This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2(R^s). The...This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2(R^s). Then, two theorems are given for constructing biorthogonal (orthogonal) two-direction refinable functions in L^2(R^s) and their biorthogonal (orthogonal) two-direction wavelets, respectively. From the constructed biorthogonal (orthogonal) two-direction wavelets, symmetric biorthogonal (orthogonal) multiwaveles in L^2(R^s) can be obtained easily. Applying the projection method to biorthogonal (orthogonal) two-direction wavelets in L^2(R^s), we can get dual (tight) two-direction wavelet frames in L^2(R^m), where m ≤ s. From the projected dual (tight) two-direction wavelet frames in L^2(R^m), symmetric dual (tight) frames in L^2(R^m) can be obtained easily. In the end, an example is given to illustrate theoretical results.展开更多
Accurate and efficient detection of building changes in remote sensing imagery is crucial for urban planning,disaster emergency response,and resource management.However,existing methods face challenges such as spectra...Accurate and efficient detection of building changes in remote sensing imagery is crucial for urban planning,disaster emergency response,and resource management.However,existing methods face challenges such as spectral similarity between buildings and backgrounds,sensor variations,and insufficient computational efficiency.To address these challenges,this paper proposes a novel Multi-scale Efficient Wavelet-based Change Detection Network(MewCDNet),which integrates the advantages of Convolutional Neural Networks and Transformers,balances computational costs,and achieves high-performance building change detection.The network employs EfficientNet-B4 as the backbone for hierarchical feature extraction,integrates multi-level feature maps through a multi-scale fusion strategy,and incorporates two key modules:Cross-temporal Difference Detection(CTDD)and Cross-scale Wavelet Refinement(CSWR).CTDD adopts a dual-branch architecture that combines pixel-wise differencing with semanticaware Euclidean distance weighting to enhance the distinction between true changes and background noise.CSWR integrates Haar-based Discrete Wavelet Transform with multi-head cross-attention mechanisms,enabling cross-scale feature fusion while significantly improving edge localization and suppressing spurious changes.Extensive experiments on four benchmark datasets demonstrate MewCDNet’s superiority over comparison methods:achieving F1 scores of 91.54%on LEVIR,93.70%on WHUCD,and 64.96%on S2Looking for building change detection.Furthermore,MewCDNet exhibits optimal performance on the multi-class⋅SYSU dataset(F1:82.71%),highlighting its exceptional generalization capability.展开更多
Scientific analysis of aeolian sand environments is fundamental for sustainable disaster mitigation along desert highways.However,significant regional variability in wind energy conditions complicates accurate charact...Scientific analysis of aeolian sand environments is fundamental for sustainable disaster mitigation along desert highways.However,significant regional variability in wind energy conditions complicates accurate characterization of wind regimes and introduces uncertainty in determining optimal monitoring timescales.Moreover,prevailing sand control measures often rely on standardized designs rather than site-specific adaptive strategies.To address these issues,this study proposes an integrated framework for aeolian environment analysis and develops targeted disaster mitigation strategies tailored for desert highways.The proposed framework employs wavelet transform to unravel the periodic characteristics of wind speed time series and integrates multi-source data(including ERA5 wind datasets,sand samples,ASTER GDEM,and multi-temporal remote sensing imagery)to enable a comprehensive aeolian environmental assessment.Concurrently,a suite of adaptive strategies is formulated to mitigate disaster risks along desert highways.Validated through a case study of the Tumushuk-Kunyu Desert Highway in Xinjiang,China,the framework exhibits high accuracy:predictions of annual aeolian sand transport activity show relative errors mostly below 7%against long-term reference sequences,and the calculated resultant drift direction exhibits a strong correlation with observed dune migration,yielding an R-squared value of 0.96.These findings confirm the framework’s reliability and provide a robust basis for designing adaptive,location-specific mitigation strategies,thereby enhancing the sustainability of desert highway infrastructure.展开更多
Image captioning,a pivotal research area at the intersection of image understanding,artificial intelligence,and linguistics,aims to generate natural language descriptions for images.This paper proposes an efficient im...Image captioning,a pivotal research area at the intersection of image understanding,artificial intelligence,and linguistics,aims to generate natural language descriptions for images.This paper proposes an efficient image captioning model named Mob-IMWTC,which integrates improved wavelet convolution(IMWTC)with an enhanced MobileNet V3 architecture.The enhanced MobileNet V3 integrates a transformer encoder as its encoding module and a transformer decoder as its decoding module.This innovative neural network significantly reduces the memory space required and model training time,while maintaining a high level of accuracy in generating image descriptions.IMWTC facilitates large receptive fields without significantly increasing the number of parameters or computational overhead.The improvedMobileNet V3 model has its classifier removed,and simultaneously,it employs IMWTC layers to replace the original convolutional layers.This makes Mob-IMWTC exceptionally well-suited for deployment on lowresource devices.Experimental results,based on objective evaluation metrics such as BLEU,ROUGE,CIDEr,METEOR,and SPICE,demonstrate that Mob-IMWTC outperforms state-of-the-art models,including three CNN architectures(CNN-LSTM,CNN-Att-LSTM,CNN-Tran),two mainstream methods(LCM-Captioner,ClipCap),and our previous work(Mob-Tran).Subjective evaluations further validate the model’s superiority in terms of grammaticality,adequacy,logic,readability,and humanness.Mob-IMWTC offers a lightweight yet effective solution for image captioning,making it suitable for deployment on resource-constrained devices.展开更多
In wave-equation migration and demigration,the cross-correlation imaging/forwarding step implicitly injects an additional copy of the source wavelet,so that the amplitude spectrum of the wavelet is applied redundantly...In wave-equation migration and demigration,the cross-correlation imaging/forwarding step implicitly injects an additional copy of the source wavelet,so that the amplitude spectrum of the wavelet is applied redundantly(effectively imposing a wavelet-spectrum weighting,often akin to an amplitude-squared bias).This redundancy degrades structural fidelity and amplitude balance yet is frequently overlooked.We(i)formalize the mechanism by which cross-correlation duplicates the source-wavelet amplitude effect in both migration and demigration,and(ii)introduce a source-equalized operator that removes the redundancy by deconvolving(or dividing by)the wavelet amplitude spectrum in the imaging condition and its demigration counterpart,while leaving phase/kinematics intact.Using a band-limited Ricker wavelet on a two-layer model and on Marmousi,we show that,if unmanaged,the redundant wavelet spectrum broadens main lobes,introduces ringing,and suppresses vertical resolution in migrated images,and inflates spectrum mismatches between demigrated and observed data even when peak times agree.With our correction,images recover observed-data-consistent bandwidth and sharpened interfaces,and demigrated data also exhibit improved spectrum conformity and reduced amplitude misfit.The results clarify when source amplitudes matter,why cross-correlation makes them redundantly matter,and how a lightweight spectral correction restores physically meaningful amplitude behavior in wave-equation migration/demigration.展开更多
