparsity penalty, providing a tighter approximation of true sparsity and a closed-form solution via a novel shrinkage operator. Furthermore, local geometric structures are preserved through hyper-Laplacian reg ularization. By integrating self-representation and spectral embedding into a monolithic optimization problem, we reduce the accumulation of errors found in multi-stage pipelines. The resulting alternating minimization algo rithm is supported by theoretical convergence proofs. Empirically, our method demonstrates superior accuracy and robustness across multiple real-world datasets, establishing a new performance benchmark for multi-view learning.

In nature, signals often appear in the form of the superposition of multiple non-stationary signals. The overlap of signal components in the time-frequency domain poses a significant challenge for signal analysis. One approach to addressing this problem is to introduce an additional chirprate parameter and use the chirplet transform (CT) to elevate the two-dimensional time-frequency representation to a three-dimensional time-frequency-chirprate representation. From a certain point of view, the CT of a signal can be regarded as a special windowed linear canonical transform of that signal, undergoing a shift and a modulation. In this paper, we develop this idea to propose a novel windowed linear canonical transform (WLCT), which provides a new time-frequency-chirprate representation. We discuss four types of WLCTs. In addition, we use a special X-ray transform to further sharpen the time-frequency-chirprate representation. Furthermore, we derive the corresponding three-dimensional synchrosqueezed transform, demonstrating that the WLCTs have great potential for three-dimensional signal separation.

Hyperspectral image super-resolution (HSI-SR) aims to reconstruct a high-resolution hyperspectral image by fusing a low-resolution hyperspectral image with a high-resolution multispectral image. Tensor nuclear norm (TNN)-based regularization has shown strong potential in model-based HSI-SR by exploiting the intrinsic low-rank structure of hyperspectral data in transform domains. However, existing transform-domain TNN methods are still predominantly formulated in linear representation spaces, including fixed analytical transforms, cascaded linear transforms, and data-adaptive linear transforms. Such linear-domain low-rank priors are insufficient to characterize the nonlinear, nonconvex, and high-order spatial–spectral dependencies widely present in real-world hyperspectral scenes. To address this limitation, this paper proposes a Multistage Nonlinear Transform Tensor Nuclear Norm, termed MNTNN, for HSI-SR. The proposed MNTNN imposes tensor low-rankness in a structured nonlinear representation domain rather than in a purely linear transform domain. Specifically, a multistage nonlinear transform is constructed by integrating nonlinear representation mapping, fixed analytical transform anchoring, and data-adaptive subspace alignment, which respectively model high-order nonlinear correlations, global structural regularities, and scene-specific low-rank characteristics. Furthermore, the proposed MNTNN is embedded into a nonlocal patch-based subspace fusion framework, and an efficient alternating direction method of multipliers (ADMM) algorithm is developed to solve the resulting optimization problem. Extensive experiments on simulated and real-world datasets demonstrate that the proposed method achieves competitive or superior reconstruction performance compared with representative state-of-the-art HSI-SR methods, especially in preserving spatial details and spectral fidelity.

For two real bases q(0),q(1)>1, a binary sequence i(1)i(2)& ctdot;is an element of{0,1}(infinity) is the (q(0),q(1))-expansion of the number pi(q0,q1)( i(1)i(2)& ctdot;)=& sum;(infinity)(k=1)i(k)/q(i1)& ctdot;q(ik). Let Uq(0),q(1 )be the set of all real numbers having a unique (q(0),q(1))-expansion. When the bases are equal, that is, q(0)=q(1)=q, Allaart and Kong (2019) established the continuity in q of the Hausdorff dimension of the univoque set U-q,U-q, building on the work of Komornik, Kong, and Li. We derive explicit formulas for the Hausdorff dimension of Uq(0),q(1 )and the entropy of the underlying subshift for arbitrary q(0),q1>1, and prove the continuity of these quantities as functions of (q(0),q(1)). Our results also concern general dynamical systems described by binary shifts with a hole, including, in particular, the doubling map with a hole and (linear) Lorenz maps.

