The aim of this study is to carry out hydrothermal alteration mapping and structural mapping using ASTER images in order to identify indices that could guide mining exploration work in the Poli area and its surroundin...The aim of this study is to carry out hydrothermal alteration mapping and structural mapping using ASTER images in order to identify indices that could guide mining exploration work in the Poli area and its surroundings. To achieve this, the ASTER images were first preprocessed to correct atmospheric effects and remove vegetation influence. Secondly, a lineament mapping was conducted by applying Discrete Wavelet Transform (DWT) algorithms to the First Principal Component Analysis (PCA1) of Visible Near-Infrared (VNIR) and Shortwave Infrared (SWIR) bands. Lastly, band ratio methods were applied to the VNIR, SWIR, and Thermal Infrared (TIR) bands to determine indices of iron oxides/hydroxides (hematite and limonite), hydroxyl-bearing minerals (chlorite, epidote, and muscovite), and the quartz index. The results obtained showed that the lineaments were mainly oriented NE-SW, ENE-WSW, and E-W, with NE-SW being the most predominant direction. Concerning hydrothermal alteration, the identified indices covered almost the entire study area and showed a strong correlation with lithological data. Overlaying the obtained lineaments with the hydrothermal alteration indices revealed a significant correlation between existing mining indices and those observed in the field. Mineralized zones generally coincided with areas of high lineament density exhibiting significant hydrothermal alteration. Based on the correlation between existing mining indices and the results of hydrothermal and structural mapping, the results obtained can then be used as a reference document for any mining exploration in the study area.展开更多
This paper describes a novel wavelet-based approach to the detection of abrupt fault of Rotorcrafi Unmanned Aerial Vehicle （RUAV） sensor system. By use of wavelet transforms that accurately localize the characterist...This paper describes a novel wavelet-based approach to the detection of abrupt fault of Rotorcrafi Unmanned Aerial Vehicle （RUAV） sensor system. By use of wavelet transforms that accurately localize the characteristics of a signal both in the time and frequency domains, the occurring instants of abnormal status of a sensor in the output signal can be identified by the multi-scale representation of the signal. Once the instants are detected, the distribution differences of the signal energy on all decomposed wavelet scales of the signal before and after the instants are used to claim and classify the sensor faults.展开更多
Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Usin...Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.展开更多
In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state its...In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state itself vary from ｜ψ〉 to Ftr, s ｜ψ〉, except for variation within the family of dilations and translations. The Parseval＇s equality, admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed. By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform, we obtain some mother wavelets. A comparison between the newly found mother wavelets is presented.展开更多
In order to make trend analysis and prediction to acquisition data in amechanical equipment condition monitoring system, a new method of trend feature extraction andprediction of acquisition data is proposed which con...In order to make trend analysis and prediction to acquisition data in amechanical equipment condition monitoring system, a new method of trend feature extraction andprediction of acquisition data is proposed which constructs an adaptive wavelet on the acquisitiondata by means of second generation wavelet transform ( SGWT), Firstly, taking the vanishing momentnumber of the predictor as a constraint, the linear predictor and updater are designed according tothe acquisition data by using symmetrical interpolating scheme. Then the trend of the data isobtained through doing SGWT decomposition , threshold processing and SGWT reconstruction. Secondly,under the constraint of the vanishing moment number of the predictor, another predictor based on theacquisition data is devised to predict the future trend of the data using a non-symmetricalinterpolating scheme, A one-step prediction algorithm is presented to predict the future evolutiontrend with historical data. The proposed method obtained a desirable effect in peak-to-peak valuetrend analysis for a machine set in an oil refinery.展开更多
Ensuring digital media security through robust image watermarking is essential to prevent unauthorized distribution,tampering,and copyright infringement.This study introduces a novel hybrid watermarking framework that...Ensuring digital media security through robust image watermarking is essential to prevent unauthorized distribution,tampering,and copyright infringement.This study introduces a novel hybrid watermarking framework that integrates Discrete Wavelet Transform(DWT),Redundant Discrete Wavelet Transform(RDWT),and Möbius Transformations(MT),with optimization of transformation parameters achieved via a Genetic Algorithm(GA).By combining frequency and spatial domain techniques,the proposed method significantly enhances both the imper-ceptibility and robustness of watermark embedding.The approach leverages DWT and RDWT for multi-resolution decomposition,enabling watermark insertion in frequency subbands that balance visibility and resistance to attacks.RDWT,in particular,offers shift-invariance,which improves performance under geometric transformations.Möbius transformations are employed for spatial manipulation,providing conformal mapping and spatial dispersion that fortify watermark resilience against rotation,scaling,and translation.The GA dynamically optimizes the Möbius parameters,selecting configurations that maximize robustness metrics such as Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Index Measure(SSIM),Bit Error Rate(BER),and Normalized Cross-Correlation(NCC).Extensive experiments conducted on medical and standard benchmark images demonstrate the efficacy of the proposed RDWT-MT scheme.Results show that PSNR exceeds 68 dB,SSIM approaches 1.0,and BER remains at 0.0000,indicating excellent imperceptibility and perfect watermark recovery.Moreover,the method exhibits exceptional resilience to a wide range of image processing attacks,including Gaussian noise,JPEG compression,histogram equalization,and cropping,achieving NCC values close to or equal to 1.0.Comparative evaluations with state-of-the-art watermarking techniques highlight the superiority of the proposed method in terms of robustness,fidelity,and computational efficiency.The hybrid framework ensures secure,adaptive watermark embedding,making it highly suitable for applications in digital rights management,content authentication,and medical image protection.The integration of spatial and frequency domain features with evolutionary optimization presents a promising direction for future watermarking technologies.展开更多
