Discrete Wavelet Transform

These notes develop the mathematical foundations and construction of a Fourier-Bessel wavelet family inspired by the disk harmonics of Shaqfa et al.[9]. We begin with the relevant properties of Bessel and modified Bessel functions and introduce the wavelet properties required for the construction. We then derive the Fourier-Bessel disk harmonics as solutions to the Helmholtz equation on the unit disk subject to a Neumann boundary condition. Building on this basis, we construct a wavelet family by applying a Gaussian spatial envelope and introducing a zero-mean correction for the zeroth angular order. We derive the corresponding normalisation constants for $L^2$-based applications and discuss $L^1$-based normalisation for frequency-domain peak consistency. Finally, we derive a closed-form Fourier-domain representation of the resulting wavelets. The main motivation is the approximately linear spacing, which converges to $π$ between consecutive radial eigenvalues. Rather than replacing the conventional dyadic organisation of wavelet families, this construction lays out the foundation to explore whether a more uniform radial frequency allocation can be useful for applications in which broad and balanced frequency coverage is desirable.

Time-warping estimation is a fundamental problem in signal processing with applications in bioacoustics, radar, and biomedical analysis. This paper introduces a Time-Warping Estimation Trainable (TWET) model for estimating timewarping functions from a single observation. The proposed approach formulates time-warping estimation as a stationarization problem in the wavelet domain and leverages a hierarchical dilated convolutional architecture to estimate the time-warping functions. A differentiable stationarity criterion is introduced for end-to-end optimization. TWET is compared with existing approaches. Experimental results show improved deformation reconstruction accuracy together with significantly reduced computation time, making the framework compatible with low-latency applications.

This study proposes an integrated framework for the processing and classification of invasive bird species vocalizations within natural soundscapes, characterized by high levels of environmental noise. We address the challenge of signal degradation by employing a Bayesian wavelet shrinkage methodology based on the Epanechnikov kernel prior, which offers a closed form decision rule and high computational efficiency for processing large bioacoustic datasets. The methodology was applied to recordings of three species obtained from the iNaturalist platform: \textit{Euphonia violacea}, \textit{Leiothrix lutea}, and \textit{Passer domesticus}. After signal denoising, we extracted a comprehensive set of features, including Mel-Frequency Cepstral Coefficients (MFCCs) and spectral indices such as entropy and zero-crossing rate. Several supervised learning models: Random Forest, Multinomial Logistic Regression and Support Vector Machine (SVM) were evaluated across different feature dimensionalities. Our results demonstrate that the proposed wavelet based preprocessing significantly enhances classification performance, with the SVM model achieving the highest accuracy (up to 0.9398) under a 10-dimensional MFCC configuration. This research provides a robust statistical tool for automated ecological monitoring and the management of biological invasions.

This work introduces a family of tunable lifting schemes for biorthogonal wavelet filter banks. We propose three lifting strategies: low-pass tuning (LS-LayLatt-LP), high-pass tuning (LS-LayLatt-HP), and a sequential lifting scheme that jointly adapts low- and high-frequency branches (LS-LayLatt-Sequential). All proposed designs are formulated using a lattice-based lifting structure, which guarantees invertibility and stability for arbitrary parameter values within the lifting functions. We evaluated the proposed methods by integrating them into a ResNet-18 backbone for image classification on the Describable Textures Dataset (DTD), as well as for anomaly detection on hazelnut images from the MVTec-AD dataset and private KRC102S dataset. Experimental results demonstrate consistent performance improvements across all evaluated tasks.

InfRared Small Target Detection (IRSTD) is a prominent and challenging task in computer vision. In recent years, text-guided methods have significantly improved detection performance. However, they still suffer from two key limitations. First, a single text description simultaneously modeling both background and target leads to semantic entanglement, which contradicts the objective of background suppression and target enhancement. Second, reliance on image-specific textual prompts (requiring additional external models such as CLIP during inference) results in deployment constraints. To address these issues, we propose a novel Dual-knowledge Guided Network (DGNet) based on multiple generalizable texts. Specifically, we design a Prior-knowledge Wavelet Modulation (PWM) module, which leverages dual textual priors that separately characterize large-scale backgrounds and sparse targets to effectively disentangle and modulate entangled semantics in the frequency domain. Furthermore, we introduce a Consensus-knowledge Directional Alignment (CDA) loss, which models the initial state and the ideal target across samples as complex background' and bright target', respectively, thereby constructing a clear and unified directional optimization trajectory for the model. Extensive experiments on three public datasets demonstrate the superior performance of DGNet and the effectiveness of each component. The source code is available at https://github.com/iLearn-Lab/MM26-DGNet.

Verifying image authenticity is increasingly difficult, posing serious risks across journalism, law enforcement, and political domains. Most existing forensic methods rely on high-level visual artifacts and treat frame detection as a simple binary task. To address this, we propose SegWave, a hybrid framework that jointly leverages spatial and frequency-domain cues for image tampering detection. SegWave integrates a transformer-based architecture with the Discrete Wavelet Transform (DWT) to capture localized, multi-scale frequency inconsistencies indicative of manipulation. To further improve localization effectiveness, we introduce an Adaptive Sub-band Attention module (ASA) that dynamically highlights the informative high-frequency wavelet components. Extensive experiments on multiple benchmark datasets demonstrate that SegWave consistently outperforms state-of-the-art tampering detection methods in challenging evaluation settings.

Accurate gust forecasting under typhoon conditions remains challenging due to the highly non-stationary and multi-scale characteristics of extreme wind fluctuations. Existing deep learning models often struggle to simultaneously capture long-term trends and rapid local variations, resulting in degraded performance during extreme events. We propose WDANet, a frequency-aware forecasting framework that integrates stationary wavelet decomposition, a Feature-wise Linear Modulation (FiLM) strategy, and a dual-branch encoder-decoder architecture, enabling separate modeling of trend and fluctuation components. Taking the offshore regions of the Western Pacific in China as an example, we conduct fine-grid wind gust prediction research. The results demonstrate that WDANet shows advantages for short lead times under the experimental setting across a 24-h forecasting horizon and achieves higher prediction accuracy than ECMWF-HRES within the first 6 h. During extreme wind events, WDANet more accurately captures gust peaks and attains the best RMSE and MAE performance. These results highlight its potential for offshore wind power operation, disaster warning, and risk mitigation.

Plasticity loss has emerged as a critical challenge in continual learning that significantly hinders the acquisition of sequential tasks. While optimizing activation designs offers a potential solution, current fixed-form functions suffer from an inherent spectral bias towards low-frequency variations, whereas learnable variants permit unconstrained updates that induce catastrophic forgetting. To address these limitations, we propose a novel learnable wavelet activation that decomposes the activation function into low-frequency and high-frequency components to explicitly counter spectral bias. Furthermore, we employ dynamic wavelet injection to adaptively enhance plasticity for new tasks, alongside a regularization strategy to ensure the stability of previous learned knowledge. Theoretically, we provide rigorous mathematical guarantees for the proposed framework, proving the structural necessity of the hybrid wavelet architecture for efficient $L^2$ approximation and demonstrating that the decoupled learning rate mechanism successfully restores network plasticity for high-frequency information. Additionally, we provide a formal derivation of the loss-driven injection trigger mechanism to precisely guide the injection. Extensive empirical evaluations demonstrate that our approach maintains superior trainability and generalization throughout the learning process and achieves state-of-the-art performance across diverse continual learning benchmarks.

The paper considers the construction of two new orthogonal multiwavelets with supercompact support by using the Fast Bauer's method for matrix spectral factorization on the matrix product filter of the orthogonal CL multiwavelet filter. The new multiwavelets possess orthogonality, symmetry/antisymmetry, and one of them provides better coding and smoothness than other supercompact multiwavelets. The performance of the new multiwavelet filters in subband-based edge detection, grayscale and color image compression and 1D and 2D signal denoising is compared with the GHM, SA4, CL, Integer Haar and Alpert multifilters. The comparative analysis shows that new multiwavelets can provides better human visual measures, SSIM and MS-SSIM in image compression and denoising applications.