Low-rank tensor recovery is pivotal in numerous applications, including image and video processing, machine learning, and data analysis. A common approach to this problem involves convex relaxation, where the tensor rank function is minimized by using the tensor nuclear norm. However, this method can be significantly suboptimal. In addition, the stochastic variance reduced gradient (SVRG) method, a variant of stochastic gradient descent, has been applied to matrix recovery problems. In this paper, we extend the SVRG method to the tensor framework, introducing the tensor stochastic variance reduced gradient (TSVRG) algorithm for tensor recovery with CP or Tucker rank constraints. TSVRG is designed to achieve higher precision solutions by escaping local minima and identifying superior global optima. Moreover, TSVRG offers reduced computational complexity compared to traditional gradient descent methods. We establish a convergence theorem for TSVRG under the tensor restricted isometry condition when the measurements are linear. Finally, we present numerical results using both synthetic and real data, demonstrating the competitive performance of TSVRG compared to other advanced algorithms.

Phishing remains a persistent cybersecurity threat that requires accurate and efficient detection methods. Existing approaches struggle to capture both fine-grained URL structures and broader contextual semantics, limiting their effectiveness. In this paper, we propose a hybrid deep learning model that integrates multi-scale Convolutional Neural Networks (CNNs), Bidirectional Long Short-Term Memory (BiLSTMs), and enhanced Gated Multi-Layer Perceptron (gMLP) layers, combined with Generative Pre-trained Transformer 2 (GPT-2) token embeddings and character-level features. The multi-scale CNNs capture diverse spatial patterns, the BiLSTMs extract sequential dependencies, and the gMLPs refine feature interactions. Evaluated on three benchmark datasets, our proposed model achieves accuracies of 99.13%, 99.15% and 99.83%, outperforming strong deep-learning baselines and demonstrating robust and consistent performance compared to existing deep learning methods. These results demonstrate the model’s robustness and generalizability, while maintaining competitive efficiency and moderate model size suitable for real-world deployment at the cost of slight performance degradation on very short URLs; suggesting future integration of page content features. Our code and datasets are publicly released to support reproducibility and further research.

Motivated by parallel decoding in masked diffusion models, we study adaptive parallel sampling of discrete vectors: in each round, a deterministic policy selects unrevealed coordinates on the basis of the values observed so far, and the selected coordinates are sampled independently from their exact conditional marginals. Approximation error is measured by forward Kullback-Leibler divergence, and serial depth is the minimum target-averaged number of rounds meeting a prescribed error budget. Our central result is an exact identity: the divergence of every policy equals the expected conditional total correlation accumulated over its reveal rounds, so conditional total correlation is the exact information cost of within-round parallelism. The identity yields zero-error schedules for finite-order Markov chains with round complexity proportional to the Markov order and logarithmic in sequence length, a matching logarithmic characterization of the Bernoulli walk at every fixed error budget, and a linear-versus-logarithmic separation between left-to-right and hierarchical reveal orders. Uniform random permutations require linearly many expected rounds at every fixed budget; their hard-cap round-error tradeoff is an exact integer-composition problem whose fixed-round asymptotics and joint-scaling frontier we determine. Uniform balanced binary strings have depth of order squared logarithm, and binary one-hot blocks have square-root depth, with rectangular versions realizing every polynomial exponent up to one half. These results separate serial depth from entropy and negative log-likelihood, and establish conditional-dependence structure as a fundamental determinant of parallelizability. Experiments with a masked diffusion language model show that the pseudo-cost distinguishes deployed decoding rules and that its policy rankings agree closely with the quality of self-sampled outputs.

Hyperspectral images (HSIs) are often contaminated by a mixture of noise such as Gaussian noise, dead lines, stripes, and so on. In this paper, we propose a multiscale low-rank tensor regularized 2 pound,p (MLTL2p) approach for HSI denoising and destriping, which consists of an orthogonal constrained minimization model and an iterative algorithm with convergence guarantees. The model of the proposed MLTL2p approach is built based on a new sparsity-enhanced Multiscale Low-rank Tensor regularization and a tensor 2 pound,p norm with p \in (0, 1). The multiscale low-rank regularization for HSI denoising utilizes the global and local spectral correlation as well as the spatial nonlo cal self-similarity priors of HSIs. The corresponding low-rank constraints are formulated based on independent higherorder singular value decomposition with sparsity enhancement on its core tensor to prompt more lowrankness. The tensor 2 pound,p norm for HSI destriping is extended from the matrix 2 pound,p norm. A proximal block coordinate descent algorithm is proposed in the MLTL2p approach to solve the resulting nonconvex nonsmooth minimization with orthogonal constraints. We show any accumulation point of the sequence generated by the proposed algorithm converges to a first-order stationary point, which is defined using three equalities of substationarity, symmetry, and feasibility for orthogonal constraints. In the numerical experiments, we compare the proposed method with state-of-the-art methods, including a deep learning based method, and test the methods on both simulated and real HSI datasets. Our proposed MLTL2p method demonstrates outperformance in terms of metrics such as mean peak signal-to-noise ratio as well as visual quality.