Image watermarking is a powerful tool for media protection and can provide promising results when combined with other defense mechanisms.Image watermarking can be used to protect the copyright of digital media by embe...Image watermarking is a powerful tool for media protection and can provide promising results when combined with other defense mechanisms.Image watermarking can be used to protect the copyright of digital media by embedding a unique identifier that identifies the owner of the content.Image watermarking can also be used to verify the authenticity of digital media,such as images or videos,by ascertaining the watermark information.In this paper,a mathematical chaos-based image watermarking technique is proposed using discrete wavelet transform(DWT),chaotic map,and Laplacian operator.The DWT can be used to decompose the image into its frequency components,chaos is used to provide extra security defense by encrypting the watermark signal,and the Laplacian operator with optimization is applied to the mid-frequency bands to find the sharp areas in the image.These mid-frequency bands are used to embed the watermarks by modifying the coefficients in these bands.The mid-sub-band maintains the invisible property of the watermark,and chaos combined with the second-order derivative Laplacian is vulnerable to attacks.Comprehensive experiments demonstrate that this approach is effective for common signal processing attacks,i.e.,compression,noise addition,and filtering.Moreover,this approach also maintains image quality through peak signal-to-noise ratio(PSNR)and structural similarity index metrics(SSIM).The highest achieved PSNR and SSIM values are 55.4 dB and 1.In the same way,normalized correlation(NC)values are almost 10%–20%higher than comparative research.These results support assistance in copyright protection in multimedia content.展开更多
EEG signals are widely used in emotion recognition due to their ability to reflect involuntary physiological responses.However,the high dimensionality of EEG signals and their continuous variability in the time-freque...EEG signals are widely used in emotion recognition due to their ability to reflect involuntary physiological responses.However,the high dimensionality of EEG signals and their continuous variability in the time-frequency plane make their analysis challenging.Therefore,advanced deep learning methods are needed to extract meaningful features and improve classification performance.This study proposes a hybrid model that integrates the Swin Transformer and Temporal Convolutional Network(TCN)mechanisms for EEG-based emotion recognition.EEG signals are first converted into scalogram images using Continuous Wavelet Transform(CWT),and classification is performed on these images.Swin Transformer is used to extract spatial features in scalogram images,and the TCN method is used to learn long-term dependencies.In addition,attention mechanisms are integrated to highlight the essential features extracted from both models.The effectiveness of the proposed model has been tested on the SEED dataset,widely used in the field of emotion recognition,and it has consistently achieved high performance across all emotional classes,with accuracy,precision,recall,and F1-score values of 97.53%,97.54%,97.53%,and 97.54%,respectively.Compared to traditional transfer learning models,the proposed approach achieved an accuracy increase of 1.43%over ResNet-101,1.81%over DenseNet-201,and 2.44%over VGG-19.In addition,the proposed model outperformed many recent CNN,RNN,and Transformer-based methods reported in the literature.展开更多
Future 6G communications will open up opportunities for innovative applications,including Cyber-Physical Systems,edge computing,supporting Industry 5.0,and digital agriculture.While automation is creating efficiencies...Future 6G communications will open up opportunities for innovative applications,including Cyber-Physical Systems,edge computing,supporting Industry 5.0,and digital agriculture.While automation is creating efficiencies,it can also create new cyber threats,such as vulnerabilities in trust and malicious node injection.Denialof-Service(DoS)attacks can stop many forms of operations by overwhelming networks and systems with data noise.Current anomaly detection methods require extensive software changes and only detect static threats.Data collection is important for being accurate,but it is often a slow,tedious,and sometimes inefficient process.This paper proposes a new wavelet transformassisted Bayesian deep learning based probabilistic(WT-BDLP)approach tomitigate malicious data injection attacks in 6G edge networks.The proposed approach combines outlier detection based on a Bayesian learning conditional variational autoencoder(Bay-LCVariAE)and traffic pattern analysis based on continuous wavelet transform(CWT).The Bay-LCVariAE framework allows for probabilistic modelling of generative features to facilitate capturing how features of interest change over time,spatially,and for recognition of anomalies.Similarly,CWT allows emphasizing the multi-resolution spectral analysis and permits temporally relevant frequency pattern recognition.Experimental testing showed that the flexibility of the Bayesian probabilistic framework offers a vast improvement in anomaly detection accuracy over existing methods,with a maximum accuracy of 98.21%recognizing anomalies.展开更多
Imaging sonar devices generate sonar images by receiving echoes from objects,which are often accompanied by severe speckle noise,resulting in image distortion and information loss.Common optical denoising methods do n...Imaging sonar devices generate sonar images by receiving echoes from objects,which are often accompanied by severe speckle noise,resulting in image distortion and information loss.Common optical denoising methods do not work well in removing speckle noise from sonar images and may even reduce their visual quality.To address this issue,a sonar image denoising method based on fuzzy clustering and the undecimated dual-tree complex wavelet transform is proposed.This method provides a perfect translation invariance and an improved directional selectivity during image decomposition,leading to richer representation of noise and edges in high frequency coefficients.Fuzzy clustering can separate noise from useful information according to the amplitude characteristics of speckle noise,preserving the latter and achieving the goal of noise removal.Additionally,the low frequency coefficients are smoothed using bilateral filtering to improve the visual quality of the image.To verify the effectiveness of the algorithm,multiple groups of ablation experiments were conducted,and speckle sonar images with different variances were evaluated and compared with existing speckle removal methods in the transform domain.The experimental results show that the proposed method can effectively improve image quality,especially in cases of severe noise,where it still achieves a good denoising performance.展开更多