For low-light image enhancement tasks,RAW images surpass RGB images due to their high information content,however,their noise and single-channel nature challenge feature extraction.Existing methods using multi-stage c...For low-light image enhancement tasks,RAW images surpass RGB images due to their high information content,however,their noise and single-channel nature challenge feature extraction.Existing methods using multi-stage convolutional neural network(CNN)frameworks struggle with global feature extraction,while single-stage CNN-transformer fusions often result in residual noise.To overcome these limitations,this paper introduces a multi-stage RAW image enhancement network combining CNN and transformer.Considering the characteristics inherent to the task,we devised a CNN-based denoising block for the denoising stage and incorporated wavelet information to enhance frequency features.A transformer-based correction block has been designed for the color and white balance recovery stage,with the white balance being adjusted dynamically using a signal-to-noise ratio(SNR)map.With this design,our method outperforms other state-of-the-art models in all metrics on the Sony and Fuji datasets of see-in-the-dark(SID),and achieves optimal structural similarity index measurement(SSIM)on the mono-colored raw(MCR)dataset.展开更多
The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secur...The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secure communications.So,this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets.The Caputo fractional Rössler attractor model is simulated into two categories,(i)Asymmetric and(ii)Symmetric.The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of the Caputo fractional Rössler attractor model,depicting each computation in graphs and tables to analyze how fractional order affects the model’s dynamics.Approximate solutions obtained through the proposed scheme for integer order are well comparable with the fourth-order Runge-Kutta method.Also,the stability analyses of the considered model are discussed for different equilibrium points.Various fractional orders are considered while performing numerical simulations for the Caputo fractional Rössler attractor model by using Mathematica.The suggested approach can solve another non-linear fractional model due to its straightforward implementation.展开更多
Modeling a non-stationary,multicomponent signal as a superposition of frequency components,each with a well-defined instantaneous frequency(IF),is crucial for extracting information,such as the underlying dynamics hid...Modeling a non-stationary,multicomponent signal as a superposition of frequency components,each with a well-defined instantaneous frequency(IF),is crucial for extracting information,such as the underlying dynamics hidden within the signal.The synchrosqueezing transform(SST)has emerged as an alternative to empirical mode decomposition(EMD)for separating non-stationary signals.However,because the SST estimates the IFs of all frequency components based on a single phase transformation,its accuracy can be limited.To address this,SST variants based on the IFembedded short-time Fourier transform(IFE-STFT)and the IF-embedded continuous wavelet transform(IFE-CWT)were developed.More recently,a direct time-frequency method called the signal separation operation(SSO)was introduced for multicomponent signal separation.SSO bypasses the second step of the two-step SST method for component recovery and is based on variants of the STFT or CWT.In this paper,we propose a direct signal separation method by combining the SSO method with IFE-CWT and IFE-STFT,creating the IFE-CWT-based SSO(IWSSO)and the IFE-STFT-based SSO(IFSSO).Both IWSSO and IFSSO directly separate multicomponent signals without the squeezing operation inherent in SST.Our algorithms and techniques yield more accurate instantaneous frequency estimates and signal separation than conventional SSO or SST methods.展开更多
Low-light image enhancement aims to improve the visibility of severely degraded images captured under insufficient illumination,alleviating the adverse effects of illumination degradation on image quality.Traditional ...Low-light image enhancement aims to improve the visibility of severely degraded images captured under insufficient illumination,alleviating the adverse effects of illumination degradation on image quality.Traditional Retinex-based approaches,inspired by human visual perception of brightness and color,decompose an image into illumination and reflectance components to restore fine details.However,their limited capacity for handling noise and complex lighting conditions often leads to distortions and artifacts in the enhanced results,particularly under extreme low-light scenarios.Although deep learning methods built upon Retinex theory have recently advanced the field,most still suffer frominsufficient interpretability and sub-optimal enhancement performance.This paper presents RetinexWT,a novel framework that tightly integrates classical Retinex theory with modern deep learning.Following Retinex principles,RetinexWT employs wavelet transforms to estimate illumination maps for brightness adjustment.A detail-recovery module that synergistically combines Vision Transformer(ViT)and wavelet transforms is then introduced to guide the restoration of lost details,thereby improving overall image quality.Within the framework,wavelet decomposition splits input features into high-frequency and low-frequency components,enabling scale-specific processing of global illumination/color cues and fine textures.Furthermore,a gating mechanism selectively fuses down-sampled and up-sampled features,while an attention-based fusion strategy enhances model interpretability.Extensive experiments on the LOL dataset demonstrate that RetinexWT surpasses existing Retinex-oriented deeplearning methods,achieving an average Peak Signal-to-Noise Ratio(PSNR)improvement of 0.22 dB over the current StateOfTheArt(SOTA),thereby confirming its superiority in low-light image enhancement.Code is available at http://gffzz188fe103f8f1460asqnxonpk6nv5k6k6k.ffgz.tsg.suse.edu.cn/CHEN-hJ516/RetinexWT(accessed on 14 October 2025).展开更多
Pipelines play a crucial role in chemical industrial production.However,due to long operating cycles,seal failures,and internal corrosion,hazardous chemical media are prone to leak,potentially leading to serious accid...Pipelines play a crucial role in chemical industrial production.However,due to long operating cycles,seal failures,and internal corrosion,hazardous chemical media are prone to leak,potentially leading to serious accidents such as explosions.To address the limitations of existing pipeline leak detection methods—specifically their insufficient recognition accuracy and poor robustness in noisy environments—this paper proposes an Acoustic Emission(AE)-driven leakage state recognition method based on wavelet time-frequency maps and the Inception-V3 deep network.First,a pipeline leak experimental platform was constructed,and AE signals were collected.The signals were denoised through wavelet decomposition reconstruction.Then,the continuous wavelet transform(CWT)was applied to perform time-frequency analysis of the AE signals,generating wavelet time-frequency maps as the dataset.Finally,a deep learning classification model based on Inception-V3 was developed to identify different pipeline leak states.Experimental results show that the proposed method achieves a recognition accuracy of 99.6%.Compared with other network models and feature-based support vector machine(SVM)models,this method exhibits superior robustness in high noise and high recognition accuracy under small leakage conditions,confirming its effectiveness and advantages in pipeline leak detection.展开更多