In this paper, we propose a simple variant of random projection-type algorithm for solving multiple-sets split feasibility problems. We employ random projection and self-adaptive step size techniques to do randomly chosen projections, which avoids computing all single constraint set projections at each iteration and the largest eigenvalue (spectral radius) of matrix. We prove the convergence theorem and sublinear convergence rate of the proposed algorithm, provided that the spectral radius of matrix is unknown or hard to compute. Furthermore, if this term is known, the linear convergence rate can be obtained. Numerical experiments are reported to illustrate the effectiveness of the proposed algorithm.

Extracting rigid transformation invariant features is still a challenge on 3D point clouds because rigid transformation changes the point coordinates, and relying on the point coordinates, most existing deep learning models fail. This paper addresses this challenge by proposing geometric edge convolution (GEConv). To facilitate rigid transformation invariant feature extraction, GEConv uses geometric features that are invariant to rigid transformations to construct a local graph and use shared multi-layer perceptron (MLP) on the graph edges to extract deep features. By leveraging these invariant geometric features to build the graph, GEConv effectively ensures the extraction of deep features that are also invariant to rigid transformations. By stacking GEConv, we construct a deep model called GEConvNet that hierarchically extracts different level rigid transformation invariant features for various point cloud tasks. To prove the effectiveness of GEConv, we provide experiments on four point cloud processing tasks; classification, parts segmentation, semantic segmentation, and point set registration. In the classification and segmentation tasks, GEConvNet performs better on robustness to rotation compared to existing models. Furthermore, our feature-matching-based approach for point set registration demonstrates strong performance, providing further evidence of GEConv’s ability to handle rotation and translation effectively. Our code is available at http://www.github.com/saifabel/GEConv.

Low-rank recovery builds upon ideas from the theory of compressive sensing, which predicts that sparse signals can be accurately reconstructed from incomplete measurements. Iterative thresholding-type algorithms-particularly the normalized iterative hard thresholding (NIHT) method-have been widely used in compressed sensing (CS) and applied to matrix recovery tasks. In this paper, we propose a tensor extension of NIHT, referred to as TNIHT, for the recovery of low-rank tensors under two widely used tensor decomposition models. This extension enables the effective reconstruction of high-order low-rank tensors from a limited number of linear measurements by leveraging the inherent low-dimensional structure of multi-way data. Specifically, we consider both the CANDECOMP/PARAFAC (CP) rank and the Tucker rank to characterize tensor low-rankness within the TNIHT framework. At the same time, we establish a convergence theorem for the proposed TNIHT method under the tensor restricted isometry property (TRIP), providing theoretical support for its recovery guarantees. Finally, we evaluate the performance of TNIHT through numerical experiments on synthetic, image, and video data, and compare it with several state-of-the-art algorithms.

Recent advances in the design of convolutional neural networks have shown that performance can be enhanced by improving the ability to represent multi-scale features. However, most existing methods either focus on designing more sophisticated attention modules, which leads to higher computational costs, or fail to effectively establish long-range channel dependencies, or neglect the extraction and utilization of structural information. This work introduces a novel module, the Multi-Branch Concatenation (MBC), designed to process input tensors and extract multi-scale feature maps. The MBC module introduces new degrees of freedom (DoF) in the design of attention networks by allowing for flexible adjustments to the types of transformation operators and the number of branches. This study considers two key transformation operators: multiplexing and splitting, both of which facilitate a more granular representation of multi-scale features and enhance the receptive field range. By integrating the MBC with an attention module, a Multi-Branch Attention (MBA) module is developed to capture channel-wise interactions within feature maps, thereby establishing long-range channel dependencies. Replacing the 3x3 convolutions in the bottleneck blocks of ResNet with the proposed MBA yields a new block, the Efficient Multi-Branch Attention (EMBA), which can be seamlessly integrated into state-of-the-art backbone CNN models. Furthermore, a new backbone network, named EMBANet, is constructed by stacking EMBA blocks. The proposed EMBANet has been thoroughly evaluated across various computer vision tasks, including classification, detection, and segmentation, consistently demonstrating superior performance compared to popular backbones.