Wavelet convolution (WTConv) has emerged as an increasingly popular drop-in replacement for standard convolutions, expanding a network's receptive field exponentially with the number of decomposition levels while keeping the parameter count linear. However, its reference implementation is severely memory-bound due to excessive data movement through high-bandwidth memory (HBM). We develop an I/O model of WTConv to characterize this bottleneck and use it to guide three algebraic reformulations: (1) recomputing the inexpensive Haar analysis butterfly on chip, (2) collapsing the multi-level synthesis cascade into a single closed-form pass indexed by output-coordinate bits, and (3) folding learned per-channel scales into the convolution weights. Together, these reformulations enable an I/O-aware fused implementation that substantially reduces HBM traffic. We evaluate the WTConvNeXt configuration across decomposition levels and a broad range of tensor shapes. Despite performing comparable arithmetic, the reference WTConv is substantially slower than the depthwise convolution it replaces. Our reformulation reduces modeled HBM traffic by approximately $2.55\times$, yielding up to a $4.35\times$ training speedup over the reference while roughly halving peak memory usage. Thus, our reformulation preserves the benefits of WTConv while substantially reducing its execution time and memory footprint, removing the systems overhead that previously limited its practical efficiency.

High-quality document images are pivotal for information archiving and downstream automatic processing. However, they are frequently compromised by diverse degradations during uncontrolled acquisition and transmission. While unified document restoration techniques have been proposed to restore images from multiple degradations, they often struggle with training multiple degradation-specific models, reliance on manual task-specific prompts, or cross-task data pairing. To address these limitations, we propose DocPure, a prompt-free unified framework that achieves degradation-aware document restoration. We design a degradation-aware structure auto-encoder with degradation-informed routing regularization to predict clean structural priors from degraded inputs. The model is prompt-free at inference, and degradation labels are only used as auxiliary supervision for the routing regularization during training. Furthermore, we introduce a structure-guided wavelet interaction mechanism to bridge frequency-domain features and spatial semantics. Within the structure-guided wavelet interaction mechanism, a cross-frequency adaptive modulation utilizes low-frequency sub-bands to modulate high-frequency recovery, ensuring structural consistency. Extensive experiments demonstrate that DocPure achieves strong performance compared with state-of-the-art methods across various tasks, including deblurring, denoising, compression artifact reduction, and deshadowing.

Unrestricted adversarial transfer attacks are important for evaluating the black-box robustness of deep visual models. Diffusion-based attacks have shown promising transferability and visual imperceptibility by optimizing adversarial perturbations along denoising trajectories in latent space. However, existing methods are limited by two challenges: memory-intensive multistep backpropagation and frequency-agnostic perturbation over intermediate latents. To address these issues, we propose IDATA, a memory-efficient diffusion framework for unrestricted adversarial transfer attack. IDATA consists of two key components: an Invertible Diffusion Module (IDM) and a Low-Frequency Constraint Module (LFCM). Specifically, IDM reformulates adversarial optimization over diffusion trajectories as an invertible process, enabling constant-memory backpropagation through on-demand reconstruction of intermediate states instead of storing the full denoising chain. Moreover, LFCM leverages Discrete Wavelet Transform (DWT) to decompose latent variables into low- and high-frequency components, restricting perturbations to semantically stable low-frequency subspaces, thereby improving transferability while preserving visual imperceptibility. Extensive experiments on multiple benchmarks and diverse model architectures demonstrate that IDATA consistently outperforms state-of-the-art baselines in attack success rate, memory efficiency, and visual imperceptibility. These results suggest that IDATA is a promising tool for black-box robustness evaluation of deep visual models. Code is available at https://github.com/colourful-pan/IDATA.

Diffusion-based face restoration that adjusts the sampling trajectory of pre-trained diffusion models has achieved remarkable progress. However, existing approaches provide insufficient constraints during reverse diffusion, causing identity-related structural drift and degraded fidelity under severe degradations. To address this, we propose WaveFreqAnchor, a training-free framework based on Wave-Structural Anchoring and Frequency Correction Diffusion. Specifically, Anchor-Space Wave-Structural Guidance (ASWG) constrains facial structures through anisotropic wave-response consistency, while Multi-scale Wavelet-Fourier Injection (MWFI) aligns the predicted low-frequency subband with the observation by replacing its phase, correcting inconsistencies accumulated during reverse diffusion. For real-world scenes, we further introduce Subband High-Frequency Enhancement (SHE), which performs bounded, spatially masked refinement on the predicted high-frequency subbands to recover fine facial details under unknown compound degradations. Together, these designs effectively preserve facial identity while restoring sharp and realistic facial details. Extensive experiments show that our method consistently outperforms existing methods, achieving high-quality and high-fidelity face restoration.

Rip currents are recurrent coastal natural hazards that threaten beachgoers and create operational challenges for lifeguards and coastal managers. Reliable monitoring from standard RGB (red-green-blue) imagery acquired by unmanned aerial vehicles (UAVs) remains difficult because hazardous channels often appear as subtle gaps in breaking waves, foam texture, or sediment patterns, and these signatures are affected by illumination, sea state, and environmental noise. This study presents a physically informed coastal environmental monitoring workflow for detecting visually expressed rip-current indicators that integrates wavelet-derived spatial-frequency texture features with deep learning. We evaluate multiple strategies for incorporating Discrete Wavelet Transform features into convolutional architectures, from computationally efficient channel replacement to dual-stream fusion with attention mechanisms. Performance is assessed against a standard RGB baseline using a task specific convolutional neural network for image-level presence classification and a YOLOv8 model for object-level localization. Under the evaluated dataset conditions, integrating wavelet derived texture features improves performance over RGB-only models. The dual-stream architecture achieves the strongest classification performance, exceeding 95% accuracy with high recall, while channel replacement is most effective for YOLOv8 object detection, reaching 94% mAP@50 for localization. Explainable artificial intelligence analyses provide qualitative evidence that the models attend to visually plausible wave-gap regions associated with rip currents. These results suggest that under the conditions of the evaluated dataset, physically informed wavelet integration may support UAV-based decision-support tools for interpretable beach-safety risk mitigation.

Short-term precipitation nowcasting is important for hydrometeorological early warning, especially when intense convective rainfall may trigger urban flooding, flash floods, and other high-impact hazards. A key challenge in warning-oriented nowcasting is that radar precipitation fields contain strongly coupled multi-scale structures, while forecast quality often degrades at later lead times, making it difficult to preserve intense precipitation cores and their spatial organization over the full warning-relevant horizon. To address this problem, we propose QWRF-Net, a quantum-wavelet framework with rectified flow for short-term precipitation nowcasting. The core idea is to improve the conditional representation of precipitation by explicitly decomposing latent features into wavelet sub-bands and then performing differentiated quantum-inspired modulation in the decomposed latent space, before generating future sequences through a rectified-flow-based non-autoregressive decoder. Experiments on the KNMI radar and SEVIR benchmarks under a unified evaluation protocol show that QWRF-Net achieves favorable overall performance, with relatively consistent gains at medium-to-high precipitation thresholds, on an extreme-event subset, and in preserving intense precipitation cores and fine-scale structures. Ablation results further indicate that wavelet-based scale disentanglement, differentiated sub-band modulation, and flow-based generation provide complementary benefits within the proposed framework. Overall, these results suggest that jointly enhancing multi-scale precipitation representation and stable multi-step generation is a promising direction for warning-oriented short-term precipitation nowcasting. The observed improvements may also provide a more useful precipitation basis for downstream hydrological and warning-related applications.

As image generation models scale to ever higher resolutions, global coherence, local detail, and texture fidelity become critical axes for generation quality. However, standard flow matching treats all spatial frequencies uniformly, ignoring the natural frequency hierarchy where high-frequency bands become indistinguishable from pure noise far earlier than coarse structures. We introduce WaiT, a Wavelet-aware image Transformer that decomposes generation into coarse and fine bands via lossless wavelets. True to its name, the high-frequency bands wait for the signal: staying pure noise until coarse structure has emerged, then joining the flow for joint refinement. Since standard FID discards fine-grained detail through aggressive downsampling, we introduce a more stringent three-axis evaluation protocol to assess quality at native resolution. On ImageNet 512x512, WaiT achieves a pixel-space FID of 1.43 and is Pareto-optimal across all three axes, reducing sampling compute by up to 50%. With our largest 2B model, we set a new state-of-the-art FID of 1.3 for pixel-space models on ImageNet 512 resolution. Our formulation outperforms even the strongest latent-space models on texture fidelity, and scales seamlessly to high-resolution OpenImages and to video generation, achieving a state-of-the-art FVD of 0.84 on Kinetics-600 with no algorithmic modifications.

