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Occluded Gait Emotion Recognition Based on Multi-Scale Suppression Graph Convolutional Network
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作者 Yuxiang Zou Ning He +2 位作者 Jiwu Sun Xunrui Huang Wenhua Wang 《Computers, Materials & Continua》 SCIE EI 2025年第1期1255-1276,共22页
In recent years,gait-based emotion recognition has been widely applied in the field of computer vision.However,existing gait emotion recognition methods typically rely on complete human skeleton data,and their accurac... In recent years,gait-based emotion recognition has been widely applied in the field of computer vision.However,existing gait emotion recognition methods typically rely on complete human skeleton data,and their accuracy significantly declines when the data is occluded.To enhance the accuracy of gait emotion recognition under occlusion,this paper proposes a Multi-scale Suppression Graph ConvolutionalNetwork(MS-GCN).TheMS-GCN consists of three main components:Joint Interpolation Module(JI Moudle),Multi-scale Temporal Convolution Network(MS-TCN),and Suppression Graph Convolutional Network(SGCN).The JI Module completes the spatially occluded skeletal joints using the(K-Nearest Neighbors)KNN interpolation method.The MS-TCN employs convolutional kernels of various sizes to comprehensively capture the emotional information embedded in the gait,compensating for the temporal occlusion of gait information.The SGCN extracts more non-prominent human gait features by suppressing the extraction of key body part features,thereby reducing the negative impact of occlusion on emotion recognition results.The proposed method is evaluated on two comprehensive datasets:Emotion-Gait,containing 4227 real gaits from sources like BML,ICT-Pollick,and ELMD,and 1000 synthetic gaits generated using STEP-Gen technology,and ELMB,consisting of 3924 gaits,with 1835 labeled with emotions such as“Happy,”“Sad,”“Angry,”and“Neutral.”On the standard datasets Emotion-Gait and ELMB,the proposed method achieved accuracies of 0.900 and 0.896,respectively,attaining performance comparable to other state-ofthe-artmethods.Furthermore,on occlusion datasets,the proposedmethod significantly mitigates the performance degradation caused by occlusion compared to other methods,the accuracy is significantly higher than that of other methods. 展开更多
关键词 KNN interpolation multi-scale temporal convolution suppression graph convolutional network gait emotion recognition human skeleton
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MSSTGCN: Multi-Head Self-Attention and Spatial-Temporal Graph Convolutional Network for Multi-Scale Traffic Flow Prediction
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作者 Xinlu Zong Fan Yu +1 位作者 Zhen Chen Xue Xia 《Computers, Materials & Continua》 2025年第2期3517-3537,共21页
Accurate traffic flow prediction has a profound impact on modern traffic management. Traffic flow has complex spatial-temporal correlations and periodicity, which poses difficulties for precise prediction. To address ... Accurate traffic flow prediction has a profound impact on modern traffic management. Traffic flow has complex spatial-temporal correlations and periodicity, which poses difficulties for precise prediction. To address this problem, a Multi-head Self-attention and Spatial-Temporal Graph Convolutional Network (MSSTGCN) for multiscale traffic flow prediction is proposed. Firstly, to capture the hidden traffic periodicity of traffic flow, traffic flow is divided into three kinds of periods, including hourly, daily, and weekly data. Secondly, a graph attention residual layer is constructed to learn the global spatial features across regions. Local spatial-temporal dependence is captured by using a T-GCN module. Thirdly, a transformer layer is introduced to learn the long-term dependence in time. A position embedding mechanism is introduced to label position information for all traffic sequences. Thus, this multi-head self-attention mechanism can recognize the sequence order and allocate weights for different time nodes. Experimental results on four real-world datasets show that the MSSTGCN performs better than the baseline methods and can be successfully adapted to traffic prediction tasks. 展开更多
关键词 Graph convolutional network traffic flow prediction multi-scale traffic flow spatial-temporal model
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A multi-scale convolutional auto-encoder and its application in fault diagnosis of rolling bearings 被引量:12
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作者 Ding Yunhao Jia Minping 《Journal of Southeast University(English Edition)》 EI CAS 2019年第4期417-423,共7页
