Discrete Wavelet Transform

This paper studies whether audio, images, and video can share a common wavelet token schema rather than relying on separate modality-specific latent grids. It introduces a preliminary continuous-token model built around a one-level Haar DWT/IDWT frontend, a shared coefficient-token layout, optional structural metadata, lightweight modality value adapters, and a shared token-wise encoder-decoder trunk. On Speech Commands, EuroSAT RGB, and DAVIS 2017 data, a dense shared model reaches 39.92 dB audio, 29.37 dB image, and 23.93 dB video PSNR. A matched-rate sweep under continuous latent scalar budgets indicates that the visual gains are not explained solely by latent capacity, while also showing that additive metadata embeddings are not a universal source of improvement. Finally, fixed-rate energy selection provides a strong non-parametric baseline: energy_global improves average PSNR over uniform selection by 16.73 dB for audio, 16.90 dB for images, and 15.86 dB for video under compressed keep ratios. Masked sparse training reaches 34.45 dB video PSNR with 50% of dense tokens. The results support a unified wavelet token schema and sparse token interface, while stopping short of establishing a universal discrete vocabulary.

Functional Magnetic Resonance Imaging (fMRI) provides non-invasive access to dynamic brain activity by measuring blood oxygen level-dependent (BOLD) signals over time. However, the resource-intensive nature of fMRI acquisition limits the availability of high-fidelity samples required for data-driven brain analysis models. While modern generative models can synthesize fMRI data, they often remain challenging in replicating their inherent non-stationarity, intricate spatiotemporal dynamics, and physiological variations of raw BOLD signals. To address these challenges, we propose Dual-Spectral Flow Matching (DSFM), a novel fMRI generative framework that cascades dual frequency representation of BOLD signals with spectral flow matching. Specifically, our framework first converts BOLD signals into a wavelet decomposition map via a discrete wavelet transform (DWT) to capture globalized transient and multi-scale variations, and projects into the discrete cosine transform (DCT) space across brain regions and time to exploit localized energy compaction of low-frequency dominant BOLD coefficients. Subsequently, a spectral flow matching model is trained to generate class-conditioned cosine-frequency representation. The generated samples are reconstructed through inverse DCT and inverse DWT operations to recover physiologically plausible time-domain BOLD signals. This dual-transform approach imposes structured frequency priors and preserves key physiological brain dynamics. Ultimately, we demonstrate the efficacy of our approach through improved downstream fMRI-based brain network classification. The code is available at https://github.com/htew0001/DSFM.git .

Current face video forgery detectors use wide or dual-stream backbones. We show that a single, lightweight fusion of two handcrafted cues can achieve higher accuracy with a much smaller model. Based on the Xception baseline model (21.9 million parameters), we build two detectors: LFWS, which adds a 1x1 convolution to combine a low-frequency Wavelet-Denoised Feature (WDF) with a phase-spectrum channel derived from Spatial-Phase Shallow Learning (SPSL), and LFWL, which merges WDF with Local Binary Patterns (LBP) in the same way. This extra module adds only 292 parameters, keeping the total at 21.9 million, smaller than F3Net (22.5 million) and less than half the size of SRM (55.3 million). Even with this minimal overhead, the fused models increase the average area under the curve (AUC) from 74.8% to 78.6% on FaceForensics++ and from 70.5% to 74.9% on DFDC-Preview, gains of 3.8% and 4.4% over the Xception baseline. They also consistently outperform F3Net, SRM, and SPSL in eight public benchmarks, without extra data or test-time augmentation. These results show that carefully paired, handcrafted features, combined through the lightweight fusion block, can provide competitive robustness at a significantly lower cost than comparable frequency-based detectors. Our findings suggest a need to reevaluate scale-driven design choices in face video forgery detection.

State-of-the-art learned image compression (LIC) schemes are increasingly based on hybrid CNN-transformer architectures. To further improve rate-distortion performance, we introduce channel-wise wavelet transforms into both the transformer and entropy-coding components. First, we propose a channel-wise wavelet-domain transformer attention (ChWDTA) mechanism. ChWDTA keeps the efficient windowed spatial self-attention used in modern LIC backbones, but computes the Q/K/V projections on channel-wise wavelet-transformed features before mapping the attention output back with the inverse transform. The resulting Channel-wise Wavelet-Domain Transformer Block (ChWDTB) therefore preserves the spatial tokenization pattern of windowed attention while sparsifying the channel covariance seen by the attention projections. Second, in the entropy-coding stage, we introduce a channel-wise wavelet packet (ChWP) decomposition that produces four equal-sized subbands, which better fit channel-wise slice-based autoregressive entropy modeling. When each channel-wise subband is divided into two slices, we use eight slices for entropy coding. With this configuration, the proposed scheme obtains BD-rate reductions of -17.82%, -19.15%, and -22.56% on the Kodak, CLIC Professional Validation, and Tecnick test sets, respectively. Even when each channel-wise subband is coded as a single slice, the scheme still retains most of the coding gains with lower complexity. The results confirm the advantage of introducing wavelet transform in CNN-transformer-based LIC schemes.