Existing invisible watermark removal methods often struggle to accurately capture the watermark-bearing features, leading to an unfavorable trade-off between watermark suppression and perceptual fidelity. In this paper, we propose the Frequency-Decoupled Diffusion Watermark Attack Network (FDDWAN), a coarse-to-fine framework that performs watermark removal through wavelet-domain decomposition and residual diffusion refinement. In the initial stage, the Wavelet-based Frequency-domain Preliminary Attack Module (WFPAM) decomposes the watermarked image into low- and high-frequency subbands and applies frequency-specific attack strategies tailored to their respective contributions to watermark robustness and perceptual quality. In the next stage, the Frequency-domain Residual Diffusion Attack Module (FRDAM) separately models the residual distributions between the preliminarily attacked outputs and the corresponding watermark-free references during training. Rather than reconstructing the entire image, FRDAM selectively refines frequency-domain residuals, directing the diffusion process toward the remaining watermark related discrepancies while minimizing modifications to image content. Extensive experiments on CelebA and ImageNet across four representative watermarking schemes demonstrate that FDDWAN achieves a more favorable trade-off between watermark removal effectiveness and visual fidelity than conventional and learning-based attack methods.

As primary consumers in the marine food chain, zooplankton play a crucial role in maintaining marine ecological balance. However, the Segment Anything Model (SAM) exhibits limited performance in microscopic image instance segmentation due to its lack of zooplankton-specific domain knowledge. To address these challenges, we propose a novel instance segmentation model based on SAM and wavelet transform (ZMIS-SAM), effectively tackling issues such as inaccurate classification, discontinuous segmentation of slender appendages, and incomplete boundary segmentation. Our framework incorporates three core innovations: ZM-ViT enhances SAM's capability to model zooplankton morphology and image intensity distributions through two lightweight adapters, the Neighboring Feature Aggregation Module (NFAM) improves continuous segmentation of semi-transparent slender appendages by integrating general-purpose and domain-specific features, and the Wavelet-based Multi-scale Multi-directional Feature Enhancement (WM2FE) module effectively recovers high-frequency details to refine boundary segmentation completeness. Extensive experiments demonstrate that ZMIS-SAM achieves state-of-the-art instance segmentation performance on the zooplankton dataset and exhibits strong generalization capability across multiple public cross-domain datasets.

Commercial mapping partnerships are often unavailable in low-resource regions, leaving satellite basemaps stale and motivating synthesis of satellite imagery from independently maintained cartographic data. Existing ControlNet-based diffusion methods typically condition on structural signals like edges or segmentation extracted from the target image itself, assuming the imagery already exists and limiting their use exactly where synthesis matters most. Map-conditioned alternatives add cues like edge detection but omit frequency-domain structure. We propose a ControlNet-based diffusion framework conditioned only on cartographic sources obtainable independently of the target imagery: OpenStreetMap (OSM) raster maps and their stationary wavelet transform (SWT) subbands, a conditioning signal previously unexplored for map-to-satellite diffusion. Two ControlNet adapters, trained separately on the map and wavelet representations atop a frozen Stable Diffusion backbone, are fused via MultiControlNet, jointly drawing on spatial structure and frequency detail without retraining a multi-input model. We evaluate on a new paired map-satellite dataset curated for Nepal, a data-scarce, topographically diverse region, alongside the Pix2Pix maps-satellite benchmark. Combined conditioning wins six of eight metric-dataset comparisons -- SSIM and PSNR on both datasets, plus LPIPS (both Alex and VGG backbones) on ours and ties map-only on both Pix2Pix LPIPS backbones while still edging past wavelet-only there. Wavelet-only takes the lowest FID on both datasets, matching the tradeoff between per-image fidelity and distributional realism. We treat this gap cautiously given our modest test-set sizes and FID's known small-sample bias.

Autonomous fleets enable mobility platforms to coordinate idle vehicles directly, making fleet-wide rebalancing possible. However, two obstacles limit reliable deployment: overlapping regional and local traffic patterns can hide roads that remain useful for dispatch, and mobility drift can make a trained policy unreliable. Existing spatial aggregation mixes these patterns, while updating all parameters from limited recent data is costly and can damage stable knowledge. We propose \name, a framework that connects a dispatch-oriented multi-scale graph wavelet module with Drift-Guided Layer-Selective Optimization (DGLS). The first module addresses the representation challenge by separating graph-frequency patterns and weighting each scale according to its value for demand prediction and feasible rebalancing. DGLS addresses the adaptation challenge by measuring Dispatch-weighted Spectral Drift, selecting affected layers within a resource budget, and separating short shocks from persistent changes through a drift-aware fast--slow update. Candidate validation further rejects updates that fail to improve held-out dispatch reward without worsening monitored service or safety constraints. Experiments on both real-world datasets and simluated environments demonstrate the effectiveness of \name\ in comparing with state-of-the-art methods. The source code and datasets are available at https://anonymous.4open.science/r/MobiWave-40F8/.

Existing Large Vision-Language Models (LVLMs) struggle with long-form video understanding due to the quadratic computational cost of visual tokens. While recent efficient methods attempt to compress tokens via hard pruning or uniform merging, they operate strictly in the spatial feature domain, where robust structural context and discriminative semantic details are inherently entangled. In this work, we propose WaveZip, a joint signal-frequency-domain framework for efficient video inference. Driven by the insight that temporal redundancy resides in low-pass approximation scales while spatial saliency strongly correlates with high-frequency components, WaveZip leverages Discrete Wavelet Transforms (DWT) to disentangle these signals. Temporally, it employs 1D DWT to analyze query-frame relevance, and the resulting high-frequency coefficients are further gated by inter-frame differences, with both signals jointly driving the dynamic allocation of a precise frame-level token budget. Spatially, a 2D DWT decomposes features into low-frequency approximations and high-frequency detail components, where the high-frequency coefficients are modulated within query-salient regions to regulate spatial reconstruction. Importantly, WaveZip requires no task-specific training and can be seamlessly integrated into off-the-shelf LVLMs to boost inference efficiency. Extensive experiments on long video understanding benchmarks demonstrate that WaveZip retains 99.6% of the full performance under an extreme 10x compression ratio, consistently outperforming state-of-the-art methods.

Repetitive transcranial magnetic stimulation (rTMS) is a non invasive therapy for Major Depressive Disorder (MDD). In this study, we generate images using two time frequency methods to represent EEG signals: Fourier-Bessel Series Expansion with Euclidean Distance (FBSE-ED) and Discrete Wavelet Transform (DWT). We propose an efficient deep learning classifier to predict the outcome of rTMS depression therapy. In this study, we use a private rTMS databases to train a lightweight custom Convolutional Neural Network (CNN) using 10-fold cross validation strategy in order to avoid any bias in our results. The results show that the FBSE-ED representation achieves the highest classification accuracy of 93.60%, outperforming traditional time-frequency technique (DWT). In addition, the proposed architecture with FBSE-ED image representation technique outperforms more complex EEG-Specific deep learning models (EEGNet, DeepConvNet, SleepEEGNet) by 3.62-10.72% and pretrained models (Xception, DenseNet201, and MobileNetV2) by 23.03-27.35%. For more experiments, we utilize another private rTMS database as test database to show the robustness of the proposed model. Our results suggest that integrating advanced signal decomposition with deep learning can facilitate early prediction of rTMS treatment response and support more targeted clinical decision-making. The proposed framework is interpretable, computationally efficient, and well-suited for deployment in real-world local psychiatric clinics.

Electron microscopy enables nanoscale cellular visualization but faces a trade-off between imaging resolution and acquisition speed. Existing learning-based methods rely on single-stream architectures that struggle to balance perceptual realism and quantitative fidelity, either over-smoothing details or generating unrealistic hallucinations. This work introduces a frequency-adaptive dual-stream architecture to resolve this conflict. Using discrete wavelet transform, we decompose images into low-frequency structures and high-frequency details, then employ a conditional diffusion model for realistic global synthesis and a transformer network for precise detail recovery. Experiments on the EMDiffuse dataset show the method achieves superior LPIPS and resolution ratio, substantially outperforming existing approaches. The method also shows strong generalization across diverse biological samples, supporting fast and reliable electron microscopy imaging for structural biology and nanotechnology applications. The source code and associated dataset are publicly available to facilitate further research.