Wind power generation is subjected to complex and variable meteorological conditions,resulting in intermittent and volatile power generation.Accurate wind power prediction plays a crucial role in enabling the power gr...Wind power generation is subjected to complex and variable meteorological conditions,resulting in intermittent and volatile power generation.Accurate wind power prediction plays a crucial role in enabling the power grid dispatching departments to rationally plan power transmission and energy storage operations.This enhances the efficiency of wind power integration into the grid.It allows grid operators to anticipate and mitigate the impact of wind power fluctuations,significantly improving the resilience of wind farms and the overall power grid.Furthermore,it assists wind farm operators in optimizing the management of power generation facilities and reducing maintenance costs.Despite these benefits,accurate wind power prediction especially in extreme scenarios remains a significant challenge.To address this issue,a novel wind power prediction model based on learning approach is proposed by integrating wavelet transform and Transformer.First,a conditional generative adversarial network(CGAN)generates dynamic extreme scenarios guided by physical constraints and expert rules to ensure realism and capture critical features of wind power fluctuations under extremeconditions.Next,thewavelet transformconvolutional layer is applied to enhance sensitivity to frequency domain characteristics,enabling effective feature extraction fromextreme scenarios for a deeper understanding of input data.The model then leverages the Transformer’s self-attention mechanism to capture global dependencies between features,strengthening its sequence modelling capabilities.Case analyses verify themodel’s superior performance in extreme scenario prediction by effectively capturing local fluctuation featureswhile maintaining a grasp of global trends.Compared to other models,it achieves R-squared(R^(2))as high as 0.95,and the mean absolute error(MAE)and rootmean square error(RMSE)are also significantly lower than those of othermodels,proving its high accuracy and effectiveness in managing complex wind power generation conditions.展开更多
Sparse representation has been highly successful in various tasks related to image processing and computer vision.For ancient mural image inpainting,traditional group sparse representation models usually lead to struc...Sparse representation has been highly successful in various tasks related to image processing and computer vision.For ancient mural image inpainting,traditional group sparse representation models usually lead to structure blur and line discontinuity due to the construction of similarity group solely based on the Euclidean distance and the randomness of dictionary initialization.To address the aforementioned issues,an improved curvature Gabor transform and group sparse representation(CGabor-GSR)model for ancient Dunhuang mural inpainting is proposed.To begin with,mutual information is introduced to weight the Euclidean distance,and then the weighted Euclidean distance acts as a new standard of similarity group.Subsequently,to mitigate the randomness of dictionary initialization,a curvature Gabor wavelet transform is proposed to extract the features and initialize the feature dictionary with dimension reduction based on principal component analysis(PCA).Ultimately,singular value decomposition(SVD)and split Bregman iteration(SBI)can be used to resolve the CGabor-GSR model to reconstruct the mural images.Experimental results on Dunhuang mural inpainting demonstrate tha the proposed CGabor-GSR achieves a better performance than compared algorithms in both objective and visual evaluation.展开更多
In the vision transformer(ViT)architecture,image data are transformed into sequential data for processing,which may result in the loss of spatial positional information.While the self-attention mechanism enhances the ...In the vision transformer(ViT)architecture,image data are transformed into sequential data for processing,which may result in the loss of spatial positional information.While the self-attention mechanism enhances the capacity of ViT to capture global features,it compromises the preservation of fine-grained local feature information.To address these challenges,we propose a spatial positional enhancement module and a wavelet transform enhancement module tailored for ViT models.These modules aim to reduce spatial positional information loss during the patch embedding process and enhance the model’s feature extraction capabilities.The spatial positional enhancement module reinforces spatial information in sequential data through convolutional operations and multi-scale feature extraction.Meanwhile,the wavelet transform enhancement module utilizes the multi-scale analysis and frequency decomposition to improve the ViT’s understanding of global and local image structures.This enhancement also improves the ViT’s ability to process complex structures and intricate image details.Experiments on CIFAR-10,CIFAR-100 and ImageNet-1k datasets are done to compare the proposed method with advanced classification methods.The results show that the proposed model achieves a higher classification accuracy,confirming its effectiveness and competitive advantage.展开更多
Cardiovascular diseases are the world’s leading cause of death;therefore cardiac health of the human heart has been a fascinating topic for decades.The electrocardiogram(ECG)signal is a comprehensive non-invasive met...Cardiovascular diseases are the world’s leading cause of death;therefore cardiac health of the human heart has been a fascinating topic for decades.The electrocardiogram(ECG)signal is a comprehensive non-invasive method for determining cardiac health.Various health practitioners use the ECG signal to ascertain critical information about the human heart.In this article,swarm intelligence approaches are used in the biomedical signal processing sector to enhance adaptive hybrid filters and empirical wavelet transforms(EWTs).At first,the white Gaussian noise is added to the input ECG signal and then applied to the EWT.The ECG signals are denoised by the proposed adaptive hybrid filter.The honey badge optimization(HBO)algorithm is utilized to optimize the EWT window function and adaptive hybrid filter weight parameters.The proposed approach is simulated by MATLAB 2018a using the MIT-BIH dataset with white Gaussian,electromyogram and electrode motion artifact noises.A comparison of the HBO approach with recursive least square-based adaptive filter,multichannel least means square,and discrete wavelet transform methods has been done in order to show the efficiency of the proposed adaptive hybrid filter.The experimental results show that the HBO approach supported by EWT and adaptive hybrid filter can be employed efficiently for cardiovascular signal denoising.展开更多