Deploying high-performing 3D medical image segmenters (e.g., nnU-Net) is often limited by memory footprint and inference latency. Compression is therefore necessary, but compact 3D encoders tend to lose fine structural cues (small lesions and sharp boundaries) as downsampling repeats across multi-resolution stages. We propose Detail Consistent Distillation (DCD), a stage-wise distillation framework that preserves structural detail across scales by aligning teacher-student features in a wavelet-decomposed representation. At each encoder stage, DCD distills directional detail components in the wavelet domain while leaving the coarse approximation comparatively unconstrained, avoiding over-regularization of global semantics. DCD is used only during training and introduces no inference-time overhead. Experiments on the BraTS 2024 and ISLES 2022 benchmarks demonstrate that our approach achieves superior performance in MRI segmentation using 3D multi-modal data. Code and implementation details for DCD are publicly available at https://github.com/ClinicaAlpha/DCD-3D-MedSeg.

The detection of unmanned aerial vehicles (UAVs) is important for the protection of civilian and military infrastructure. In this paper we propose a cost effective UAV detection system using sound signals obtained from microphones. The recorded signals are passed through a signal processing pipeline which employs interpretable adaptive feature extractors using so-called rational Gaussian wavelets. These adaptive wavelet transformations are embedded into and trained together with an underlying small neural network which detects and classifies UAVs based on the obtained features. This leads to a physically interpretable machine learning algorithm that in addition to classifying UAVs is also capable of detecting UAV swarms. We demonstrate our results using data collected in indoor studio and noisy outdoor environments. We conclude that the proposed method outperforms traditional machine learning approaches for detecting and classifying single UAVs as well as drone swarms, while retaining a high degree of interpretability. Our implementation of the proposed methods is made publicly available for reproducibility.

Neural PDE solvers have followed the scaling trajectory of vision and language, with recent foundation models reaching billions of parameters. We argue that scale is a poor substitute for architectural inductive bias in this domain: structured priors deliver outsized parameter efficiency, and the pattern of where they succeed and fail is itself informative about what they capture. We instantiate this argument in WaveLiT, an architecture combining a discrete wavelet transform for lossless multi-resolution tokenization, an augmented linear attention block, a shared-weight multiscale feature pyramid, and a wavelet-domain auxiliary loss. Bespoke 1-10M-parameter WaveLiT models compete with foundation models of 100-1000$\times$ their size across eight TheWell benchmarks, with the largest gains on wave and acoustic-dominated benchmarks where the wavelet-multiscale prior fits the dominant dynamical structure and small per-step errors do not compound geometrically under rollout. Trained jointly across all eight benchmarks, a 10M-parameter foundation variant exhibits a structured, physically interpretable transfer pattern -- strongest where the wavelet-multiscale prior matches the dynamics, weakest on chaotic advection-dominated flows. The entire pipeline trains on a single GPU. The results suggest that small-model PDE performance is shaped by architectural inductive bias rather than scale, and that the structure of a prior's failures is a useful empirical signal about its content.

Event cameras offer significant advantages over conventional frame-based counterparts, including high temporal resolution, low latency, and energy efficiency. These characteristics make them suitable for high-speed and high-dynamic range scene acquisition scenarios; however, the lack of dense intensity frames limits the direct applicability of conventional computer vision methods for scene understanding. Event-to-video (E2V) reconstruction seeks to bridge this gap by converting asynchronous event streams into a sequence of synchronous video frames. Existing E2V reconstruction methods based on convolutional neural networks and transformers operate primarily in the spatial domain and often struggle to recover fine structural details while suppressing severe reconstruction artifacts. To address these issues, we propose MSFET-E2V, a novel multiscale frequency-enhanced transformer model. At its core lies a cross-domain attention module, which fuses spatio-temporal features with frequency-aware representations derived from the discrete wavelet transform. Unlike prior methods relying solely on spatial attention, our approach effectively captures both local and global structures by taking into account low- and high-frequency components, enhancing detail preservation and robustness across various motion scenarios. Furthermore, we propose a lightweight wavelet-enhanced skip block that serves as a skip connection, facilitating artifact suppression and structural detail refinement through joint spatial-frequency domain processing. Extensive experiments demonstrate that MSFET-E2V achieves superior performance over state-of-the-art methods on multiple real-world event datasets, offering significant gains in reconstruction quality. Moreover, compared to the existing transformer-based method, our proposed model significantly reduces the number of parameters, the GPU memory usage, and inference time.