Scientific machine learning methods such as neural operators and physics-informed neural networks have advanced engineering applications and inverse problems, but their training typically requires large volumes of simulated data. This makes data preparation and model training expensive. We propose Graph Wavelet Compressed Sensing (GWCS), a learning-based framework for offline compression of graph signals by representing them as sparse, interpretable wavelet-domain representations using the spectral graph wavelet transform. The framework combines a nonparametric multilevel importance sampler, which retains high-energy wavelet coefficients within each scale for a given compression ratio, with a scale-aware graph neural network that reconstructs the signal from the sparse coefficients. We evaluate the proposed framework on synthetic approximately band-limited graph signals over random graphs and four PDE simulation datasets over meshes, which include Turbulent Radiative Layer, Viscoelastic Instability, Kolmogorov Flow, and Dynamic Stall. We compare against graph signal sampling methods and graph autoencoder baselines. Results demonstrate that the framework achieves high reconstruction fidelity and substantial data compression compared to existing benchmarks.

Traffic-utilisation measurements for network monitoring are corrupted by additive noise and statistical drift: time-dependent change in the signal's mean, variance, distributional shape, or tail behaviour. Static wavelet denoising, calibrated under stationary independent and identically distributed (i.i.d.) Gaussian assumptions, becomes mismatched under drift and, at moderate-to-high signal-to-noise ratio (SNR), over-suppresses useful structure and degrades monitoring decisions. We propose a drift-aware framework treating adaptive wavelet denoising as a preprocessing layer optimised for two tasks: anomaly detection, recovering the multi-scale transient load bursts that noise and drift obscure, and capacity estimation, recovering the operational required capacity $C_{95}$ (95th percentile of utilisation). Because localised bursts are multi-scale structure a wavelet preserves but a low-pass filter removes, detection discriminates denoiser families. A four-detector gate (Page-Hinkley, variance-ratio, Jensen-Shannon, Anderson-Darling) determines when to invoke a learned policy, and a Proximal Policy Optimization agent selects a per-window wavelet configuration over a mixed discrete-continuous action space. Unlike prior work, the reward is downstream task utility, not reconstruction fidelity. The denoiser is benchmarked, per drift type and input SNR, against a low-pass moving-average filter, VisuShrink, SureShrink, BayesShrink, and a Wiener filter. Defining the anomaly target on the clean signal and the drift gate on the corruption keeps both stages non-circular.

Existing iterative stereo matching methods primarily adopt two types of correspondence representation: explicit matching search via correlation volumes and local residual refinement via warped features, yet the two remain separately modeled. We propose WAVE-Stereo, built on a core insight: correlation volumes and feature warping provide complementary matching cues. \textbf{GeoWarp Correspondence Encoder (GWCE)} encodes matching search, residual alignment, and disparity prior in parallel at the ConvGRU input. To mitigate matching degradation in textureless regions, we propose \textbf{Periodic Global Context Propagation (PGCP)}, which propagates global spatial information in a periodic manner. On five real-world benchmarks -- Middlebury, ETH3D, KITTI 2012, KITTI 2015, and Booster -- WAVE-Stereo achieves competitive zero-shot generalization accuracy without any external foundation model prior, achieving 3.18% D1-all on KITTI 2015, 4.42% Bad-2.0 on Booster, and 66ms real-time inference, striking a favorable balance between accuracy and efficiency. Our code is available at https://github.com/yamanoko-do/WAVE-Stereo.

High deployment cost, poor spatial coverage and susceptibility to storm conditions are all challenges faced by traditional in-situ methods. This paper presents a video-based and high performance computing (HPC) enabled deep learning framework for joint sensor free estimation of five coastal wave parameters, namely significant wave height (Hs), maximum wave height (Hmax), peak period (Tp), zero upcrossing period (Tz) and wave direction (theta) from monocular coastal video. The proposed architecture comprises of a V-JEPA (self supervised) ViT Small backbone for robust spatiotemporal feature extraction in visually challenging scenarios, a dual-stream SlowFast temporal encoder for broad bandwidth representation of wave motion in both hydrodynamic breaking and swell regimes, an optical flow stream based on Farneback optical flow algorithm for adding saliency information to the structure with emphasis on hydrodynamically active wavelength bands of waves, and a multi-task regression layer with dispersion constraints (Airy wave dispersion lambda_p = 0.1). The model was trained on an NVIDIA DGX A100 cluster and was early stopped at epoch 31 and achieved Pearson correlation coefficients of 0.451, 0.578, 0.643, 0.680 and 0.832 for Hs, Hmax, Tp, Tz and wave direction respectively, with generalization ability to geographically diverse held out test data sites. While operating in a data-limited regime (6 annotated training scenes), the framework demonstrates statistically significant temporal correlations (PCC of 0.451 to 0.832), confirming proof of concept feasibility; R2 values (max 0.246) indicate that variance capture will improve with larger annotated datasets.

Accurate dengue forecasting is crucial for public health planning, but remains challenging because incidence series are often short, noisy, non-stationary, nonlinear, and often affected by long-range temporal dependence. Fractional differencing in Autoregressive Fractionally Integrated Moving Average (ARFIMA) helps balance non-stationarity and persistence, but its linear structure limits its ability to capture nonlinear dynamics. Deep neural networks can model nonlinear patterns, but usually require large training samples and do not explicitly encode statistical long memory. Echo State Networks (ESNs), a widely used reservoir computing framework, are attractive in this setting because they retain nonlinear recurrent dynamics while training only a simple readout, making them suitable for data-scarce scenarios. However, standard ESNs lack long-term memory from a time-series perspective. This study proposes a long-memory reservoir computing framework that integrates dedicated long-memory and short-memory ESN reservoirs with a ridge-regression readout. We introduce two variants: Fractional ESN (fESN), which incorporates fractional-differencing dynamics into the reservoir to encode long-range dependence directly, and Wavelet ESN (wESN), which extracts stable low-frequency components through wavelet smoothing before modeling them with a memory-aware reservoir. We establish theoretical guarantees for closed-loop reservoir dynamics, showing that standard ESNs induce short-memory processes under mild conditions, whereas the proposed long-memory reservoirs generate polynomially decaying dependence consistent with statistical long memory. Across multiple dengue datasets and forecasting horizons, fESN and wESN outperform statistical and deep learning baselines. Combining conformal prediction with fESN and wESN provides distribution-free calibrated uncertainty intervals.

VectorizationLLM is a specialized Large Language Model based on Google open-weight LLMs. The model is designed to assist students to learn smart vectorization, time/wave vector analysis, piecewise functions, Fourier analysis, and differential equations in MATLAB. The course application is CTEC 247: Applied Computational Analysis II by the Department of Electrical & Computer Engineering Technology at New York Institute of Technology Old Westbury. The LLM model is designed to be an instructive assistant, providing detailed explanations of concepts with examples from in-class notes without providing direct answers to questions. The model is designed with a RAG (Retrieval Augmented Generation) knowledge base and system prompt architecture. Examples in both code, text, and images are provided in the LLM responses.

Schizophrenia is a debilitating neuropsychiatric disorder characterized by profound cortical network dysregulation, for which objective, clinically translatable EEG based biomarkers remain underdeveloped. Existing automated classification pipelines rely predominantly on static power spectral density features inherently blind to amplitude modulation dynamics and cross-frequency coupling, phenomena central to schizophrenia pathophysiology, while adopting epoch level cross validation strategies that introduce temporal data leakage, artificially inflate reported performance. This study introduces a mathematically principled diagnostic framework integrating the multi-order Wavelet Scattering Transform(WST), strict Leave One Subject Out (LOSO) cross-validation, and SHAP explainability for simultaneous EEG classification and biomarker discovery. Hierarchical WST coefficients capturing multi-scale amplitude modulation structure were extracted from resting state multichannel EEG. Subject-level ANOVA with Benjamini Hochberg false discovery rate correction identified significant biomarkers, with Random Forest and SVM classifiers evaluated under strict LOSO cross validation and subject-level majority voting. Second-order scattering coefficients encoding cross frequency coupling dominated the discriminative biomarker set, with gamma-band features most prevalent, demonstrating that temporal amplitude modulation constitutes the primary electrophysiological signature of schizophrenia. Electrode P3 was identified as the single most discriminative site. Under rigorous subject independent evaluation, the Random Forest achieved 90.48% accuracy (AUC = 0.9339; sensitivity = 95.56%). The proposed WST framework establishes a rigorous, interpretable standard for EEG-driven psychiatric biomarker discovery that can also be applicable in the detection of schizophrenia subtypes in the future.