Stratigraphic correlations are essential for the fine-scale characterization of reservoirs.However,conventional data-driven methods that rely solely on log data struggle to construct isochronous stratigraphic framewor...Stratigraphic correlations are essential for the fine-scale characterization of reservoirs.However,conventional data-driven methods that rely solely on log data struggle to construct isochronous stratigraphic frameworks for complex sedimentary environments and multi-source geological settings.In response,this study proposed an intelligent,automatic,log-seismic integrated stratigraphic correlation method that incorporates wavelet frequency-division transform(WFT)and dynamic time warping(DTW)(also referred to as the WFT-DTW method).This approach integrates seismic data as constraints into stratigraphic correlations,enabling accurate tracking of the seismic marker horizons through WFT.Under the constraints of framework construction,a DTW algorithm was introduced to correlate sublayer boundaries automatically.The effectiveness of the proposed method was verified through a stratigraphic correlation experiment on the SA0 Formation of the Xingshugang block in the Lasaxing oilfield,the Songliao Basin,China.In this block,the target layer exhibits sublayer thicknesses ranging from 5 m to 8 m,an average sandstone thickness of 2.1 m,and pronounced heterogeneity.The verification using 1760 layers in 160 post-test wells indicates that the WFT-DTW method intelligently compared sublayers in zones with underdeveloped faults and distinct marker horizons.As a result,the posterior correlation of 1682 layers was performed,with a coincidence rate of up to 95.6%.The proposed method can complement manual correlation efforts while also providing valuable technical support for the lithologic and sand body characterization of reservoirs.展开更多
This paper discusses the principle and procedures of the second-generation wavelet transform and its application to the denoising of seismic data. Based on lifting steps, it is a flexible wavelet construction method u...This paper discusses the principle and procedures of the second-generation wavelet transform and its application to the denoising of seismic data. Based on lifting steps, it is a flexible wavelet construction method using linear and nonlinear spatial prediction and operators to implement the wavelet transform and to make it reversible. The lifting scheme transform -includes three steps： split, predict, and update. Deslauriers-Dubuc （4, 2） wavelet transforms are used to process both synthetic and real data in our second-generation wavelet transform. The processing results show that random noise is effectively suppressed and the signal to noise ratio improves remarkably. The lifting wavelet transform is an efficient algorithm.展开更多
Decomposition and reconstruction of Mallat fast wavelet transformation （WT） is described. A fast algorithm, which can greatly decrease the processing burden and can be very easy for hardware implementation in real-t...Decomposition and reconstruction of Mallat fast wavelet transformation （WT） is described. A fast algorithm, which can greatly decrease the processing burden and can be very easy for hardware implementation in real-time, is analyzed. The algorithm will no longer have the processing of decimation and interpolation of usual WT. The formulae of the decomposition and the reconstruction are given. Simulation results of the MEMS （micro-electro mechanical systems） gyroscope drift signal show that the algorithm spends much less processing time to finish the de-noising process than the usual WT. And the de-noising effect is the same. The fast algorithm has been implemented in a TMS320C6713 digital signal processor. The standard variance of the gyroscope static drift signal decreases from 78. 435 5 （°）/h to 36. 763 5 （°）/h. It takes 0. 014 ms to process all input data and can meet the real-time analysis of signal.展开更多
Combining wavelet transforms with conventional log differential curves is used to identify fractured sections is a new idea.In this paper,we first compute the mother wavelet transform of conventional logs and the wave...Combining wavelet transforms with conventional log differential curves is used to identify fractured sections is a new idea.In this paper,we first compute the mother wavelet transform of conventional logs and the wavelet decomposed signals are compared with fractures identified from image logs to determine the fracture-matched mother wavelet.Then the mother wavelet-based decomposed signal combined with the differential curves of conventional well logs create a fracture indicator curve,identifying the fractured zone.Finally the fracture density can be precisely evaluated by the linear relationship of the indicator curve and image log fracture density.This method has been successfully used to evaluate igneous reservoir fractures in the southern Songnan basin and the calculated density from the indicator curve and density from image logs are both basically consistent.展开更多
In view of the feature of flight flutter test data with atmospheric turbulence excitation, a method which combines wavelet transformation with random decrement technique for identifying flight flutter modal parameters...In view of the feature of flight flutter test data with atmospheric turbulence excitation, a method which combines wavelet transformation with random decrement technique for identifying flight flutter modal parameters is presented. This approach firstly uses random decrement technique to gain free decays corresponding to the acceleration response of the structure to some non-zero initial conditions. Then the continuous Morlet wavelet transformation of the free decays is performed; and the Parseval formula and residue theorem are used to simplify the transformation. The maximal wavelet transformation coefficients in different scales are searched out by means of band-filtering characteristic of Morlet wavelet, and then the modal parameters are identified according to the relationships with maximal modulus and angle of the wavelet transform. In addition, the condition of modal uncoupling is discussed according to variation trend of flight flutter modal parameters in the flight flutter state. The analysis results of simulation and flight flutter test data show that this approach is not only simple, effective and feasible, but also having good noise immunity.展开更多