This work introduces the Wavelet-Laplace Neural Operator (WLNO), a novel neural operator that fuses Haar wavelet multi-scale spatial decomposition with the Laplace-domain pole-residue formulation of the Laplace Neural Operator (LNO). While LNO captures transient and steady-state dynamics through learnable system poles and residues, it lacks an explicit mechanism for extracting spatially localized multi-scale features inherent in complex PDE solutions. WLNO addresses this by augmenting the LNO core with a parallel single-level Haar discrete wavelet transform (DWT) branch that decomposes the lifted feature map into four frequency subbands: approximation (LL), horizontal detail (LH), vertical detail (HL), and diagonal detail (HH) and applies independent learned $1\times1$ convolutions to each subband before reconstruction via the inverse DWT. The two branches are fused through a learnable sigmoid-gated weight $α_\mathrm{wav}$, initialized to give a small initial contribution to the wavelet branch, allowing the model to adaptively balance Laplace-domain dynamics against spatial multi-scale features throughout training. WLNO is evaluated against LNO on five benchmark PDE problems using identical hyperparameters, training data, and evaluation protocols: the diffusion equation, the Burgers equation, the reaction-diffusion system, Darcy flow, and the two-dimensional Navier-Stokes equation. WLNO consistently outperforms LNO on all five problems, with the most pronounced improvement on problems with strong spatial multi-scale structure, such as the Burgers equation with sharp shock fronts and the Navier-Stokes equation with coherent vortical structures, while remaining consistent across smoother and elliptic problems. These results demonstrate that wavelet-based multi-scale spatial decomposition is a principled and effective complement to Laplace-domain operator learning.

Scattering transforms achieve Lipschitz stability and translation invariance, but dense prediction tasks require preserving spatial structure lost in global averaging. We propose Phase-Aware Scattering Encoder-Decoder, which restores this information by explicitly preserving phase in skip connections. On image denoising (BSD68), breaking translation invariance improves PSNR by $+2.17$~dB; phase preservation adds $+1.03$~dB. A novel spatial shuffling ablation ($-1.26$~dB penalty) demonstrates phase encodes location-dependent structure. We conduct a preliminary extensibility study on a second dense prediction task (ISIC skin lesion segmentation), with full cross-validation as ongoing work. This work advances principled wavelet-deep learning integration, showing how phase information complements scattering's stability-expressiveness trade-off in pixel-level prediction.

Digital elevation models (DEMs) underpin terrain analysis in Geographic Information Systems (GIS), but in their common raster form, they rely on interpolation for off-grid sampling and finite-difference operators for derivative-based analysis. Implicit neural representations (INRs) offer a continuous alternative, but prior terrain INRs lack explicit frequency control, neglect the gradient structure of terrain, and remain too large and costly to train for practical deployment. We present ImplicitTerrainV2, which advances terrain INRs toward a compact, efficient neural terrain data format by combining a spectral control mechanism with wavelet-guided spatial adaptivity, derivative-aware supervision, and post-training model compression. At its core, a wavelet complexity field (WCF) derives spatially-adaptive frequency masks from analytically computed wavelet coefficients, localizing high-frequency capacity to complex terrain regions. The same field guides complexity-aware adaptive sampling that concentrates training in high-complexity regions, while gradient matching applies extra supervision to enforce the smooth manifold structure of terrain DEMs for improved derivative fidelity. Post-training mixed-precision quantization and entropy coding reduce storage to 1.23 bpp with a 0.28 dB PSNR drop. On 50 Swiss terrain tiles, ImplicitTerrainV2 reaches 66.25 dB end-to-end PSNR, improving over the prior work by 5.70 dB while using 3.2x fewer parameters and training in 55 s per tile on a single GPU. Our compressed neural format is competitive with several established DEM codecs in rate-distortion performance, while additionally supporting off-grid point queries, closed-form derivative evaluation, and resolution-independent reconstruction, which may benefit many downstream GIS applications.

The success of self-supervised learning (SSL) in vision and NLP has motivated its rapid adoption for time series. However, research has focused primarily on Generative paradigms and forecasting tasks, leaving the broader utility of learned representations unquantified. We establish a controlled framework to evaluate the "pre-training dividend": the value added by SSL across diverse temporal tasks. We systematically compare Generative paradigms against Latent Alignment architectures, introducing adaptations of LeJEPA and DINO for time series. These adaptations utilize Discrete Wavelet Transform (DWT) augmentations to enforce invariance to local fluctuations. Our analysis reveals that the pre-training dividend is highly asymmetric: SSL yields gains of up to 375% for anomaly detection and classification, yet remains marginal for forecasting. We demonstrate that representational utility is non-universal, governed by a precision-invariance trade-off where the specific signal resolution required by the task must align with the objective. Finally, we show that representation quality is largely independent of data origin and saturates at moderate architectural depths, suggesting a path to scaling via massive synthetic generation. Our code is available at: https://github.com/noammajor/Models