Traditional malware detection methods struggle to generalize to obfuscated or previously unseen threats. This paper introduces ThreatVisionAI, a hybrid malware family classification framework that integrates a raw-image CNN, a wavelet-based CNN, and a Vision Transformer (ViT) to capture complementary spatial, frequency-domain, and global relational features in malware images. The wavelet-based CNN captures multi-scale frequency information that helps distinguish closely related families, while the ViT branch models long-range dependencies across the image. Evaluated on the Malimg dataset, ThreatVisionAI achieves 98.01% accuracy and a weighted F1 score of 0.9742, with wavelet-domain features providing measurable gains on minority and visually similar families. These results confirm that frequency-aware and transformer-based representations improve image-based malware family classification.

Deep learning (DL) methods dominate thyroid nodule segmentation in ultrasound (US) images, achieving high Dice scores but at the cost of millions of parameters, GPU-dependent training via backpropagation, and limited mathematical tractability. These limitations impede deployment in resource-constrained environments. In this paper, we propose MedSaab-US, a backpropagation-free segmentation framework grounded in the Green Learning paradigm. MedSaab-US extracts multi-scale spatial-frequency features by combining multi-level Discrete Wavelet Transform (DWT) with multi-scale channel-wise Saab (Subspace Approximation with Adjusted Bias) transforms at patch sizes of 5 x 5, 11 x 11, and 21 x 21 pixels. Label-Assisted Greedy (LAG) feature selection retains the most discriminative features, which are fed to an XGBoost classifier for pixel-wise prediction. The Saab transform parameters are determined analytically from data statistics, while XGBoost employs iterative greedy tree construction without requiring backpropagation. Evaluated on the TN3K dataset (2,879 training and 614 test images), MedSaab-US achieves a mean Dice coefficient of 0.4784 +/- 0.2190, precision of 0.5768, and recall of 0.5604, with a model footprint under 500K parameters and CPU-only inference in approximately 0.3 seconds per image. We present this result as an exploratory non-DL baseline for thyroid ultrasound segmentation and analyze the specific challenges posed by isoechoic nodules. An ablation study further quantifies the contribution of each pipeline component, including separate evaluations of LAG feature selection and training-set size.

Most existing knowledge distillation methods focus on homogeneous models (e.g., CNN-to-CNN), thereby overlooking the flexibility and potential of knowledge transfer across heterogeneous models. Due to intrinsic inductive bias discrepancies between heterogeneous models that cause spatial distribution inconsistencies, prior heterogeneous distillation methods often weaken or discard spatial information in heterogeneous representations. However, the spatial information in representations often encodes transferable global structural semantics as well as architecture-specific local details, and therefore should not be directly ignored. To better leverage the spatial information encoded in heterogeneous representations, we propose a Spatial-Frequency Joint-Aware Heterogeneous Knowledge Distillation framework (SFKD). By leveraging the complementary properties of wavelet transform spatial locality and Fourier representations in characterizing global energy distributions, we first apply multi-level discrete wavelet transform to explicitly decouple spatial information. The resulting wavelet sub-bands are further refined by a dual-stream dual-stage refinement module, and finally combined with a Gaussian-filtered frequency loss to selectively capture informative global information. Extensive experiments on multiple benchmark datasets under both homogeneous and heterogeneous models demonstrate the superiority of our method.

Camouflaged Object Detection (COD) aims to locate and segment objects that blend into their surroundings, presenting challenges due to weak edge cues and ill-defined boundaries. Traditional COD models rely on hand-designed architectures and multi-scale feature fusion, which are often guided by intuition rather than systematic search. This paper introduces CamoNAS, a frequency-aware multi-resolution Neural Architecture Search (NAS) framework for COD. CamoNAS automatically searches both cell-level operations and network-level downsampling paths, forming a hierarchical search space tailored to detect camouflaged objects. Additionally, it adopts an RGB frequency dual-stream architecture, where a learnable wavelet transform complements the RGB spatial stream. CamoNAS achieves state-of-the-art performance on four COD benchmarks (CAMO, COD10K, NC4K, CHAMELEON), highlighting the effectiveness of NAS for COD. Our code is available at https://github.com/rendaweiSIMIT/CamoNAS.

We introduce Point-supervised Multi-Object Tracking (PS-MOT) as a cost-effective alternative to traditional bounding box supervision, shifting the focus from spatial fitting to topological center-driven representation. However, PS-MOT faces challenges, e.g., spatial ambiguity and identity drift due to the lack of explicit geometric structure and scale constraints. To address these, we propose PS-Track, a hierarchical pipeline transitioning from points to instances across data, model, and loss levels. At the data level, we introduce Temporal-Feedback Prompting (TFP) to evolve points into temporally consistent pseudo-labels using negative spatial cues and motion priors. At the model level, we design the Point-Excited Wavelet Attention (PEWA) module, which leverages semantic correlations to activate high-frequency components, ``hallucinating'' object boundaries. At the loss level, Uncertainty-Guided Gaussian Learning (UGL) models pseudo-labels as probabilistic distributions, dynamically calibrating supervision intensity. Experiments on DanceTrack, EmboTrack, SportsMOT, and JRDB demonstrate that PS-Track provides a feasible and effective point-supervised alternative across diverse tracking scenarios, establishing a new state-of-the-art for point-supervised tracking. The source code is available at https://github.com/xifen523/PS-MOT.

Deep learning has demonstrated remarkable success in high-throughput histopathology image analysis. However, the performance of learning-based models critically depends on the quality and size of annotations by expert pathologists, which is a resource-intensive and time-consuming process. To address the limitations of data scarcity and annotation burden, several methods have been proposed to synthesize paired histopathology data. Nevertheless, these frameworks typically still require annotation data, albeit in reduced quantities, to impose structural constraints during training. In this work, we present CHIS, a plug-in framework that guides the sampling trajectory of a pretrained diffusion model through two key stages: structural initialization at the start and textural modulation during generation. The initial noise state is refined by fusing the phase information from a prior mask with the amplitude of Gaussian noise in the frequency domain, yielding a structurally informed starting point. During the reverse diffusion process, we adaptively modulate both coarse-grained and fine-grained textures at different wavelet decomposition levels. This enables a diffusion model pretrained solely on unlabeled images to generate outputs that align with prior structural masks while preserving the reference tissue style. We conducted extensive experiments demonstrating the superiority of CHIS in generation fidelity and its substantial benefits for downstream segmentation tasks. Code is available at https://github.com/IBIL-Code/CHIS.

Large language models (LLMs) are attractive for context-aware time series forecasting because they can integrate heterogeneous textual signals, yet their discrete, language-oriented tokenization and embedding interfaces are misaligned with continuous numerical values, often harming numerical ordering and forecasting reliability. We propose TempoWave, a plug-and-play temporal wavelet digit interface that maps each scalar observation into digit-wise embeddings constructed from multi-wavelet, multi-scale coefficients. By directly overriding standard token representations, TempoWave seamlessly exposes both fine-grained local fluctuations and macro global structures in a transformer-compatible form, ensuring that precise numerical formatting, distinct digit identity, and robustness to common normalization operations are maintained throughout the LLM pipeline. Experiments across five context-enriched forecasting benchmarks demonstrate that TempoWave consistently improves LLM-based forecasters over standard numeric tokenization and alternative embedding interfaces, achieving a new state-of-the-art. These results highlight the numeric interface as a key bottleneck and suggest that principled multi-resolution embeddings can better couple LLMs' contextual reasoning with precise forecasting. Our code is available at https://github.com/DC-research/TempoWAVE and our model can be accessed at https://huggingface.co/Melady/TempoWAVE.

Physics-informed surrogate models can accelerate computational fluid dynamics simulations. However, many existing methods reproduce global flow patterns more reliably than localized multiscale structures. This study presents a physics-informed Fourier-wavelet transformer for next-step velocity-field reconstruction in real-world flow benchmarks. The proposed formulation combines hybrid Fourier-wavelet spectral encoding with physics-biased self-attention based on partial differential equation residual diagnostics. It also uses self-supervised pretraining through Masked Physics Prediction and Equation Consistency Prediction. The experiments are conducted on two real benchmark cases: cylinder-wake flow and fluid-structure interaction. All approaches are evaluated under a shared local protocol and compared with spectral, transformer-based, operator-learning, and physics-informed neural-network baselines. On the cylinder-wake benchmark, the proposed model achieves the best aggregate accuracy, with an all-channel normalized mean-squared error of 0.05875 and an all-channel Pearson correlation coefficient of 0.97019. On the fluid-structure-interaction benchmark, it gives the lowest all-channel normalized mean-squared error of $2.70 \times 10^{-4}$, compared with $4.02 \times 10^{-4}$ for the strongest baseline. Component-wise field comparisons and scale-separated diagnostics further show stronger recovery of localized wake structures, including near-body, wake-core, and far-wake features. The results demonstrate improved real-world flow reconstruction while maintaining a practical accuracy-cost tradeoff.