The wavelet multi-resolution interpolation Galerkin method(WMIGM)is combined with a mixed explicit-implicit time-stepping scheme to solve the onedimensional Burgers'equation at high Reynolds numbers,where the solu...The wavelet multi-resolution interpolation Galerkin method(WMIGM)is combined with a mixed explicit-implicit time-stepping scheme to solve the onedimensional Burgers'equation at high Reynolds numbers,where the solutions exhibit evolving steep local gradients.In the proposed framework,a dynamic sequence of node distributions with local multi-resolution refinement is adaptively constructed according to the gradient information identified by a wavelet transform.The approximate solution at previous time levels,required in the time-stepping procedure,is represented by the same wavelet expansion used in its original construction,thereby eliminating the need for interpolation between different node distributions.Several representative numerical examples are presented to assess the accuracy,convergence,and robustness of the proposed adaptive wavelet method.The results demonstrate that the proposed approach possesses a higher accuracy and a faster convergence rate than many existing numerical methods,and can accurately capture complex shock dynamics without spurious oscillations,including boundary layer formation from smooth initial profiles and shock merging processes.展开更多
Neural-network-based computer-generated holography(CGH)has been extensively confirmed to break the tradeoff between algorithm runtime and reconstruction quality.However,conventional U-Net-based CGH methods lose high-f...Neural-network-based computer-generated holography(CGH)has been extensively confirmed to break the tradeoff between algorithm runtime and reconstruction quality.However,conventional U-Net-based CGH methods lose high-frequency detail due to inadequate global context modeling,which constrains the enhancement of realism and immersion in holographic displays.To address these challenges,we propose WGCNet:a two-stage wavelet global context network for generating speckle-free,high-fidelity 4K phase-only holograms(POHs).This framework integrates a two-dimensional(2D)wavelet down-sampling technique to enhance the U-Net backbone network and leverages physical prior knowledge to preserve high-frequency details.A lightweight global attention module is introduced to model long-range dependencies.We demonstrate that the proposed model achieves a peak signalto-noise ratio of 38.68 dB and a structural similarity index of 0.9615 on the DIV2K dataset at 4K resolution.The method significantly reduces the speckle noise in reconstruction while effectively preserving fine details.This synergistic approach establishes an effective solution for high-resolution holographic displays,offering potential for enhancing visual realism and immersion in virtual reality(VR)and augmented reality(AR)applications.展开更多
Digital pathology is rapidly transforming histopathological diagnosis,yet many existing deep learning models treat all spatial regions uniformly and do not exploit the multi-frequency structure of tissue,which limits ...Digital pathology is rapidly transforming histopathological diagnosis,yet many existing deep learning models treat all spatial regions uniformly and do not exploit the multi-frequency structure of tissue,which limits both diagnostic accuracy and computational efficiency.This paper proposes WaSA-Net,an end-to-end architecture that integrates three complementary modules for histopathological image analysis.First,the Wavelet-Guided Tokenization(WGT)module decomposes input images into frequency-aware representations using learnable wavelet-like filters,so that both global tissue structures and fine-grained cellular patterns are exposed to attention from the first layer.Second,the Dynamic Sparse Attention with Pathology Priors(DSA-PP)module adaptively selects diagnostically informative tokens through a lightweight gating mechanism and incorporates learnable pathology prior tokens that embed domain-specific inductive biases,reducing attention complexity while preserving critical contextual information.Third,the Cross-Frequency Feature Pyramid Fusion(CFFPF)module performs bidirectional cross-attention across frequency bands and applies adaptive per-sample frequency weighting to identify the most discriminative frequency components for each tissue type.The proposed architecture is evaluated on three widely used histopathology benchmarks:PatchCamelyon for metastasis detection,PathMNIST for multi-class colorectal tissue classification,and BreakHis for breast cancer diagnosis.WaSA-Net achieves strong performance with only 4.8 M parameters,reaching 95.91%accuracy(AUC 0.9981)on PathMNIST,93.47%accuracy(AUC 0.9812)on PatchCamelyon,and 96.72%accuracy(AUC 0.9923)on BreakHis.Despite its compact design,WaSA-Net matches or surpasses larger models while requiring no external pretraining data.These results indicate that frequency-aware representations and dynamic sparse attention can improve both efficiency and diagnostic performance in digital pathology.展开更多
Vehicle-induced response separation is a crucial issue in structural health monitoring(SHM).This paper proposes a block-wise sliding recursive wavelet transform algorithm to meet the real-time processing requirements ...Vehicle-induced response separation is a crucial issue in structural health monitoring(SHM).This paper proposes a block-wise sliding recursive wavelet transform algorithm to meet the real-time processing requirements of monitoring data.To extend the separation target from a fixed dataset to a continuously updating data stream,a block-wise sliding framework is first developed.This framework is further optimized considering the characteristics of real-time data streams,and its advantage in computational efficiency is theoretically demonstrated.During the decomposition and reconstruction processes,information from neighboring data blocks is fully utilized to reduce algorithmic complexity.In addition,a delay-setting strategy is introduced for each processing window to mitigate boundary effects,thereby balancing accuracy and efficiency.Simulated signal experiments are conducted to determine the optimal delay configuration and to verify the algorithm’s superior performance,achieving a lower Root Mean Square Error(RMSE)and only 0.0249 times the average computational time compared with the original algorithm.Furthermore,strain signals from the Lieshi River Bridge are employed to validate the method.The proposed algorithm successfully separates the static trend from vehicle-induced responses in real time across different sampling frequencies,demonstrating its effectiveness and applicability in real-time bridge monitoring.展开更多