Many natural and engineered time series -- equity returns, climate anomalies, turbulent velocities, neural recordings, packet-level network traffic -- are approximately self-similar: their horizon-$T$ distribution is tied to the horizon-$1$ distribution by one scaling exponent $H$. Standard deep generative sequence models (transformers, dilated TCNs, the WaveNet family) ignore this. Their receptive fields are wide, but kernel parameters live independently at every dilation level, yielding a multi-scale architecture, not a scale-equivariant one. We make three contributions. First, we give a precise definition of discrete scale equivariance for 1D causal networks and prove that dyadic dilation commutes (up to boundary effects) with any dilated-convolution stack whose kernel weights are shared across levels. Tying the kernel shrinks the convolutional parameter budget by an $L$-fold factor (where $L$ is depth) and hard-wires self-similarity in as an inductive bias. Second, we wrap this Scale-Equivariant WaveNet (SE-WaveNet) backbone in three components that carry the same prior: a one-level Daubechies-4 wavelet input, a Hurst-FiLM block exposing the local scaling exponent, and a spectral-consistency training term targeting the $|f|^{-(2H+1)}$ power-law spectrum. The head is a conditional normalising flow, chosen to preserve equivariance. Third, on 30 years of S&P 500 daily log-returns, SE-WaveNet samples reproduce the empirical scaling-collapse diagnostic on the Allan-Variance top-25 universe (median $\mathcal{C}^\star = 0.020$), while a vanilla WaveNet at matched capacity does not ($\geq 0.06$). NLL, KS-calibration, and tail energy distance tie or beat the baseline, with $L\times$ fewer convolutional parameters.

To fit diverse display and bandwidth constraints, high-frame-rate videos are temporally downscaled to low-frame-rate (LFR) and later upscaled, requiring joint optimization for effective frame-rate rescaling. However, existing methods typically link the two operations via training objectives, without fully exploiting their reciprocal nature, which may cause high-frequency information loss. Moreover, they overlook the impact of lossy codecs on LFR videos, limiting real-world applicability. In this work, we propose an end-to-end framework for compression-aware frame-rate rescaling, named TVRN. To regularize high-frequency information lost during frame-rate downscaling, TVRN adopts an invertible architecture that combines a Multi-Input Multi-Output Temporal Wavelet Transform with a high-frequency reconstruction module. To enable end-to-end training through non-differentiable lossy codecs, we design a surrogate network that approximates their gradients. Finally, to improve robustness under various compression levels, we extend TVRN to an asymmetric architecture by incorporating compression-aware features learned via a learning-to-rank strategy. Extensive experiments show that TVRN outperforms existing methods in reconstruction quality under industrial video compression settings. Source code is publicly available at https://github.com/fengxinmin/TVRN_public.

We present an in-depth analysis of the Koopman semigroup via wavelet transform. Towards this goal, we start by introducing the wavelet-based observables and show that they are eigenfunctions of the Koopman semigroup when this semigroup is considered over the Banach space of continuous functions on a compact forward-invariant set endowed with the supremum norm. We then construct closed-form expressions of the action of the Koopman semigroup and its resolvent in terms of these observables. To approximate the action of Koopman semigroup numerically, we combine Extended Dynamic Mode Decomposition (EDMD) with the proposed wavelet-based observables leading to the Wavelet Dynamic Mode Decomposition via Continuous Wavelet Transform (cWDMD) algorithm. We validate our theoretical results on two numerical examples.

Thermal infrared imaging is robust to illumination variations and smoke interference, making it important for all-weather perception. However, the lack of natural color and fine texture limits target recognition, human visual interpretation, and the transfer of visible-light models. Existing infrared colorization methods mainly rely on single-band images, where insufficient spectral cues may lead to structural distortion and semantic confusion. Although infrared hyperspectral images provide rich spectral responses and material information, existing single-band frameworks remain limited in modeling spatial-spectral coupling and weak texture details. To address these issues, this paper presents FSCM, a spectral-information-guided GAN framework. Within FSCM, a frequency-enhanced spatial-spectral state-space generator composed of cascaded FSB units is constructed. Each FSB integrates three complementary components: state-space modeling captures global spatial-spectral dependencies; the frequency enhancement module (FEM) combines multi-level wavelet decomposition and Fourier gating to recover structural contours, directional high-frequency details, and global frequency responses; and the dual-stream hybrid gating module (DGM) integrates deformation-aware sampling with sparse attention to enhance effective local structures and suppress background interference. Additionally, an online semantic segmentation-guided loss is introduced to constrain the generated results, improving semantic consistency in complex road scenes. Experiments show that FSCM outperforms existing infrared colorization methods in visual quality and semantic fidelity.

Infrared-visible object detection improves detection performance by combining complementary features from multispectral images. Existing backbone-specific and backbone-shared approaches still suffer from the problems of severe bias of modality-shared features and the insufficiency of modality-specific features. To address these issues, we propose a novel detection framework WD-FQDet that explicitly decouples modality-shared and modality-specific information from infrared and visible modalities in the new view of low- and high-frequency domains, allowing fusion strategies tailored to their frequency characteristics. Specifically, a low-frequency homogeneity alignment module is proposed to align modality-shared features across modalities via a cross-modal attention mechanism, and a high-frequency specificity retention module is proposed to preserve modality-specific features through the multi-scale gradient consistency loss. To reinforce the feature representation in the frequency domain, we propose a hybrid feature enhancement module that incorporates spatial cues. Furthermore, considering that the contributions of homogeneous and modality-specific features to object detection vary across scenarios, we propose a frequency-aware query selection module to dynamically regulate their contributions. Experimental results on the FLIR, LLVIP, and M3FD datasets demonstrate that WD-FQDet achieves state-of-the-art performance across multiple evaluation metrics.