Traditional time-domain prediction of vessel motions in irregular waves usually relies on superposing responses from many regular-wave components, which is computationally expensive for long-duration simulation and real-time applications. This issue is particularly relevant to unmanned surface vehicles (USVs), for which efficient and realistic motion prediction is needed for seakeeping assessment, simulation-based testing, and control-system development. This study applies an impulse response function (IRF)-based time-domain framework to predict vessel motions in short-crested irregular waves. Froude-Krylov, diffraction, and radiation loads are obtained from frequency-domain analysis and transformed into the time domain. Instantaneous responses are then evaluated directly through convolution-based force reconstruction, reducing the need for repeated regular-wave simulations. Weak nonlinear restoring effects are included by instantaneous wetted-surface pressure integration, and directional wave spectra are used to represent realistic sea states. The framework is validated against model-test measurements of an offshore supply vessel in long-crested beam irregular waves and full-scale measurements of a USV operating in real sea conditions. Predicted significant amplitudes, mean zero-crossing periods, standard deviations, and motion time histories agree well with measurements. The effect of directional-spectrum discretization is also examined. Results show that motion amplitudes are moderately sensitive to directional resolution, whereas motion periods are relatively insensitive. A 30 deg directional interval provides a practical balance between prediction accuracy and computational cost. The proposed framework offers an efficient tool for high-fidelity time-domain prediction of USV motions in realistic directional irregular seas.

As Large Language Models asymptotically approach human-level fluency in natural language generation, solely relying on surface-level semantic artifacts for detecting LLM-generated texts has become increasingly precarious. Existing detectors often falter when facing three critical challenges: adversarial perturbations, cross-domain shifts, and the rapid temporal evolution of the foundation model. To address these issues, we propose \wavedetect, a novel framework that reformulates text detection as a signal processing task within the time-frequency domain. Unlike previous methods that analyze static token probability distributions, \wavedetect models the generated output as a probability signal, upon which a differentiable Continuous Wavelet Transform is applied to convert them into learnable spectral representations. This process reveals the intrinsic ``spectral fingerprints'' in machine-generated texts--patterns that remain invisible in time domain. Comprehensive evaluations on three well-curated datasets (RAID, EvoBench, and Domain-Shift) show that our method achieves a new state-of-the-art. It not only achieves superior accuracy but also exhibits remarkable robustness against sophisticated attacks, generalization across out-of-distribution topics and unseen evolving LLMs. Our results validate the efficacy of spectral analysis as a promising paradigm for LLM-generated texts detection.

Three-dimensional full waveform inversion (3DFWI) is a powerful technique for reconstructing high-resolution subsurface velocity models. However, its application is often limited by high memory requirements, computational costs, and sensitivity to cycle skipping. To overcome these challenges, we propose a novel tensor train (TT) decomposition-based 3D implicit full waveform inversion framework (TT-3DIFWI) combined with a multi-scale structural similarity (M-SSIM) objective function. In this framework, the 3D velocity model is represented by TT decomposition as a product of a series of low-rank core tensors. Then, three axis-specific implicit neural network representations (INR) based on one-dimensional vector coordinates as input are constructed to predict these core tensors, rather than directly predicting the velocity model. This INR reparameterization method based on TT decomposition can significantly reduce the memory consumption of INR training while maintaining the accuracy and resolution of the 3D velocity model reconstruction. Meanwhile, the low-rank structure of TT decomposition also ensures the structural consistency of the reconstruction velocity, thereby improving the accuracy and continuity of the inversion result. Furthermore, the M-SSIM objective function can compare the multi-scale structural differences between predicted and observed data, and utilize the ultra-low frequency features to reduce cycle skipping. Numerical experiments on synthetic and challenging land datasets demonstrate that TT-3DIFWI with M-SSIM achieves accurate and continuous velocity reconstruction, even with poor initial models or missing low-frequency data.

Thermal infrared (TIR) imaging has been a popular choice for field robotics due to its robust perception capability under low light visual degradation, but it suffers from severe stochastic and fixed-pattern noise that breaks downstream estimation. This noise is intensified indoors due to low thermal contrast and uniform temperature distributions, contributing to the relative lack of indoor TIR deployments. Existing TIR denoising methods exhibit a poor accuracy-efficiency tradeoff, either too slow for online deployment required in robotics or insufficiently robust to severe degradation, while typically being trained on synthetic noise. Addressing these problems, we propose TIDY, a lightweight wavelet-domain denoiser trained on real clean-noisy TIR data. By reformulating TIR denoising in the wavelet domain, TIDY explicitly disentangles noise from structural content, enabling targeted suppression with reduced spatial complexity, significantly improving inference speed over prior methods (~34Hz). TIDY introduces two new metrics, Wavelet Entropy and Wavelet Directional Stripe Index, as complementary loss terms to explicitly suppress stochastic noise and stripe artifacts. Across severe indoor corruption and zero-shot settings, TIDY improves robustness and yields consistent gains in downstream robotics tasks including thermal inertial odometry and monocular depth estimation. Code and dataset is available at: https://github.com/williamrheeth/TIDY

Spiking neural networks (SNNs) have garnered significant interest in computer vision due to their potential for efficiency and biological inspiration. While spiking CNN-based methods have shown promise for image restoration (IR) tasks, their performance is constrained by the inherent receptive field limitations of CNN operations. In the paper, we explore the benefits of discrete wavelet transformation and propose a spiking pyramid wavelet-based model (SPWM) for high-efficient and low-energy target. Specifically, we develop a spiking dual pyramid wavelet (SDPW) block to model long-range dependency and exploit the properties of the degradation in the wavelet domain. Experimental results on several benchmarks demonstrate that SPWM significantly lowers computational costs and energy consumption while maintaining image quality. Our method showcases the potential of SNNs in the field of IR, offering new insights for future applications of resource-limited devices.

Cyclicity and trend are important components of time series data and many studies based on cyclicity and trend have achieved good results in long-term time series forecasting. However, we believe that current work neglects the influence of real-world inter-channel correlations in time series data which leads to suboptimal predictions. Furthermore, these models rely on complex designs to capture diverse information so that resulting in low computational efficiency. To address this challenge, we propose McWC, a long-term time series forecasting model that separately models the cyclicity, trend, and inter-channel correlations. Specifically, McWC first decouples cyclical information from data using a multi-layer cyclicity construction module. Then, it extracts inter-channel correlations using multi-layer perceptron. Next, it models and fuses the multi-layer high-frequency and low-frequency information from data using a multi-level wavelet decomposition module. Finally, it aggregates the results of different components to obtain the output. Simultaneously, we decouple intra-channel autocorrelations by calculating a loss function in the frequency domain. Experiments on six real-world datasets demonstrate that McWC achieves state-of-the-art performance, exhibiting excellent computational efficiency and historical information extraction capabilities.

We propose a novel Bayesian framework for joint image reconstruction and uncertainty quantification from compressed sensing magnetic resonance imaging data. The problem is formulated as a linear inverse problem, where prior distributions are assigned to the unknown image parameters. Specifically, the image is assumed to be sparse in a given transform domain. We develop a general framework applicable to any sparsifying transform and demonstrate its performance using (1) a total variation transform based on image spatial gradients and (2) a wavelet-domain transform. Bayesian inference is performed using a split-and-augmented Gibbs sampler, while the resulting non-differentiable conditional distributions are efficiently sampled using a proximal Markov chain Monte Carlo method. The proposed algorithms are validated on both single-coil and multi-coil datasets using various k-space sampling patterns and acceleration factors. The results demonstrate that the proposed Bayesian methods consistently outperform their optimisation-based counterparts in image reconstruction while providing uncertainty estimates for the reconstructed images. Furthermore, the estimated uncertainty maps show a strong correlation with the true reconstruction errors and substantially outperformed deep learning-based uncertainty estimation methods.