BACKGROUND Attention-deficit/hyperactivity disorder(ADHD)is a common neurodevelopmental condition characterized by inattention,impulsivity,and hyperactivity.Traditional diagnosis relies on clinical evaluation,which is...BACKGROUND Attention-deficit/hyperactivity disorder(ADHD)is a common neurodevelopmental condition characterized by inattention,impulsivity,and hyperactivity.Traditional diagnosis relies on clinical evaluation,which is timeconsuming and subjective.Electroencephalography(EEG)signals provide an objective alternative,and machine learning methods can improve their diagnostic utility.AIM To develop an explainable EEG-based model for ADHD detection by integrating a novel combination ternary pattern(CTP)feature extractor with twin wavelet transform(TWT)for multilevel signal analysis,and to evaluate its effectiveness in providing accurate,channel-wise,and fusion-based classification results for objective and rapid ADHD diagnosis.METHODS A new EEG dataset containing more than 7000 segments from 137 ADHD patients and 150 controls was studied.A novel feature engineering framework was developed,combining a new CTP extractor with statistical features.A multilevel feature extraction structure was designed using a newly proposed TWT for signal decomposition.Extracted features were reduced to the most informative 263 using neighborhood component analysis.Channelwise classification was performed with k-nearest neighbors,followed by iterative majority voting across 20 EEG channels.RESULTS Single-channel analysis achieved up to 99.12%accuracy.By applying majority voting,overall classification accuracy increased to 99.97%,with similarly high sensitivity and specificity.CONCLUSION Our study introduces a large ADHD EEG dataset and a novel model integrating TWT and CTP.The model provides highly accurate,channel-wise,and fusion-based results,offering a promising objective tool for rapid ADHD diagnosis.展开更多
Fault Identification in Renewable Energy Transmission Lines Using Wavelet Packet Decomposition and Voltage Waveform Analysis,vol.123,no.3,pp.20,2026.http://gffzzd3cc09b8251d45dfsqnxonpk6nv5k6k6k.ffgz.tsg.suse.edu.cn/10.32604/ee.2026.071768.Following publication of the...Fault Identification in Renewable Energy Transmission Lines Using Wavelet Packet Decomposition and Voltage Waveform Analysis,vol.123,no.3,pp.20,2026.http://gffzzd3cc09b8251d45dfsqnxonpk6nv5k6k6k.ffgz.tsg.suse.edu.cn/10.32604/ee.2026.071768.Following publication of the article,a request was received to correct the institutional affiliation of the authors.The request was supported by relevant documentation and approved by all authors.展开更多
To improve the accuracy of detecting prohibited items in X-ray images,this study proposes a wavelet-guided multi-feature fusion module(WaveMFFM),an easy-tointegrate,plug-and-play module that can be seamlessly incorpor...To improve the accuracy of detecting prohibited items in X-ray images,this study proposes a wavelet-guided multi-feature fusion module(WaveMFFM),an easy-tointegrate,plug-and-play module that can be seamlessly incorporated into existing detectors.WaveMFFM innovatively introduces the wavelet transform and pioneers the de-occlusion wavelet convolution(DOWC)structure,which dynamically integrates low-frequency global contour information and high-frequency detailed texture features through a frequency-domain decoupling mechanism.This approach effectively resolves the feature confusion issue inherent in conventional convolutional operations under occlusion scenarios,achieving a groundbreaking synergistic enhancement between edge features and region-specific deep features.Consequently,the proposed method significantly improves the discriminative power of detection features.Extensive experiments on YOLOv8,ViT,and SSD detectors demonstrate that WaveMFFM effectively mitigates occlusion problems,thus improving the prohibited item detection performance of these representative methods.展开更多
The structure damage detection with spatial wavelets was approached. First, a plane stress problem, a rectangular plate containing a short crack under a distributed loading on the edge, was investigated. The displacem...The structure damage detection with spatial wavelets was approached. First, a plane stress problem, a rectangular plate containing a short crack under a distributed loading on the edge, was investigated. The displacement response data along the parallel and perpendicular lines at different positions from the crack were analyzed with the Haar wavelet. The peak in the spatial variations of the wavelets indicates the direction of the crack. In addition, a transverse crack in a cantilever beam was also investigated in the same ways. For these problems, the different crack positions were also simulated to testify the effectiveness of the technique. All the above numerical simulations were processed by the finite element analysis code, ABACUS. The results show that the spatial wavelet is a powerful tool for damage detection, and this new technique sees wide application fields with broad prospects. (Edited author abstract) 14 Refs.展开更多
Air-gun arrays are used in marine-seismic exploration. Far-field wavelets in subsurface media represent the stacking of single air-gun ideal wavelets. We derived single air-gun ideal wavelets using near-field wavelets...Air-gun arrays are used in marine-seismic exploration. Far-field wavelets in subsurface media represent the stacking of single air-gun ideal wavelets. We derived single air-gun ideal wavelets using near-field wavelets recorded from near-field geophones and then synthesized them into far-field wavelets. This is critical for processing wavelets in marine- seismic exploration. For this purpose, several algorithms are currently used to decompose and synthesize wavelets in the time domain. If the traveltime of single air-gun wavelets is not an integral multiple of the sampling interval, the complex and error-prone resampling of the seismic signals using the time-domain method is necessary. Based on the relation between the frequency-domain phase and the time-domain time delay, we propose a method that first transforms the real near-field wavelet to the frequency domain via Fourier transforms; then, it decomposes it and composes the wavelet spectrum in the frequency domain, and then back transforms it to the time domain. Thus, the resampling problem is avoided and single air-gun wavelets and far-field wavelets can be reliably derived. The effect of ghost reflections is also considered, while decomposing the wavelet and removing the ghost reflections. Modeling and real data processing were used to demonstrate the feasibility of the proposed method.展开更多
基金supported by the Natural Science Foundation China(11126343)Guangxi Natural Science Foundation(2013GXNSFBA019010)+1 种基金supported by Natural Science Foundation China(11071152)Natural Science Foundation of Guangdong Province(10151503101000025,S2011010004511)
摘要This article aims at studying two-direction refinable functions and two-direction wavelets in the setting R^s, s 〉 1. We give a sufficient condition for a two-direction refinable function belonging to L^2(R^s). Then, two theorems are given for constructing biorthogonal (orthogonal) two-direction refinable functions in L^2(R^s) and their biorthogonal (orthogonal) two-direction wavelets, respectively. From the constructed biorthogonal (orthogonal) two-direction wavelets, symmetric biorthogonal (orthogonal) multiwaveles in L^2(R^s) can be obtained easily. Applying the projection method to biorthogonal (orthogonal) two-direction wavelets in L^2(R^s), we can get dual (tight) two-direction wavelet frames in L^2(R^m), where m ≤ s. From the projected dual (tight) two-direction wavelet frames in L^2(R^m), symmetric dual (tight) frames in L^2(R^m) can be obtained easily. In the end, an example is given to illustrate theoretical results.