In this paper performances of wavelet transform domain (WTD) adaptive equalizers based on the least mean￣square (LMS) algorithm are analyzed. The optimum Wiener solution, the condition of convergence, the minimum ...In this paper performances of wavelet transform domain (WTD) adaptive equalizers based on the least mean￣square (LMS) algorithm are analyzed. The optimum Wiener solution, the condition of convergence, the minimum mean square error (MSE) and the steady state excess MSE of the WTD adaptive equalizer are obtained. Constant and time varying convergence factor adaptive algorithms are studied respectively. Computational complexities of WTD LMS equalizers are given. The equalizer in WTD shows much better convergence performance than that of the conventional in time domain.展开更多
文摘The aim of this study is to carry out hydrothermal alteration mapping and structural mapping using ASTER images in order to identify indices that could guide mining exploration work in the Poli area and its surroundings. To achieve this, the ASTER images were first preprocessed to correct atmospheric effects and remove vegetation influence. Secondly, a lineament mapping was conducted by applying Discrete Wavelet Transform (DWT) algorithms to the First Principal Component Analysis (PCA1) of Visible Near-Infrared (VNIR) and Shortwave Infrared (SWIR) bands. Lastly, band ratio methods were applied to the VNIR, SWIR, and Thermal Infrared (TIR) bands to determine indices of iron oxides/hydroxides (hematite and limonite), hydroxyl-bearing minerals (chlorite, epidote, and muscovite), and the quartz index. The results obtained showed that the lineaments were mainly oriented NE-SW, ENE-WSW, and E-W, with NE-SW being the most predominant direction. Concerning hydrothermal alteration, the identified indices covered almost the entire study area and showed a strong correlation with lithological data. Overlaying the obtained lineaments with the hydrothermal alteration indices revealed a significant correlation between existing mining indices and those observed in the field. Mineralized zones generally coincided with areas of high lineament density exhibiting significant hydrothermal alteration. Based on the correlation between existing mining indices and the results of hydrothermal and structural mapping, the results obtained can then be used as a reference document for any mining exploration in the study area.
文摘This paper describes a novel wavelet-based approach to the detection of abrupt fault of Rotorcrafi Unmanned Aerial Vehicle （RUAV） sensor system. By use of wavelet transforms that accurately localize the characteristics of a signal both in the time and frequency domains, the occurring instants of abnormal status of a sensor in the output signal can be identified by the multi-scale representation of the signal. Once the instants are detected, the distribution differences of the signal energy on all decomposed wavelet scales of the signal before and after the instants are used to claim and classify the sensor faults.
基金Supported by the Foundation of the National Natural Science of China( No.1 0 0 71 0 39) and the Foundation of Edu-cation Commission of Jiangsu Province
文摘Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.
基金supported by the Startup Research Fund for Introducing Talents of Anhui Polytechnic University (Grant No. 2009YQQ006)the Research Foundation of the Education Department of Anhui Province of China (Grant No. KJ2011B031)
文摘In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state itself vary from ｜ψ〉 to Ftr, s ｜ψ〉, except for variation within the family of dilations and translations. The Parseval＇s equality, admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed. By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform, we obtain some mother wavelets. A comparison between the newly found mother wavelets is presented.
文摘In order to make trend analysis and prediction to acquisition data in amechanical equipment condition monitoring system, a new method of trend feature extraction andprediction of acquisition data is proposed which constructs an adaptive wavelet on the acquisitiondata by means of second generation wavelet transform ( SGWT), Firstly, taking the vanishing momentnumber of the predictor as a constraint, the linear predictor and updater are designed according tothe acquisition data by using symmetrical interpolating scheme. Then the trend of the data isobtained through doing SGWT decomposition , threshold processing and SGWT reconstruction. Secondly,under the constraint of the vanishing moment number of the predictor, another predictor based on theacquisition data is devised to predict the future trend of the data using a non-symmetricalinterpolating scheme, A one-step prediction algorithm is presented to predict the future evolutiontrend with historical data. The proposed method obtained a desirable effect in peak-to-peak valuetrend analysis for a machine set in an oil refinery.
文摘Ensuring digital media security through robust image watermarking is essential to prevent unauthorized distribution,tampering,and copyright infringement.This study introduces a novel hybrid watermarking framework that integrates Discrete Wavelet Transform(DWT),Redundant Discrete Wavelet Transform(RDWT),and Möbius Transformations(MT),with optimization of transformation parameters achieved via a Genetic Algorithm(GA).By combining frequency and spatial domain techniques,the proposed method significantly enhances both the imper-ceptibility and robustness of watermark embedding.The approach leverages DWT and RDWT for multi-resolution decomposition,enabling watermark insertion in frequency subbands that balance visibility and resistance to attacks.RDWT,in particular,offers shift-invariance,which improves performance under geometric transformations.Möbius transformations are employed for spatial manipulation,providing conformal mapping and spatial dispersion that fortify watermark resilience against rotation,scaling,and translation.The GA dynamically optimizes the Möbius parameters,selecting configurations that maximize robustness metrics such as Peak Signal-to-Noise Ratio(PSNR),Structural Similarity Index Measure(SSIM),Bit Error Rate(BER),and Normalized Cross-Correlation(NCC).Extensive experiments conducted on medical and standard benchmark images demonstrate the efficacy of the proposed RDWT-MT scheme.Results show that PSNR exceeds 68 dB,SSIM approaches 1.0,and BER remains at 0.0000,indicating excellent imperceptibility and perfect watermark recovery.Moreover,the method exhibits exceptional resilience to a wide range of image processing attacks,including Gaussian noise,JPEG compression,histogram equalization,and cropping,achieving NCC values close to or equal to 1.0.Comparative evaluations with state-of-the-art watermarking techniques highlight the superiority of the proposed method in terms of robustness,fidelity,and computational efficiency.The hybrid framework ensures secure,adaptive watermark embedding,making it highly suitable for applications in digital rights management,content authentication,and medical image protection.The integration of spatial and frequency domain features with evolutionary optimization presents a promising direction for future watermarking technologies.