Interferometric Synthetic Aperture Radar (InSAR) enables effective monitoring of volcanic deformation; however, the observed signals are often corrupted by atmospheric phase delays, seasonal surface changes, and decorrelation effects. Existing atmospheric correction methods, such as numerical weather model-based methods, can reduce these effects but do not consistently remove atmospheric artefacts and may introduce residual biases. To address these limitations, we propose a novel learning-based method for denoising unwrapped InSAR interferograms, using a hybrid training strategy that combines physically motivated synthetic deformation with real atmospheric noise. Specifically, we introduce WaveDINO, a wavelet-based multi-scale denoising framework conditioned on frozen DINOv3 foundation-model features and terrain information. Training uses synthetic magma-source deformation superimposed on short-term interferograms to expose the network to realistic atmospheric statistics while retaining known ground truth. Performance is evaluated on both controlled synthetic data and long-term real interferograms from Laguna del Maule (Chile) and Campi Flegrei (Italy), with independent GNSS measurements used for validation. WaveDINO consistently outperforms competing models, improving agreement with GNSS measurements, and reducing mean GNSS misfit by approximately 3% and 19% at two sites, respectively, while surpassing weather-model-based corrections.

Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models. Empirically, exploiting similarity across different problems, instead of solving them individually, can significantly improve overall performance. While the generalization and sample complexity properties of multitask learning have been widely studied, the parametric complexity of joint approximation in comparison to separate approximation remains less well understood. The question is particularly relevant in modern deep learning, where models are increasingly required to satisfy structural constraints such as equivariance, conservation laws, or orthogonality. We prove lower and upper bounds on the description-length for separate and joint approximation classes, respectively, in uniform norm. We build a class of orthogonal functions by composing a shared hard feature, realized by a Rademacher-Haar wavelet series, with Sawtooth-Walsh readouts to enforce orthogonality of output coordinates. The dyadic tree structure of the Rademacher-Haar wavelet concentrates the approximation hardness in the common feature component, while the readouts act as task-specific heads. Using an information-theoretic framework, we obtain a sharp gap between the optimal approximation rates achievable by joint and separate coding. Finally, we realize this separation in a neural network model using Heaviside activations via reduction to triangle-wave approximation. Our results show that even under an orthogonality constraint joint approximation requires strictly fewer bits in compositional architectures, provided the tasks share a latent hard feature. This provides theoretical insight into the description-length-efficiency of compositional multi-output architectures and clarifies how neural networks can retain expressivity under geometric constraints.

Operational disturbance monitoring in power networks requires decisions to be made from waveform windows as they arrive, rather than from completed records after the event. This study evaluates full-vector Wigner--Ville Distribution Slice (WVDS) spectra for sequential anomaly-onset detection in high-voltage grid-voltage waveforms. The approach keeps the bilinear midpoint interaction structure of the Wigner--Ville distribution and represents each 128-sample voltage window by a 128-dimensional slice spectrum, avoiding manually selected fault-frequency markers. WVDS is used with a baseline-normalized deviation (BND) score and is compared against the BND of Fast Fourier Transform (FFT-BND), raw-window autoencoders, FFT autoencoders, and WVDS autoencoders under the same thresholding and three-window persistence rule. A synthetic autoencoder--clustering teacher is used to select RTE fault records that start from an initially normal region and then transition to anomalous behavior. On the filtered test set, FFT-BND achieves the highest sensitivity, whereas WVDS-BND provides the lowest false-alarm operating point, reducing record-level pre-onset false alarms to 0.69%. The autoencoder comparison follows the same selectivity pattern: WVDS reconstruction decreases false alarms relative to FFT reconstruction but misses more examples. The results indicate that preserved WVD cross-term information can form a selective representation for online grid-waveform anomaly monitoring when false alarms are costly.

Fully sampled MRI requires dense k-space acquisition, leading to long scan times, reduced clinical throughput, and increased sensitivity to patient motion. Accelerated MRI addresses this by acquiring undersampled k-space data and reconstructing the missing information computationally. However, reconstruction from undersampled measurements is highly ill-posed and can introduce aliasing artifacts, noise amplification, and loss of anatomical detail. Although conventional parallel imaging and compressed sensing methods mitigate these issues, and deep learning methods have further improved reconstruction quality, preserving high-frequency structures under aggressive undersampling remains challenging. In this work, we propose a Variational Network with a Wavelet-based U-Net (W-UNet) for accelerated MRI reconstruction. The framework combines physics-guided iterative reconstruction with learnable multi-scale frequency representations. Standard pooling operations are replaced with Discrete Wavelet Transform and Inverse Wavelet Transform modules, enabling lossless downsampling while preserving low-frequency structure and high-frequency edge details. Integrated into the refinement and sensitivity map estimation stages, the proposed design improves artifact suppression, feature preservation, and reconstruction fidelity in both single-coil and multi-coil settings. Experiments on fastMRI knee and M4Raw brain datasets show state-of-the-art performance. Ablation studies further confirm the effectiveness of wavelet-based feature decomposition for accelerated MRI reconstruction.

Anomaly detection in multivariate time series is challenged by four structurally distinct anomaly types -- point (isolated spikes), distributional (level shifts), temporal (rhythm changes), and collective (inter-sensor correlation breakdowns) -- each requiring different feature representations. Most unsupervised methods target only one or two types and provide limited interpretability. We present CRAFTIIF (Cross-Resolution Analytic Four-Type Interpretable Isolation Forest), a fully unsupervised framework targeting all four types without dataset-specific tuning. CRAFTIIF generates K=500 random analytic wavelet feature draws across four families (Morlet, DOG, Haar, Coiflet), each targeting a specific anomaly type, feeding five structured Isolation Forests -- one per type plus a meta-IF for compound anomalies. An adaptive Otsu/MAD threshold calibrates detection automatically across anomaly rates from 0.1% to 69.2%. Because each IF is trained exclusively on type-specific features, branch firing provides direct anomaly-type attribution by construction, without post-hoc explanation. Evaluated on all 19 datasets of the mTSBench benchmark (Zhou et al., TMLR 2026), CRAFTIIF achieves mean F1=0.228 (all 19 datasets) and F1=0.322 (13 detectable datasets), ranking first among all 25 evaluated methods on VUS-PR (0.463 vs. previous best 0.329, +40.7%). A diagnostic framework -- oracle F1, detectability limits, and branch separation ratios -- identifies 6 of 19 datasets as fundamentally undetectable by any unsupervised method. Ablation over 11 conditions confirms adaptive thresholding (+38% F1), four-branch structure (+20%), and meta-IF (+23%) are each essential. Code: https://github.com/smitswil/craftiif

Wave parameters in the nearshore are crucial for coastal engineering, shoreline protection, marine hazard assessment, and coastal management for climate resilience. Traditional monitoring systems like buoys and radar platforms offer accurate monitoring but can have high installation and maintenance expenses and limited spatial coverage. Passive ocean monitoring using video has been achieved by leveraging deep learning, however, many methods are not physically interpretable, feasible, and validated for oceanography. In thiswork, a Physics-Guided Deep Spatiotemporal Learning Framework for direct estimation of nearshore wave peak periods from passive coastal video stream is proposed. The framework combines automated temporal-variance based region-of-interest detection, multi-stage Sim-to-Real transfer learning, and physics-informed regularization to enhance the predictive accuracy and physical consistency. A variety of spatiotemporal architectures were assessed, such as transformer-based and recurrent-convolutional ones, alongside synthetic pretraining,silver-label adaptation, and expert fine-tuning. The results show that transformer-based architectures outperformed in terms of the accuracy of the instantaneous prediction, while lightweight recurrent-convolutional architectures achieved higher temporal stability and operational oceanographic skill. Ablation studies also demonstrated the benefits of physics-guided regularization in terms of trend-following consistency, and physically implausible predictions. Explainability auditing also helped to focus attention in hydrodynamically active surf-zone regions and showed good agreement with the physically derived wave propagation behavior. In general, the proposed framework shows the promise of physics-guided video-based deep learning systems for long-term coastal wave monitoring that are cost-efficient and operationally feasible.

Rotary Position Embedding (RoPE) is widely adopted in Transformer models, yet its extension to high-dimensional domains lacks a unified theoretical formulation. Most existing approaches either apply rotations independently along each axis or empirically mix frequencies, which limits cross-dimensional interactions and yields direction-dependent representations. To address these limitations, we propose nD-RoPE, a decomposition-free generalization of RoPE to arbitrary dimensions. From a translation-invariant formulation in continuous Hilbert space, we derive a spectral condition for isotropy that requires treating positions and frequencies as coupled $n$-dimensional vectors. We instantiate this formulation with a multi-scale regular-simplex wave-vector design, which provides non-degenerate spatial coverage and a symmetric, directionally balanced second-order response. Experiments across images, videos, and point clouds demonstrate consistent performance gains and improved generalization in high-dimensional settings.