基金supported by the Henan Province Key R&D Project under Grant 241111210400the Henan Provincial Science and Technology Research Project under Grants 252102211047,252102211062,252102211055 and 232102210069+2 种基金the Jiangsu Provincial Scheme Double Initiative Plan JSS-CBS20230474,the XJTLU RDF-21-02-008the Science and Technology Innovation Project of Zhengzhou University of Light Industry under Grant 23XNKJTD0205the Higher Education Teaching Reform Research and Practice Project of Henan Province under Grant 2024SJGLX0126。
摘要Accurate and efficient detection of building changes in remote sensing imagery is crucial for urban planning,disaster emergency response,and resource management.However,existing methods face challenges such as spectral similarity between buildings and backgrounds,sensor variations,and insufficient computational efficiency.To address these challenges,this paper proposes a novel Multi-scale Efficient Wavelet-based Change Detection Network(MewCDNet),which integrates the advantages of Convolutional Neural Networks and Transformers,balances computational costs,and achieves high-performance building change detection.The network employs EfficientNet-B4 as the backbone for hierarchical feature extraction,integrates multi-level feature maps through a multi-scale fusion strategy,and incorporates two key modules:Cross-temporal Difference Detection(CTDD)and Cross-scale Wavelet Refinement(CSWR).CTDD adopts a dual-branch architecture that combines pixel-wise differencing with semanticaware Euclidean distance weighting to enhance the distinction between true changes and background noise.CSWR integrates Haar-based Discrete Wavelet Transform with multi-head cross-attention mechanisms,enabling cross-scale feature fusion while significantly improving edge localization and suppressing spurious changes.Extensive experiments on four benchmark datasets demonstrate MewCDNet’s superiority over comparison methods:achieving F1 scores of 91.54%on LEVIR,93.70%on WHUCD,and 64.96%on S2Looking for building change detection.Furthermore,MewCDNet exhibits optimal performance on the multi-class⋅SYSU dataset(F1:82.71%),highlighting its exceptional generalization capability.
基金jointly funded by the Joint Funds of the National Natural Science Foundation of China(Grant No.U2568210)the Interdisciplinary Research Program of Shihezi University(Grant No.JCYJ202317)the National Natural Science Foundation of China(Grant No.12362035)。
摘要Scientific analysis of aeolian sand environments is fundamental for sustainable disaster mitigation along desert highways.However,significant regional variability in wind energy conditions complicates accurate characterization of wind regimes and introduces uncertainty in determining optimal monitoring timescales.Moreover,prevailing sand control measures often rely on standardized designs rather than site-specific adaptive strategies.To address these issues,this study proposes an integrated framework for aeolian environment analysis and develops targeted disaster mitigation strategies tailored for desert highways.The proposed framework employs wavelet transform to unravel the periodic characteristics of wind speed time series and integrates multi-source data(including ERA5 wind datasets,sand samples,ASTER GDEM,and multi-temporal remote sensing imagery)to enable a comprehensive aeolian environmental assessment.Concurrently,a suite of adaptive strategies is formulated to mitigate disaster risks along desert highways.Validated through a case study of the Tumushuk-Kunyu Desert Highway in Xinjiang,China,the framework exhibits high accuracy:predictions of annual aeolian sand transport activity show relative errors mostly below 7%against long-term reference sequences,and the calculated resultant drift direction exhibits a strong correlation with observed dune migration,yielding an R-squared value of 0.96.These findings confirm the framework’s reliability and provide a robust basis for designing adaptive,location-specific mitigation strategies,thereby enhancing the sustainability of desert highway infrastructure.
基金funded by National Social Science Fund of China,grant number 23BYY197.
摘要Image captioning,a pivotal research area at the intersection of image understanding,artificial intelligence,and linguistics,aims to generate natural language descriptions for images.This paper proposes an efficient image captioning model named Mob-IMWTC,which integrates improved wavelet convolution(IMWTC)with an enhanced MobileNet V3 architecture.The enhanced MobileNet V3 integrates a transformer encoder as its encoding module and a transformer decoder as its decoding module.This innovative neural network significantly reduces the memory space required and model training time,while maintaining a high level of accuracy in generating image descriptions.IMWTC facilitates large receptive fields without significantly increasing the number of parameters or computational overhead.The improvedMobileNet V3 model has its classifier removed,and simultaneously,it employs IMWTC layers to replace the original convolutional layers.This makes Mob-IMWTC exceptionally well-suited for deployment on lowresource devices.Experimental results,based on objective evaluation metrics such as BLEU,ROUGE,CIDEr,METEOR,and SPICE,demonstrate that Mob-IMWTC outperforms state-of-the-art models,including three CNN architectures(CNN-LSTM,CNN-Att-LSTM,CNN-Tran),two mainstream methods(LCM-Captioner,ClipCap),and our previous work(Mob-Tran).Subjective evaluations further validate the model’s superiority in terms of grammaticality,adequacy,logic,readability,and humanness.Mob-IMWTC offers a lightweight yet effective solution for image captioning,making it suitable for deployment on resource-constrained devices.