Determinantal point processes (DPPs) have emerged as a kernelized alternative to vanilla independent sampling for generating efficient minibatches, coresets and other parsimonious representations of large-scale datasets. While theoretical foundations and promising empirical performance have been demonstrated, there are two challenges for current proposals for DPP-based coresets or minibatches. The first is the need for families of DPPs with certain key variance reduction properties, usually constructed in a continuous setting, of which there are few known examples. The second is the need for an ad-hoc construction of a discrete DPP defined on a given dataset, that inherits such variance reduction. In this work, we contribute to the programme of establishing DPPs as a subsampling toolbox for ML by advancing on these two fronts. First, we propose new DPPs on the Euclidean space based on wavelets, with provably better accuracy guarantees than the best known rates. Second, we introduce a general method to convert such continuous DPPs, which are more amenable to proving analytical statements, into discrete kernels, which are pertinent for subsampling tasks such as minibatch and coreset constructions. This conversion mechanism simultaneously preserves the desired variance decay and reveals a low-rank decomposition of the discrete kernel, which makes sampling the corresponding DPP computationally inexpensive. En route, we enlarge the class of ML tasks amenable to improvements via DPP-based minibatches and coresets to include objective functions with arbitrarily low regularity, and rate guarantees that explicitly adapt to this regularity.

Spike-based encodings are sparse and energy-efficient, but have largely been formulated probabilistically, disconnected from most signal processing literature. We recast spike encoders as time-causal wavelet frames with quantitative bandwidths and reconstruction error bounds. The proposed wavelets preserve the sparsity and locality of spiking representations, with reconstruction up to spike quantization and time discretization. We demonstrate reconstruction on ECG and audio datasets, achieving a normalized RMSE comparable to continuous wavelet transforms. The spiking wavelets map directly to neuromorphic hardware.

Multivariate time series forecasting remains a challenge due to the complexity of local temporal dynamics and global dependencies across multiple variables. In this paper, we propose \textbf{N}eighboring \textbf{P}atching \textbf{Mixer} (\textbf{NPMixer}), a hierarchical architecture featuring a Learnable Stationary Wavelet Transform that adaptively learns filter coefficients to decompose signals into trend and detail components in a data-dependent manner. Our framework introduces a Neighboring Mixer Block that captures local temporal dynamics through a series of hierarchical MLP layers operating on non-overlapping patches. Specifically, the mixer block utilizes MLPs to learn temporal patterns within and across these patches, expanding the receptive field to capture multi-scale dependencies. A Channel-Mixing Encoder is applied to high-frequency components to learn channel correlations while preserving the stability of the underlying global trend. Extensive experiments on seven benchmark datasets demonstrate that NPMixer consistently outperforms state-of-the-art models, achieving better performance in 20 out of 28 ($71.4\%$) evaluated experimental setups for MSE.

Accurate cloud workload forecasting is pivotal for efficient resource management but remains challenging as workloads are highly volatile and prone to sudden bursts. Although wavelets preserve temporal locality, rigid fixed bases struggle with complex patterns and isolated processing neglects critical spatial dependencies. To address this, we propose SWIFT, a pure convolutional framework designed for high-efficiency workload forecasting. We introduce a Learnable Cascaded Wavelet Path that reformulates the traditional fixed wavelet bases into adaptive convolutional operators, enabling precise, data-driven feature peeling. Complementing this, our Multivariate Interaction Module sequentially models inter-variable spatial and intra-variable feature interactions to stabilize and refine noisy workload states. Extensive experiments demonstrate that SWIFT achieves SOTA accuracy with linear O(L) complexity, reducing prediction error by up to 31.04% while cutting latency by 79.74%.

Point forecasting for graph-structured multivariate time series is a fundamental problem, but rigorous uncertainty quantification for such predictions is still underexplored. Conformal prediction (CP) offers uncertainty estimation with a solid coverage guarantee under the exchangeability assumption, which requires the joint data distribution to be unchanged under permutation. However, in graph-structured time series, inherent cross-node coupling can violate the exchangeability condition, making direct application of CP unreliable. Inspired by the spectral graph theory, such coupling resides in global trends and can be characterized by the low-frequency components, while high-frequency components are nearly exchangeable. Therefore, we propose a novel concept named Spectral Graph Conditional Exchangeability (SGCE), which conditions exchangeable high-frequency components on low-frequency ones to preserve global trends and enable effective CP in the spectral domain. Based on SGCE, we further propose Spectral Conformal prediction via wAveLEt transform (SCALE). SCALE uses graph wavelets to decompose low/high-frequency components and conformalizes high-frequency residuals via adaptive gating over a low-frequency embedding. Experimental results on real-world traffic datasets show that SCALE not only achieves valid coverage but also consistently improves the coverage-efficiency trade-off over the state-of-the-art CP methods.