基金supported by the researcher supporting Project number(RSPD2025R636),King Saud University,Riyadh,Saudi Arabia.
文摘Image watermarking is a powerful tool for media protection and can provide promising results when combined with other defense mechanisms.Image watermarking can be used to protect the copyright of digital media by embedding a unique identifier that identifies the owner of the content.Image watermarking can also be used to verify the authenticity of digital media,such as images or videos,by ascertaining the watermark information.In this paper,a mathematical chaos-based image watermarking technique is proposed using discrete wavelet transform(DWT),chaotic map,and Laplacian operator.The DWT can be used to decompose the image into its frequency components,chaos is used to provide extra security defense by encrypting the watermark signal,and the Laplacian operator with optimization is applied to the mid-frequency bands to find the sharp areas in the image.These mid-frequency bands are used to embed the watermarks by modifying the coefficients in these bands.The mid-sub-band maintains the invisible property of the watermark,and chaos combined with the second-order derivative Laplacian is vulnerable to attacks.Comprehensive experiments demonstrate that this approach is effective for common signal processing attacks,i.e.,compression,noise addition,and filtering.Moreover,this approach also maintains image quality through peak signal-to-noise ratio(PSNR)and structural similarity index metrics(SSIM).The highest achieved PSNR and SSIM values are 55.4 dB and 1.In the same way,normalized correlation(NC)values are almost 10%–20%higher than comparative research.These results support assistance in copyright protection in multimedia content.
文摘EEG signals are widely used in emotion recognition due to their ability to reflect involuntary physiological responses.However,the high dimensionality of EEG signals and their continuous variability in the time-frequency plane make their analysis challenging.Therefore,advanced deep learning methods are needed to extract meaningful features and improve classification performance.This study proposes a hybrid model that integrates the Swin Transformer and Temporal Convolutional Network(TCN)mechanisms for EEG-based emotion recognition.EEG signals are first converted into scalogram images using Continuous Wavelet Transform(CWT),and classification is performed on these images.Swin Transformer is used to extract spatial features in scalogram images,and the TCN method is used to learn long-term dependencies.In addition,attention mechanisms are integrated to highlight the essential features extracted from both models.The effectiveness of the proposed model has been tested on the SEED dataset,widely used in the field of emotion recognition,and it has consistently achieved high performance across all emotional classes,with accuracy,precision,recall,and F1-score values of 97.53%,97.54%,97.53%,and 97.54%,respectively.Compared to traditional transfer learning models,the proposed approach achieved an accuracy increase of 1.43%over ResNet-101,1.81%over DenseNet-201,and 2.44%over VGG-19.In addition,the proposed model outperformed many recent CNN,RNN,and Transformer-based methods reported in the literature.
文摘Future 6G communications will open up opportunities for innovative applications,including Cyber-Physical Systems,edge computing,supporting Industry 5.0,and digital agriculture.While automation is creating efficiencies,it can also create new cyber threats,such as vulnerabilities in trust and malicious node injection.Denialof-Service(DoS)attacks can stop many forms of operations by overwhelming networks and systems with data noise.Current anomaly detection methods require extensive software changes and only detect static threats.Data collection is important for being accurate,but it is often a slow,tedious,and sometimes inefficient process.This paper proposes a new wavelet transformassisted Bayesian deep learning based probabilistic(WT-BDLP)approach tomitigate malicious data injection attacks in 6G edge networks.The proposed approach combines outlier detection based on a Bayesian learning conditional variational autoencoder(Bay-LCVariAE)and traffic pattern analysis based on continuous wavelet transform(CWT).The Bay-LCVariAE framework allows for probabilistic modelling of generative features to facilitate capturing how features of interest change over time,spatially,and for recognition of anomalies.Similarly,CWT allows emphasizing the multi-resolution spectral analysis and permits temporally relevant frequency pattern recognition.Experimental testing showed that the flexibility of the Bayesian probabilistic framework offers a vast improvement in anomaly detection accuracy over existing methods,with a maximum accuracy of 98.21%recognizing anomalies.
基金the National Natural Science Foundation of China(No.62065001)the Yunnan Young and Middle-aged Academic and Technical Leaders Reserve Talent Project(No.202205AC160001)+1 种基金the Science and Technology Programs of Yunnan Provincial Science and Technology Department(No.202101BA070001-054)the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities Association(No.2019FH001(-066))。
文摘Imaging sonar devices generate sonar images by receiving echoes from objects,which are often accompanied by severe speckle noise,resulting in image distortion and information loss.Common optical denoising methods do not work well in removing speckle noise from sonar images and may even reduce their visual quality.To address this issue,a sonar image denoising method based on fuzzy clustering and the undecimated dual-tree complex wavelet transform is proposed.This method provides a perfect translation invariance and an improved directional selectivity during image decomposition,leading to richer representation of noise and edges in high frequency coefficients.Fuzzy clustering can separate noise from useful information according to the amplitude characteristics of speckle noise,preserving the latter and achieving the goal of noise removal.Additionally,the low frequency coefficients are smoothed using bilateral filtering to improve the visual quality of the image.To verify the effectiveness of the algorithm,multiple groups of ablation experiments were conducted,and speckle sonar images with different variances were evaluated and compared with existing speckle removal methods in the transform domain.The experimental results show that the proposed method can effectively improve image quality,especially in cases of severe noise,where it still achieves a good denoising performance.