Point cloud semantic segmentation requires architectures that capture both fine-grained local geometry and broad global scene structure. Transformer-based networks have demonstrated strong performance by focusing on detailed local feature aggregation; however, global context is conveyed primarily through skip connections across encoder-decoder stages, which we argue is insufficient for full scene understanding. We hypothesize that augmenting skip connections with a learnable global feature extraction module allows the network to acquire scene-level knowledge before descending into local detail, leading to richer and more contextually grounded representations. To this end, we propose Point Transformer with Wavelet Neural Operato (PT-WNO), which integrates a shared Wavelet Neural Operator (WNO) branch alongside the skip connections of a point cloud transformer backbone. At each encoder-decoder transition, point features are projected onto a dense 3D volumetric grid where the WNO captures multi-scale global spectral context through learnable wavelet decomposition and reconstruction. These global features are fused back into the network via lightweight adapters, complementing rather than replacing the existing skip connections. Experiments on four large-scale 3D point cloud benchmarks demonstrate the effectiveness of PT-WNO. On S3DIS (Area 5), PT-WNO achieves 71.59% mIoU, outperforming the Point Transformer v3 (PTv3) baseline by +1.03 points. On DALES it achieves 81.05% mIoU (+1.47 over the baseline). On ScanNet~v2, PT-WNO obtains 76.19% mIoU, remaining competitive with the baseline (76.36%).

Accurate segmentation of carotid arteries in ultrasound imaging is critical for stroke risk assessment. However, speckle noise, low contrast, and blurred boundaries remain major challenges. In this paper, we propose a Frequency-Spatial Synergy Network (FSS-Net) to achieve noise-robust and high-precision carotid artery segmentation. The network integrates wavelet transform, multi-domain attention, and edge enhancement into a unified encoder-decoder architecture. Specifically, a Channel-Spatial-Wavelet Attention (CSWA) module is designed to suppress noise and purify semantic features in the frequency domain. A Wavelet-Enhanced Bottleneck (WEB) module is introduced to capture long-range global dependencies efficiently. Furthermore, a Laplacian-Guided Adaptive Edge Fusion (LAEF) module compensates high-frequency details and maintains boundary continuity. Extensive experiments on carotid ultrasound datasets show that FSS-Net achieves a Dice score (DSC) of 96.46% and strong robustness under low SNR conditions, outperforming several state-of-the-art methods. This method realizes accurate segmentation of carotid artery in ultrasonic imaging, effectively identifies carotid atherosclerotic plaque, and is verified by other task (such as segmentation of breast cancer), suggesting that it has good clinical application potential in identifying abnormal tissue masses in ultrasonic images.

In this study, we propose an overlapped wavelet diffusion framework for Low-Light Image Enhancement (LLIE), which incorporates two complementary components to achieve blocking artifact-free and detail-preserving enhancement. Although recent diffusion-based LLIE methods have demonstrated remarkable performance compared with traditional approaches, DiffLL still suffers from blocking artifacts caused by the Haar Wavelet Transform (WT) and blurred edges or over-smoothed textures due to the limitations of its High-Frequency Restoration Module (HFRM). To overcome these issues, we introduce an Overlapped WT (OWT) that incorporates correlations across neighboring regions, thereby structurally preventing blocking artifacts. Furthermore, we integrate a low-frequency-guided High-Frequency Enhance Block (HFEBlock) to strengthen detail recovery, yielding sharper edges and more reliable textures. Extensive experiments on the LOLv1 and LOLv2-real datasets demonstrate that our framework, termed OWDiff, consistently outperforms existing LLIE methods both qualitatively and quantitatively, achieving superior visual quality while maintaining computational efficiency. OWDiff effectively addresses the structural limitations of the Haar WT and the HFRM, achieving an average PSNR gain of 0.58 dB, along with a 1.64% relative improvement in SSIM and a 5.9% relative reduction in LPIPS, compared to DiffLL across both the LOLv1 and LOLv2-real datasets.

Deep learning has become prevalent in computational pathology pipelines that support tasks such as cancer screening and digital pathology analysis. However, the susceptibility of neural networks to adversarial perturbations raises safety concerns for reliable deployment in clinical practice. In histopathological images, this challenge is exacerbated by the difficulty of distinguishing high-frequency adversarial noise from subtle and diagnostically relevant tissue structures. To address this issue, we propose Stain-Aware Wavelet Regularization (SAWR), an adversarial purification framework that leverages multi-level wavelet-domain regularization based on Haar transform to hierarchically disentangle adversarial perturbations from diagnostic structural information. This spectral constraint is further extended to individual histological channels, enabling stain-specific frequency regulation consistent with the biological properties of Hematoxylin and Eosin. Extensive experiments demonstrate that SAWR improves adversarial robustness by up to 10.69% over the baseline approach, while maintaining texture and spectral fidelity under adversarial perturbations.

Large and demographically balanced datasets are essential for reliable neuroimaging biomarkers. Full-resolution 3D brain MRI synthesis can support data augmentation in this setting, but existing approaches either incur prohibitive computational cost at volumetric scale or rely on lossy latent compression that may compromise anatomical detail. As a result, practical 3D generative augmentation often requires specialized compute infrastructure. We propose WaveDiT, a conditional flow matching framework operating in the coefficient space of a 3D Haar Discrete Wavelet Transform. The model combines factorized spatio-depth attention with band-wise heteroscedastic uncertainty modeling derived from higher-order wavelet statistics. Predicted log-variance is integrated directly into both the flow objective and conditioning pathway, enabling adaptive precision consistent with the heavy-tailed and input-dependent variance structure of anatomical detail. This formulation supports full-resolution 3D synthesis under practical memory and time constraints on a single modern GPU. Evaluation on a multi-site cohort demonstrates improved alignment between generated and real MRI distributions, together with enhanced downstream brain age prediction and region-level anatomical agreement relative to diffusion, latent, and wavelet-based baselines. Code is available at https://github.com/sisinflab/WaveDiT

Score-based generative models have had remarkable success over the last decade in generating a diverse set of visually plausible images. A variety of architectures including CNNs, U-Nets, and Transformers have been used as the score-approximation network in such diffusion modeling; however, to date, relatively little is known about how these architectural choices impact generative behavior. In this work, to provide insight into this area, we propose an analytically solvable parameterization of the score function using an expansion in a 2D orthogonal wavelet basis. In particular, we derive interpretable optimal score functions in terms of the moments of the data distribution. We use this parametrization to provide an architecture-agnostic, moment-based analysis that reveals which attributes of the data distribution tend to matter most for denoising. Our score machine is flexible enough to partially mimic the relevant inductive biases of multiple architectures, including U-Nets, and CNNs, taking a step towards understanding why different score architectures can exhibit distinct generative behavior. Since our score is solvable in terms of the moments of the data, we can begin to understand how the data distribution interacts with the score network to produce the behavior we observe in diffusion models.

In this paper, we propose a reconstruction framework that leverages the Wavelet Scattering Transform (WST) as a multi-scale feature extractor to impose statistical priors under sparse observation conditions. The reconstruction problem is formulated as an optimization task and solved using a neural field, with the WST incorporated into the training loss function. As a proof of concept, we validate the proposed method on HRTF upsampling. A masking strategy is applied to the WST coefficients, resulting in a two-phase procedure. The first phase learns a binary mask from a small multi-subject dataset, while the second phase applies the learned mask to the WST coefficients of an individual HRTF to preserve informative statistical structures during reconstruction. Validation against baseline methods, which also serve as an ablation study of the different components of the framework, demonstrates the effectiveness of the proposed approach.

Standard positional encodings for transformers - sinusoidal and rotary (RoPE) - treat every position as equally local: they encode where a token is, but not how far its positional influence should extend. We propose that the Morlet wavelet, which simultaneously minimises uncertainty in position and frequency, is the natural basis for positional encoding, and introduce Morlet Positional Encoding (MoPE): each embedding dimension learns its own frequency and locality bandwidth from data. The main theoretical result is a unification: sinusoidal PE and the RoPE correlation kernel both emerge as limiting cases of MoPE when locality is switched off (sigma_i -> infinity). The phase of MoPE recovers the RoPE rotation angle exactly; the amplitude adds a learned Gaussian locality kernel that standard encodings lack. Empirically, MoPE combined with Energy-Gated Attention achieves +0.119 improvement over standard attention on TinyShakespeare, outperforming either component alone. Analysis of the learned parameters reveals that all 128 frequency-bandwidth pairs converge to the wavelet admissibility boundary - an empirical observation consistent with a companion result on energy gating, suggesting a reproducible property of character-level language signals that warrants further investigation.