Conventional wavelet-domain methods for room impulse response denoising rely on thresholding detail coefficients, which is unsuited for low frequencies. In this work, we introduce a wavelet-based post-processing algorithm that extends denoising to approximation coefficients by means of sparse dictionary learning with a time-varying error tolerance. The proposed method leverages an exponential decay envelope model to adapt reconstruction accuracy according to the local signal-to-noise ratio. This approach significantly improves low-frequency denoising of synthetic and measured room impulse responses compared to the baseline method, leading to more accurate estimation of acoustic parameters such as decay time.

The Laplacian operator transforms the image into its Laplacian field, which usually is sparse and satisfies a stable distribution. On the other hand, an image can be uniquely reconstructed from its Laplacian field via solving a Poisson equation with a proper boundary condition. Such uniqueness is mathematically guaranteed. Thanks to these properties, we propose to use the sparse Laplacian field to present the image. We first show that the Laplacian field is sparse and satisfies a stable distribution on hundreds images. Then, we show that the image can be accurately reconstruct from its Laplacian field. For the reconstruction task, we propose a shared-kernel wavelet neural network, which solves the Poisson equation and has three advantages. First, it has less than {\bf 0.0002M} parameters, which is compact enough for most of devices. Second, it has linear computation complexity, leading to a real-time reconstruction. Third, it achieves higher accuracy than previous methods. Several numerical experiments are conducted to show the effectiveness and efficiency of the sparse Laplacian field and the proposed Poisson solver. The proposed method can be applied in a large range of applications such as image compression, low light enhancement, object tracking, etc.

Summarizing long, domain-specific documents with large language models (LLMs) remains challenging due to context limitations, information loss, and hallucinations, particularly in clinical and legal settings. We propose a Discrete Wavelet Transform (DWT)-based multi-resolution framework that treats text as a semantic signal and decomposes it into global (approximation) and local (detail) components. Applied to sentence- or word-level embeddings, DWT yields compact representations that preserve overall structure and critical domain-specific details, which are used directly as summaries or to guide LLM generation. Experiments on clinical and legal benchmarks demonstrate comparable ROUGE-L scores. Compared to a GPT-4o baseline, the DWT based summarization consistently improve semantic similarity and grounding, achieving gains of over 2% in BERTScore, more than 4% in Semantic Fidelity, factual consistency in legal tasks, and large METEOR improvements indicative of preserved domain-specific semantics. Across multiple embedding models, Fidelity reaches up to 97%, suggesting that DWT acts as a semantic denoising mechanism that reduces hallucinations and strengthens factual grounding. Overall, DWT provides a lightweight, generalizable method for reliable long-document and domain-specific summarization with LLMs.

While standard flow-matching models transport noise to data uniformly, incorporating an explicit generation order - specifically, establishing coarse, low-frequency structure before fine detail - has proven highly effective for synthesizing natural images. Two recent works offer distinct paradigms for this. K-Flow imposes a hard frequency constraint by reinterpreting a frequency scaling variable as flow time, running the trajectory inside a transformed amplitude space. Latent Forcing provides a soft ordering mechanism by coupling the pixel flow with an auxiliary semantic latent flow via asynchronous time schedules, leaving the pixel interpolation path itself untouched. Viewed from the angle of improving pixel generation, we observe that forcing - guiding generation with an earlier-maturing auxiliary stream - offers a highly compatible route to scale-ordered generation without rewriting the core flow coordinate. Building on this, we propose Frequency-Forcing, which realizes K-Flow's frequency ordering through Latent Forcing's soft mechanism: a standard pixel flow is guided by an auxiliary low-frequency stream that matures earlier in time. Unlike Latent Forcing, whose scratchpad relies on a heavy pretrained encoder (e.g., DINO), our frequency scratchpad is derived from the data itself via a lightweight learnable wavelet packet transform. We term this a self-forcing signal, which avoids external dependencies while learning a basis better adapted to data statistics than the fixed bases used in hard frequency flows. On ImageNet-256, Frequency-Forcing consistently improves FID over strong pixel- and latent-space baselines, and naturally composes with a semantic stream to yield further gains. This illustrates that forcing-based scale ordering is a versatile, path-preserving alternative to hard frequency flows.

Time series forecasting plays a pivotal role in critical sectors such as finance, energy, transportation, and meteorology. However, Long-term Time Series Forecasting (LTSF) remains a significant challenge because real-world signals contain highly entangled temporal dynamics that are difficult to fully capture from a purely 1D perspective. To break this representation bottleneck, we propose TriTS, a novel cross-modal disentanglement framework that projects 1D time series into orthogonal time, frequency, and 2D-vision spaces.To seamlessly bridge the 1D-to-2D modality gap without the prohibitive $O(N^2)$ computational overhead of Vision Transformers (ViTs), we introduce a Period-Aware Reshaping strategy and incorporate Visual Mamba (Vim). This approach efficiently models cross-period dependencies as global visual textures while maintaining linear computational complexity. Complementing this, we design a Multi-Resolution Wavelet Mixing (MR-WM) module for the frequency modality, which explicitly decouples non-stationary signals into trend and noise components to achieve fine-grained time-frequency localization. Finally, a streaming linear branch is retained in the time domain to anchor numerical stability. By dynamically fusing these three complementary representations, TriTS effectively adapts to diverse data contexts. Extensive experiments across multiple benchmark datasets demonstrate that TriTS achieves state-of-the-art (SOTA) performance, fundamentally outperforming existing vision-based forecasters by drastically reducing both parameter count and inference latency.