基金funded by the Science and Technology Project of State Grid Corporation of China under Grant No.5108-202218280A-2-299-XG.
文摘Wind power generation is subjected to complex and variable meteorological conditions,resulting in intermittent and volatile power generation.Accurate wind power prediction plays a crucial role in enabling the power grid dispatching departments to rationally plan power transmission and energy storage operations.This enhances the efficiency of wind power integration into the grid.It allows grid operators to anticipate and mitigate the impact of wind power fluctuations,significantly improving the resilience of wind farms and the overall power grid.Furthermore,it assists wind farm operators in optimizing the management of power generation facilities and reducing maintenance costs.Despite these benefits,accurate wind power prediction especially in extreme scenarios remains a significant challenge.To address this issue,a novel wind power prediction model based on learning approach is proposed by integrating wavelet transform and Transformer.First,a conditional generative adversarial network(CGAN)generates dynamic extreme scenarios guided by physical constraints and expert rules to ensure realism and capture critical features of wind power fluctuations under extremeconditions.Next,thewavelet transformconvolutional layer is applied to enhance sensitivity to frequency domain characteristics,enabling effective feature extraction fromextreme scenarios for a deeper understanding of input data.The model then leverages the Transformer’s self-attention mechanism to capture global dependencies between features,strengthening its sequence modelling capabilities.Case analyses verify themodel’s superior performance in extreme scenario prediction by effectively capturing local fluctuation featureswhile maintaining a grasp of global trends.Compared to other models,it achieves R-squared(R^(2))as high as 0.95,and the mean absolute error(MAE)and rootmean square error(RMSE)are also significantly lower than those of othermodels,proving its high accuracy and effectiveness in managing complex wind power generation conditions.
基金supported by National Natural Science Foundation of China(No.61963023)Humanities and Social Sciences Youth Foundation of Ministry of Education(No.19YJC760012)Lanzhou Jiaotong University Basic Top-Notch Personnel Project(No.2022JC36).
文摘Sparse representation has been highly successful in various tasks related to image processing and computer vision.For ancient mural image inpainting,traditional group sparse representation models usually lead to structure blur and line discontinuity due to the construction of similarity group solely based on the Euclidean distance and the randomness of dictionary initialization.To address the aforementioned issues,an improved curvature Gabor transform and group sparse representation(CGabor-GSR)model for ancient Dunhuang mural inpainting is proposed.To begin with,mutual information is introduced to weight the Euclidean distance,and then the weighted Euclidean distance acts as a new standard of similarity group.Subsequently,to mitigate the randomness of dictionary initialization,a curvature Gabor wavelet transform is proposed to extract the features and initialize the feature dictionary with dimension reduction based on principal component analysis(PCA).Ultimately,singular value decomposition(SVD)and split Bregman iteration(SBI)can be used to resolve the CGabor-GSR model to reconstruct the mural images.Experimental results on Dunhuang mural inpainting demonstrate tha the proposed CGabor-GSR achieves a better performance than compared algorithms in both objective and visual evaluation.
基金National Natural Science Foundation of China(No.62176052)。
文摘In the vision transformer(ViT)architecture,image data are transformed into sequential data for processing,which may result in the loss of spatial positional information.While the self-attention mechanism enhances the capacity of ViT to capture global features,it compromises the preservation of fine-grained local feature information.To address these challenges,we propose a spatial positional enhancement module and a wavelet transform enhancement module tailored for ViT models.These modules aim to reduce spatial positional information loss during the patch embedding process and enhance the model’s feature extraction capabilities.The spatial positional enhancement module reinforces spatial information in sequential data through convolutional operations and multi-scale feature extraction.Meanwhile,the wavelet transform enhancement module utilizes the multi-scale analysis and frequency decomposition to improve the ViT’s understanding of global and local image structures.This enhancement also improves the ViT’s ability to process complex structures and intricate image details.Experiments on CIFAR-10,CIFAR-100 and ImageNet-1k datasets are done to compare the proposed method with advanced classification methods.The results show that the proposed model achieves a higher classification accuracy,confirming its effectiveness and competitive advantage.
文摘Cardiovascular diseases are the world’s leading cause of death;therefore cardiac health of the human heart has been a fascinating topic for decades.The electrocardiogram(ECG)signal is a comprehensive non-invasive method for determining cardiac health.Various health practitioners use the ECG signal to ascertain critical information about the human heart.In this article,swarm intelligence approaches are used in the biomedical signal processing sector to enhance adaptive hybrid filters and empirical wavelet transforms(EWTs).At first,the white Gaussian noise is added to the input ECG signal and then applied to the EWT.The ECG signals are denoised by the proposed adaptive hybrid filter.The honey badge optimization(HBO)algorithm is utilized to optimize the EWT window function and adaptive hybrid filter weight parameters.The proposed approach is simulated by MATLAB 2018a using the MIT-BIH dataset with white Gaussian,electromyogram and electrode motion artifact noises.A comparison of the HBO approach with recursive least square-based adaptive filter,multichannel least means square,and discrete wavelet transform methods has been done in order to show the efficiency of the proposed adaptive hybrid filter.The experimental results show that the HBO approach supported by EWT and adaptive hybrid filter can be employed efficiently for cardiovascular signal denoising.