基金supported by the National Natural Science Foundation of China(42430303)Strategy Priority Research Program(Category B)of the Chinese Academy of Sciences(XDB0710000)+2 种基金National Natural Science Foundation of China(42288201)the National Key R&D Program of China(2023YFF0803203)the IGGCAS start-up funding(Grant No.E251510101).
摘要In wave-equation migration and demigration,the cross-correlation imaging/forwarding step implicitly injects an additional copy of the source wavelet,so that the amplitude spectrum of the wavelet is applied redundantly(effectively imposing a wavelet-spectrum weighting,often akin to an amplitude-squared bias).This redundancy degrades structural fidelity and amplitude balance yet is frequently overlooked.We(i)formalize the mechanism by which cross-correlation duplicates the source-wavelet amplitude effect in both migration and demigration,and(ii)introduce a source-equalized operator that removes the redundancy by deconvolving(or dividing by)the wavelet amplitude spectrum in the imaging condition and its demigration counterpart,while leaving phase/kinematics intact.Using a band-limited Ricker wavelet on a two-layer model and on Marmousi,we show that,if unmanaged,the redundant wavelet spectrum broadens main lobes,introduces ringing,and suppresses vertical resolution in migrated images,and inflates spectrum mismatches between demigrated and observed data even when peak times agree.With our correction,images recover observed-data-consistent bandwidth and sharpened interfaces,and demigrated data also exhibit improved spectrum conformity and reduced amplitude misfit.The results clarify when source amplitudes matter,why cross-correlation makes them redundantly matter,and how a lightweight spectral correction restores physically meaningful amplitude behavior in wave-equation migration/demigration.
摘要For low-light image enhancement tasks,RAW images surpass RGB images due to their high information content,however,their noise and single-channel nature challenge feature extraction.Existing methods using multi-stage convolutional neural network(CNN)frameworks struggle with global feature extraction,while single-stage CNN-transformer fusions often result in residual noise.To overcome these limitations,this paper introduces a multi-stage RAW image enhancement network combining CNN and transformer.Considering the characteristics inherent to the task,we devised a CNN-based denoising block for the denoising stage and incorporated wavelet information to enhance frequency features.A transformer-based correction block has been designed for the color and white balance recovery stage,with the white balance being adjusted dynamically using a signal-to-noise ratio(SNR)map.With this design,our method outperforms other state-of-the-art models in all metrics on the Sony and Fuji datasets of see-in-the-dark(SID),and achieves optimal structural similarity index measurement(SSIM)on the mono-colored raw(MCR)dataset.
基金"La derivada fraccional generalizada,nuevos resultados y aplicaciones a desigualdades integrales"Cod UIO-077-2024supported via funding from Prince Sattam bin Abdulaziz University project number(PSAU/2025/R/1446).
摘要The Rössler attractor model is an important model that provides valuable insights into the behavior of chaotic systems in real life and is applicable in understanding weather patterns,biological systems,and secure communications.So,this work aims to present the numerical performances of the nonlinear fractional Rössler attractor system under Caputo derivatives by designing the numerical framework based on Ultraspherical wavelets.The Caputo fractional Rössler attractor model is simulated into two categories,(i)Asymmetric and(ii)Symmetric.The Ultraspherical wavelets basis with suitable collocation grids is implemented for comprehensive error analysis in the solutions of the Caputo fractional Rössler attractor model,depicting each computation in graphs and tables to analyze how fractional order affects the model’s dynamics.Approximate solutions obtained through the proposed scheme for integer order are well comparable with the fourth-order Runge-Kutta method.Also,the stability analyses of the considered model are discussed for different equilibrium points.Various fractional orders are considered while performing numerical simulations for the Caputo fractional Rössler attractor model by using Mathematica.The suggested approach can solve another non-linear fractional model due to its straightforward implementation.
摘要Modeling a non-stationary,multicomponent signal as a superposition of frequency components,each with a well-defined instantaneous frequency(IF),is crucial for extracting information,such as the underlying dynamics hidden within the signal.The synchrosqueezing transform(SST)has emerged as an alternative to empirical mode decomposition(EMD)for separating non-stationary signals.However,because the SST estimates the IFs of all frequency components based on a single phase transformation,its accuracy can be limited.To address this,SST variants based on the IFembedded short-time Fourier transform(IFE-STFT)and the IF-embedded continuous wavelet transform(IFE-CWT)were developed.More recently,a direct time-frequency method called the signal separation operation(SSO)was introduced for multicomponent signal separation.SSO bypasses the second step of the two-step SST method for component recovery and is based on variants of the STFT or CWT.In this paper,we propose a direct signal separation method by combining the SSO method with IFE-CWT and IFE-STFT,creating the IFE-CWT-based SSO(IWSSO)and the IFE-STFT-based SSO(IFSSO).Both IWSSO and IFSSO directly separate multicomponent signals without the squeezing operation inherent in SST.Our algorithms and techniques yield more accurate instantaneous frequency estimates and signal separation than conventional SSO or SST methods.
基金supported in part by the National Natural Science Foundation of China[Grant number 62471075]the Major Science and Technology Project Grant of the Chongqing Municipal Education Commission[Grant number KJZD-M202301901].