Adverse lighting conditions, such as cast shadows and irregular illumination, pose significant challenges to computer vision systems by degrading visibility and color fidelity. Consequently, effective shadow removal and ALN are critical for restoring underlying image content, improving perceptual quality, and facilitating robust performance in downstream tasks. However, while achieving state-of-the-art results on specific benchmarks is a primary goal in image restoration challenges, real-world applications often demand robust models capable of handling diverse domains. To address this, we present a comprehensive study on lighting-related image restoration by exploring two contrasting strategies. We leverage a robust framework for ALN, DINOLight, as a specialized baseline to exploit the characteristics of each individual dataset, and extend it to OmniLight, a generalized alternative incorporating our proposed Wavelet Domain Mixture-of-Experts (WD-MoE) that is trained across all provided datasets. Through a comparative analysis of these two methods, we discuss the impact of data distribution on the performance of specialized and unified architectures in lighting-related image restoration. Notably, both approaches secured top-tier rankings across all three lighting-related tracks in the NTIRE 2026 Challenge, demonstrating their outstanding perceptual quality and generalization capabilities. Our codes are available at https://github.com/OBAKSA/Lighting-Restoration.

3D Gaussian Splatting (3DGS) has emerged as a powerful paradigm for real-time and high-fidelity 3D reconstruction from posed images. However, recent studies reveal its vulnerability to adversarial corruptions in input views, where imperceptible yet consistent perturbations can drastically degrade rendering quality, increase training and rendering time, and inflate memory usage, even leading to server denial-of-service. In our work, to mitigate this issue, we begin by analyzing the distinct behaviors of adversarial perturbations in the low- and high-frequency components of input images using wavelet transforms. Based on this observation, we design a simple yet effective frequency-aware defense strategy that reconstructs training views by filtering high-frequency noise while preserving low-frequency content. This approach effectively suppresses adversarial artifacts while maintaining the authenticity of the original scene. Notably, it does not significantly impair training on clean data, achieving a desirable trade-off between robustness and performance on clean inputs. Through extensive experiments under a wide range of attack intensities on multiple benchmarks, we demonstrate that our method substantially enhances the robustness of 3DGS without access to clean ground-truth supervision. By highlighting and addressing the overlooked vulnerabilities of 3D Gaussian Splatting, our work paves the way for more robust and secure 3D reconstructions.

Low-resolution image representation can be regarded as a special form of sparse representation that retains only low-frequency information while discarding high-frequency components. This property reduces storage and transmission costs and benefits various image processing tasks. However, a key challenge is to preserve essential visual content while maintaining the ability to accurately reconstruct the original images. This work proposes LR2Flow, a nonlinear framework that learns low-resolution image representations by integrating wavelet tight frame blocks with normalizing flows. We conduct a reconstruction error analysis of the proposed network, which demonstrates the necessity of designing invertible neural networks in the wavelet tight frame domain. Experimental results on various tasks, including image rescaling, compression, and denoising, demonstrate the effectiveness of the learned representations and the robustness of the proposed framework. Code is available at https://github.com/Evanescentlove/LR2Flow-main.

Gravitational-wave data analysis relies on accurate and efficient methods to extract physical information from noisy detector signals, yet the increasing rate and complexity of observations represent a growing challenge. Deep learning provides a powerful alternative to traditional inference, but existing neural models typically lack the flexibility to handle variations in data analysis settings. Such variations accommodate imperfect observations or are required for specialized tests, and could include changes in detector configurations, overall frequency ranges, or localized cuts. We introduce a flexible transformer-based architecture paired with a training strategy that enables adaptation to diverse analysis settings at inference time. Applied to parameter estimation, we demonstrate that a single flexible model, called Dingo-T1, can (i) analyze 48 gravitational-wave events from the third LIGO-Virgo-KAGRA Observing Run under a wide range of analysis configurations, (ii) enable systematic studies of how detector and frequency configurations impact inferred posteriors, and (iii) perform inspiral-merger-ringdown consistency tests probing general relativity. Dingo-T1 also improves median sample efficiency on real events from a baseline of 1.4% to 4.2%. Our approach thus demonstrates flexible and scalable inference with a principled framework for handling missing or incomplete data, key capabilities for current and next-generation observatories.

This letter presents a CWT-enhanced vibration sensing framework for bearing fault monitoring through localized time-frequency region detection on continuous wavelet transform (CWT) spectrograms. Vibration signals are transformed into CWT spectrograms to improve the observability of weak and non-stationary fault signatures, and YOLOv9, YOLOv10, and YOLOv11 are employed to detect and identify localized fault-related energy regions in the time-frequency domain. Experiments on the CWRU, PU, and IMS datasets show that the proposed framework improves the detectability and robustness of fault-related sensing patterns compared with conventional time-series models, modern vision backbones, and short-time Fourier transform (STFT)-based representations, achieving mean average precision (mAP) values up to 99.4%, 97.8%, and 99.5%, respectively. In addition, the localized region detection framework provides a more interpretable relationship between time-frequency energy distributions and characteristic bearing fault frequencies. These results demonstrate an effective and generalizable approach for interpretable vibration sensing in noisy industrial environments.