基金funded by the Major Science and Technology Project of China National Petroleum Corporation(No.2023ZZ22YJ01).
文摘Stratigraphic correlations are essential for the fine-scale characterization of reservoirs.However,conventional data-driven methods that rely solely on log data struggle to construct isochronous stratigraphic frameworks for complex sedimentary environments and multi-source geological settings.In response,this study proposed an intelligent,automatic,log-seismic integrated stratigraphic correlation method that incorporates wavelet frequency-division transform(WFT)and dynamic time warping(DTW)(also referred to as the WFT-DTW method).This approach integrates seismic data as constraints into stratigraphic correlations,enabling accurate tracking of the seismic marker horizons through WFT.Under the constraints of framework construction,a DTW algorithm was introduced to correlate sublayer boundaries automatically.The effectiveness of the proposed method was verified through a stratigraphic correlation experiment on the SA0 Formation of the Xingshugang block in the Lasaxing oilfield,the Songliao Basin,China.In this block,the target layer exhibits sublayer thicknesses ranging from 5 m to 8 m,an average sandstone thickness of 2.1 m,and pronounced heterogeneity.The verification using 1760 layers in 160 post-test wells indicates that the WFT-DTW method intelligently compared sublayers in zones with underdeveloped faults and distinct marker horizons.As a result,the posterior correlation of 1682 layers was performed,with a coincidence rate of up to 95.6%.The proposed method can complement manual correlation efforts while also providing valuable technical support for the lithologic and sand body characterization of reservoirs.
文摘This paper discusses the principle and procedures of the second-generation wavelet transform and its application to the denoising of seismic data. Based on lifting steps, it is a flexible wavelet construction method using linear and nonlinear spatial prediction and operators to implement the wavelet transform and to make it reversible. The lifting scheme transform -includes three steps： split, predict, and update. Deslauriers-Dubuc （4, 2） wavelet transforms are used to process both synthetic and real data in our second-generation wavelet transform. The processing results show that random noise is effectively suppressed and the signal to noise ratio improves remarkably. The lifting wavelet transform is an efficient algorithm.
基金The National High Technology Research and Devel-opment Program of China (863Program) (No2002AA812038)
文摘Decomposition and reconstruction of Mallat fast wavelet transformation （WT） is described. A fast algorithm, which can greatly decrease the processing burden and can be very easy for hardware implementation in real-time, is analyzed. The algorithm will no longer have the processing of decimation and interpolation of usual WT. The formulae of the decomposition and the reconstruction are given. Simulation results of the MEMS （micro-electro mechanical systems） gyroscope drift signal show that the algorithm spends much less processing time to finish the de-noising process than the usual WT. And the de-noising effect is the same. The fast algorithm has been implemented in a TMS320C6713 digital signal processor. The standard variance of the gyroscope static drift signal decreases from 78. 435 5 （°）/h to 36. 763 5 （°）/h. It takes 0. 014 ms to process all input data and can meet the real-time analysis of signal.
基金sponsored by National Science and Technology Major Project of China (No. 2008 ZX 05009-001)
文摘Combining wavelet transforms with conventional log differential curves is used to identify fractured sections is a new idea.In this paper,we first compute the mother wavelet transform of conventional logs and the wavelet decomposed signals are compared with fractures identified from image logs to determine the fracture-matched mother wavelet.Then the mother wavelet-based decomposed signal combined with the differential curves of conventional well logs create a fracture indicator curve,identifying the fractured zone.Finally the fracture density can be precisely evaluated by the linear relationship of the indicator curve and image log fracture density.This method has been successfully used to evaluate igneous reservoir fractures in the southern Songnan basin and the calculated density from the indicator curve and density from image logs are both basically consistent.
基金National Natural Science Foundation of China(60134010)
文摘In view of the feature of flight flutter test data with atmospheric turbulence excitation, a method which combines wavelet transformation with random decrement technique for identifying flight flutter modal parameters is presented. This approach firstly uses random decrement technique to gain free decays corresponding to the acceleration response of the structure to some non-zero initial conditions. Then the continuous Morlet wavelet transformation of the free decays is performed; and the Parseval formula and residue theorem are used to simplify the transformation. The maximal wavelet transformation coefficients in different scales are searched out by means of band-filtering characteristic of Morlet wavelet, and then the modal parameters are identified according to the relationships with maximal modulus and angle of the wavelet transform. In addition, the condition of modal uncoupling is discussed according to variation trend of flight flutter modal parameters in the flight flutter state. The analysis results of simulation and flight flutter test data show that this approach is not only simple, effective and feasible, but also having good noise immunity.
文摘In this paper performances of wavelet transform domain (WTD) adaptive equalizers based on the least mean￣square (LMS) algorithm are analyzed. The optimum Wiener solution, the condition of convergence, the minimum mean square error (MSE) and the steady state excess MSE of the WTD adaptive equalizer are obtained. Constant and time varying convergence factor adaptive algorithms are studied respectively. Computational complexities of WTD LMS equalizers are given. The equalizer in WTD shows much better convergence performance than that of the conventional in time domain.