摘要Low-light image enhancement aims to improve the visibility of severely degraded images captured under insufficient illumination,alleviating the adverse effects of illumination degradation on image quality.Traditional Retinex-based approaches,inspired by human visual perception of brightness and color,decompose an image into illumination and reflectance components to restore fine details.However,their limited capacity for handling noise and complex lighting conditions often leads to distortions and artifacts in the enhanced results,particularly under extreme low-light scenarios.Although deep learning methods built upon Retinex theory have recently advanced the field,most still suffer frominsufficient interpretability and sub-optimal enhancement performance.This paper presents RetinexWT,a novel framework that tightly integrates classical Retinex theory with modern deep learning.Following Retinex principles,RetinexWT employs wavelet transforms to estimate illumination maps for brightness adjustment.A detail-recovery module that synergistically combines Vision Transformer(ViT)and wavelet transforms is then introduced to guide the restoration of lost details,thereby improving overall image quality.Within the framework,wavelet decomposition splits input features into high-frequency and low-frequency components,enabling scale-specific processing of global illumination/color cues and fine textures.Furthermore,a gating mechanism selectively fuses down-sampled and up-sampled features,while an attention-based fusion strategy enhances model interpretability.Extensive experiments on the LOL dataset demonstrate that RetinexWT surpasses existing Retinex-oriented deeplearning methods,achieving an average Peak Signal-to-Noise Ratio(PSNR)improvement of 0.22 dB over the current StateOfTheArt(SOTA),thereby confirming its superiority in low-light image enhancement.Code is available at http://gffzz188fe103f8f1460asqnxonpk6nv5k6k6k.ffgz.tsg.suse.edu.cn/CHEN-hJ516/RetinexWT(accessed on 14 October 2025).
基金supported by the National Key R&D Program of China(2023YFC3010500).
摘要Pipelines play a crucial role in chemical industrial production.However,due to long operating cycles,seal failures,and internal corrosion,hazardous chemical media are prone to leak,potentially leading to serious accidents such as explosions.To address the limitations of existing pipeline leak detection methods—specifically their insufficient recognition accuracy and poor robustness in noisy environments—this paper proposes an Acoustic Emission(AE)-driven leakage state recognition method based on wavelet time-frequency maps and the Inception-V3 deep network.First,a pipeline leak experimental platform was constructed,and AE signals were collected.The signals were denoised through wavelet decomposition reconstruction.Then,the continuous wavelet transform(CWT)was applied to perform time-frequency analysis of the AE signals,generating wavelet time-frequency maps as the dataset.Finally,a deep learning classification model based on Inception-V3 was developed to identify different pipeline leak states.Experimental results show that the proposed method achieves a recognition accuracy of 99.6%.Compared with other network models and feature-based support vector machine(SVM)models,this method exhibits superior robustness in high noise and high recognition accuracy under small leakage conditions,confirming its effectiveness and advantages in pipeline leak detection.
基金Project supported by the National Natural Science Foundation of China(Nos.12172154 and12532010)the Natural Science Foundation of Gansu Province of China(No.23JRRA1035)+1 种基金the Fundamental Research Funds for the Central Universities of China(No.lzujbky-2025-jdzx03)the Fundamental and Interdisciplinary Disciplines Breakthrough Plan of the Ministry of Education of China(No.JYB2025XDXM105)。
摘要The wavelet multi-resolution interpolation Galerkin method(WMIGM)is combined with a mixed explicit-implicit time-stepping scheme to solve the onedimensional Burgers'equation at high Reynolds numbers,where the solutions exhibit evolving steep local gradients.In the proposed framework,a dynamic sequence of node distributions with local multi-resolution refinement is adaptively constructed according to the gradient information identified by a wavelet transform.The approximate solution at previous time levels,required in the time-stepping procedure,is represented by the same wavelet expansion used in its original construction,thereby eliminating the need for interpolation between different node distributions.Several representative numerical examples are presented to assess the accuracy,convergence,and robustness of the proposed adaptive wavelet method.The results demonstrate that the proposed approach possesses a higher accuracy and a faster convergence rate than many existing numerical methods,and can accurately capture complex shock dynamics without spurious oscillations,including boundary layer formation from smooth initial profiles and shock merging processes.
基金National Natural Science Foundation of China(62441613,62205173)。
摘要Neural-network-based computer-generated holography(CGH)has been extensively confirmed to break the tradeoff between algorithm runtime and reconstruction quality.However,conventional U-Net-based CGH methods lose high-frequency detail due to inadequate global context modeling,which constrains the enhancement of realism and immersion in holographic displays.To address these challenges,we propose WGCNet:a two-stage wavelet global context network for generating speckle-free,high-fidelity 4K phase-only holograms(POHs).This framework integrates a two-dimensional(2D)wavelet down-sampling technique to enhance the U-Net backbone network and leverages physical prior knowledge to preserve high-frequency details.A lightweight global attention module is introduced to model long-range dependencies.We demonstrate that the proposed model achieves a peak signalto-noise ratio of 38.68 dB and a structural similarity index of 0.9615 on the DIV2K dataset at 4K resolution.The method significantly reduces the speckle noise in reconstruction while effectively preserving fine details.This synergistic approach establishes an effective solution for high-resolution holographic displays,offering potential for enhancing visual realism and immersion in virtual reality(VR)and augmented reality(AR)applications.
摘要Digital pathology is rapidly transforming histopathological diagnosis,yet many existing deep learning models treat all spatial regions uniformly and do not exploit the multi-frequency structure of tissue,which limits both diagnostic accuracy and computational efficiency.This paper proposes WaSA-Net,an end-to-end architecture that integrates three complementary modules for histopathological image analysis.First,the Wavelet-Guided Tokenization(WGT)module decomposes input images into frequency-aware representations using learnable wavelet-like filters,so that both global tissue structures and fine-grained cellular patterns are exposed to attention from the first layer.Second,the Dynamic Sparse Attention with Pathology Priors(DSA-PP)module adaptively selects diagnostically informative tokens through a lightweight gating mechanism and incorporates learnable pathology prior tokens that embed domain-specific inductive biases,reducing attention complexity while preserving critical contextual information.Third,the Cross-Frequency Feature Pyramid Fusion(CFFPF)module performs bidirectional cross-attention across frequency bands and applies adaptive per-sample frequency weighting to identify the most discriminative frequency components for each tissue type.The proposed architecture is evaluated on three widely used histopathology benchmarks:PatchCamelyon for metastasis detection,PathMNIST for multi-class colorectal tissue classification,and BreakHis for breast cancer diagnosis.WaSA-Net achieves strong performance with only 4.8 M parameters,reaching 95.91%accuracy(AUC 0.9981)on PathMNIST,93.47%accuracy(AUC 0.9812)on PatchCamelyon,and 96.72%accuracy(AUC 0.9923)on BreakHis.Despite its compact design,WaSA-Net matches or surpasses larger models while requiring no external pretraining data.These results indicate that frequency-aware representations and dynamic sparse attention can improve both efficiency and diagnostic performance in digital pathology.