Adapting large pretrained vision models to medical image classification is often limited by memory, computation, and task-specific specializations. Parameter-efficient fine-tuning (PEFT) methods like LoRA reduce this cost by learning low-rank updates, but operating directly in feature space can struggle to capture the localized, multi-scale features common in medical imaging. We propose WaRA, a wavelet-structured adaptation module that performs low-rank adaptation in a wavelet domain. WaRA reshapes patch tokens into a spatial grid, applies a fixed discrete wavelet transform, updates subband coefficients using a shared low-rank adapter, and reconstructs the additive update through an inverse wavelet transform. This design provides a compact trainable interface while biasing the update toward both coarse structure and fine detail. For extremely low-resource settings, we introduce Tiny-WaRA, which further reduces trainable parameters by learning only a small set of coefficients in a fixed basis derived from the pretrained weights through a truncated SVD. Experiments on medical image classification across four modalities and datasets demonstrate that WaRA consistently improves performance over strong PEFT baselines, while retaining a favorable efficiency profile. Our code is publicly available at https://github.com/moeinheidari7829/WaRA.

Image demoiréing remains a challenging task due to the complex interplay between texture corruption and color distortions caused by moiré patterns. Existing methods, especially those relying on direct image-to-image restoration, often fail to disentangle these intertwined artifacts effectively. While frequency-aware approaches offer a promising direction, their potential is hindered by the discrete transform (e.g., Haar wavelet or block-based DCT), which may suffer from spatial discontinuity, channel redundancy, and further cause error accumulation during their fixed inverse processes. In this paper, we present Freqformer, a Transformer-based framework specifically designed for image demoiréing through targeted frequency separation. Our method performs an effective frequency decomposition that splits moiré patterns into high-frequency spatially-localized textures and low-frequency scale-robust color distortions, which are then handled by a dual-branch architecture and an asymmetric training scheme tailored to their distinct characteristics. We further propose a learnable Frequency Composition Transform (FCT) module to adaptively fuse the frequency-specific outputs, enabling consistent and high-fidelity reconstruction. To better aggregate the spatial dependencies and the inter-channel complementary information, we introduce a Spatial-Aware Channel Attention (SA-CA) module that refines moiré-sensitive regions without incurring high computational cost. Extensive experiments on various demoiréing benchmarks demonstrate that Freqformer achieves state-of-the-art performance with a compact model size. The code will be made publicly available at https://github.com/xyLiu339/Freqformer.

Conventional visuomotor imitation learning usually predicts future robot actions directly in the time domain. Such formulations often have limited physical scene awareness and weak memory. In this work, we propose Wavelet Policy, a lightweight imitation learning framework that combines World Prior Memory (WPM) with wavelet-based multi-scale action modeling. Our key idea is to encode persistent physical scene structure from static background images into compact memory tokens, which are fused into world-prior tokens and injected into the encoder during forward propagation. Based on this memory-conditioned representation, we further perform wavelet-domain decomposition over horizon-aligned latent action tokens and adopt a Single-Encoder Multiple-Decoder (SE2MD) architecture to model latent components at different temporal scales. The resulting latent subbands are reconstructed through inverse wavelet transform and finally projected into executable action chunks. To facilitate efficient world prior learning, we introduce a world-prior adaptation loss, encouraging the background encoder to retain persistent scene knowledge while remaining lightweight and stable. Extensive experiments on four simulated and six real-world robotic manipulation tasks show that Wavelet Policy consistently outperforms strong baselines. These results demonstrate that combining scale-domain action modeling with world-prior memory provides an effective and efficient solution for embodied manipulation.

Rapid advancements in video diffusion models have enabled the creation of realistic videos, raising concerns about unauthorized use and driving the demand for techniques to protect model ownership. Existing watermarking methods suffer from two key limitations: they overlook temporal consistency due to conventional watermark decoders and degrade the visual quality of the generated videos. To address these issues, we introduce a robust watermarking method for latent video diffusion models named Latent Video Diffusion Watermarking (LVMark). We propose a novel watermark decoder tailored for generated videos by learning the consistency between adjacent frames. It ensures accurate message decoding, even under malicious attacks, by combining the low-frequency components of the three-dimensional wavelet domain with the color features of the video. Additionally, we train a latent decoder to maintain the visual fidelity of the generated video. Watermarks are embedded into layers with minimal impact on visual appearance using an importance-based weight modulation strategy. We optimize both the watermark decoder and the latent decoder of diffusion model, effectively balancing the trade-off between visual quality and bit accuracy. Our experiments show that our method embeds invisible watermarks into video diffusion models, ensuring robust decoding accuracy with 512-bit capacity, even under distortions.