基金the support of the Major Science and Technology Project of Yunnan Province,China(Grant No.202502AD080007)the National Natural Science Foundation of China(Grant No.52378288)。
摘要Vehicle-induced response separation is a crucial issue in structural health monitoring(SHM).This paper proposes a block-wise sliding recursive wavelet transform algorithm to meet the real-time processing requirements of monitoring data.To extend the separation target from a fixed dataset to a continuously updating data stream,a block-wise sliding framework is first developed.This framework is further optimized considering the characteristics of real-time data streams,and its advantage in computational efficiency is theoretically demonstrated.During the decomposition and reconstruction processes,information from neighboring data blocks is fully utilized to reduce algorithmic complexity.In addition,a delay-setting strategy is introduced for each processing window to mitigate boundary effects,thereby balancing accuracy and efficiency.Simulated signal experiments are conducted to determine the optimal delay configuration and to verify the algorithm’s superior performance,achieving a lower Root Mean Square Error(RMSE)and only 0.0249 times the average computational time compared with the original algorithm.Furthermore,strain signals from the Lieshi River Bridge are employed to validate the method.The proposed algorithm successfully separates the static trend from vehicle-induced responses in real time across different sampling frequencies,demonstrating its effectiveness and applicability in real-time bridge monitoring.
摘要BACKGROUND Attention-deficit/hyperactivity disorder(ADHD)is a common neurodevelopmental condition characterized by inattention,impulsivity,and hyperactivity.Traditional diagnosis relies on clinical evaluation,which is timeconsuming and subjective.Electroencephalography(EEG)signals provide an objective alternative,and machine learning methods can improve their diagnostic utility.AIM To develop an explainable EEG-based model for ADHD detection by integrating a novel combination ternary pattern(CTP)feature extractor with twin wavelet transform(TWT)for multilevel signal analysis,and to evaluate its effectiveness in providing accurate,channel-wise,and fusion-based classification results for objective and rapid ADHD diagnosis.METHODS A new EEG dataset containing more than 7000 segments from 137 ADHD patients and 150 controls was studied.A novel feature engineering framework was developed,combining a new CTP extractor with statistical features.A multilevel feature extraction structure was designed using a newly proposed TWT for signal decomposition.Extracted features were reduced to the most informative 263 using neighborhood component analysis.Channelwise classification was performed with k-nearest neighbors,followed by iterative majority voting across 20 EEG channels.RESULTS Single-channel analysis achieved up to 99.12%accuracy.By applying majority voting,overall classification accuracy increased to 99.97%,with similarly high sensitivity and specificity.CONCLUSION Our study introduces a large ADHD EEG dataset and a novel model integrating TWT and CTP.The model provides highly accurate,channel-wise,and fusion-based results,offering a promising objective tool for rapid ADHD diagnosis.
摘要Fault Identification in Renewable Energy Transmission Lines Using Wavelet Packet Decomposition and Voltage Waveform Analysis,vol.123,no.3,pp.20,2026.http://gffzzd3cc09b8251d45dfsqnxonpk6nv5k6k6k.ffgz.tsg.suse.edu.cn/10.32604/ee.2026.071768.Following publication of the article,a request was received to correct the institutional affiliation of the authors.The request was supported by relevant documentation and approved by all authors.
摘要To improve the accuracy of detecting prohibited items in X-ray images,this study proposes a wavelet-guided multi-feature fusion module(WaveMFFM),an easy-tointegrate,plug-and-play module that can be seamlessly incorporated into existing detectors.WaveMFFM innovatively introduces the wavelet transform and pioneers the de-occlusion wavelet convolution(DOWC)structure,which dynamically integrates low-frequency global contour information and high-frequency detailed texture features through a frequency-domain decoupling mechanism.This approach effectively resolves the feature confusion issue inherent in conventional convolutional operations under occlusion scenarios,achieving a groundbreaking synergistic enhancement between edge features and region-specific deep features.Consequently,the proposed method significantly improves the discriminative power of detection features.Extensive experiments on YOLOv8,ViT,and SSD detectors demonstrate that WaveMFFM effectively mitigates occlusion problems,thus improving the prohibited item detection performance of these representative methods.
基金The project supported by the National Natural Science Foundation of China
摘要The structure damage detection with spatial wavelets was approached. First, a plane stress problem, a rectangular plate containing a short crack under a distributed loading on the edge, was investigated. The displacement response data along the parallel and perpendicular lines at different positions from the crack were analyzed with the Haar wavelet. The peak in the spatial variations of the wavelets indicates the direction of the crack. In addition, a transverse crack in a cantilever beam was also investigated in the same ways. For these problems, the different crack positions were also simulated to testify the effectiveness of the technique. All the above numerical simulations were processed by the finite element analysis code, ABACUS. The results show that the spatial wavelet is a powerful tool for damage detection, and this new technique sees wide application fields with broad prospects. (Edited author abstract) 14 Refs.
基金supported by the Geosciences and Technology Academy of China University of Petroleum(East China)
摘要Air-gun arrays are used in marine-seismic exploration. Far-field wavelets in subsurface media represent the stacking of single air-gun ideal wavelets. We derived single air-gun ideal wavelets using near-field wavelets recorded from near-field geophones and then synthesized them into far-field wavelets. This is critical for processing wavelets in marine- seismic exploration. For this purpose, several algorithms are currently used to decompose and synthesize wavelets in the time domain. If the traveltime of single air-gun wavelets is not an integral multiple of the sampling interval, the complex and error-prone resampling of the seismic signals using the time-domain method is necessary. Based on the relation between the frequency-domain phase and the time-domain time delay, we propose a method that first transforms the real near-field wavelet to the frequency domain via Fourier transforms; then, it decomposes it and composes the wavelet spectrum in the frequency domain, and then back transforms it to the time domain. Thus, the resampling problem is avoided and single air-gun wavelets and far-field wavelets can be reliably derived. The effect of ghost reflections is also considered, while decomposing the wavelet and removing the ghost reflections. Modeling and real data processing were used to demonstrate the feasibility of the proposed method.