Aiming at the difficulty of fault identification caused by manual extraction of fault features of rotating machinery,a one-dimensional multi-scale convolutional auto-encoder fault diagnosis model is proposed,based on ... Aiming at the difficulty of fault identification caused by manual extraction of fault features of rotating machinery,a one-dimensional multi-scale convolutional auto-encoder fault diagnosis model is proposed,based on the standard convolutional auto-encoder.In this model,the parallel convolutional and deconvolutional kernels of different scales are used to extract the features from the input signal and reconstruct the input signal;then the feature map extracted by multi-scale convolutional kernels is used as the input of the classifier;and finally the parameters of the whole model are fine-tuned using labeled data.Experiments on one set of simulation fault data and two sets of rolling bearing fault data are conducted to validate the proposed method.The results show that the model can achieve 99.75%,99.3%and 100%diagnostic accuracy,respectively.In addition,the diagnostic accuracy and reconstruction error of the one-dimensional multi-scale convolutional auto-encoder are compared with traditional machine learning,convolutional neural networks and a traditional convolutional auto-encoder.The final results show that the proposed model has a better recognition effect for rolling bearing fault data. 展开更多
关键词 fault diagnosis deep learning convolutional auto-encoder multi-scale convolutional kernel feature extraction
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Holder’s inequalities for a class of analytic functions connected with a certain hybrid-type convolution operator
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作者 H.M.Srivastava Sheza M.El-Deeb 《Applied Mathematics(A Journal of Chinese Universities)》 2025年第2期443-457,共15页
By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several propertie... By using a certain hybrid-type convolution operator,we first introduce a new subclass of normalized analytic functions in the open unit disk.For members of this analytic function class,we then derive several properties and characteristics including(for example)the modified Hadamard products,Holder's inequalities and convolution properties as well as some closure properties under a general family of integral transforms. 展开更多
关键词 analytic functions univalent functions binomial series:hybrid-type convolution operator Holder's inequalities modi ed Hadamard product convolution properties closure properties under integral transforms
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Land cover classification from remote sensing images based on multi-scale fully convolutional network 被引量:17
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作者 Rui Li Shunyi Zheng +2 位作者 Chenxi Duan Libo Wang Ce Zhang 《Geo-Spatial Information Science》 SCIE EI CSCD 2022年第2期278-294,共17页
Although the Convolutional Neural Network(CNN)has shown great potential for land cover classification,the frequently used single-scale convolution kernel limits the scope of informa-tion extraction.Therefore,we propos... Although the Convolutional Neural Network(CNN)has shown great potential for land cover classification,the frequently used single-scale convolution kernel limits the scope of informa-tion extraction.Therefore,we propose a Multi-Scale Fully Convolutional Network(MSFCN)with a multi-scale convolutional kernel as well as a Channel Attention Block(CAB)and a Global Pooling Module(GPM)in this paper to exploit discriminative representations from two-dimensional(2D)satellite images.Meanwhile,to explore the ability of the proposed MSFCN for spatio-temporal images,we expand our MSFCN to three-dimension using three-dimensional(3D)CNN,capable of harnessing each land cover category’s time series interac-tion from the reshaped spatio-temporal remote sensing images.To verify the effectiveness of the proposed MSFCN,we conduct experiments on two spatial datasets and two spatio-temporal datasets.The proposed MSFCN achieves 60.366%on the WHDLD dataset and 75.127%on the GID dataset in terms of mIoU index while the figures for two spatio-temporal datasets are 87.753%and 77.156%.Extensive comparative experiments and abla-tion studies demonstrate the effectiveness of the proposed MSFCN. 展开更多
关键词 Spatio-temporal remote sensing images multi-scale Fully convolutional Network land cover classification
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Multi-Scale Convolutional Gated Recurrent Unit Networks for Tool Wear Prediction in Smart Manufacturing 被引量:3
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作者 Weixin Xu Huihui Miao +3 位作者 Zhibin Zhao Jinxin Liu Chuang Sun Ruqiang Yan 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2021年第3期130-145,共16页
As an integrated application of modern information technologies and artificial intelligence,Prognostic and Health Management(PHM)is important for machine health monitoring.Prediction of tool wear is one of the symboli... As an integrated application of modern information technologies and artificial intelligence,Prognostic and Health Management(PHM)is important for machine health monitoring.Prediction of tool wear is one of the symbolic applications of PHM technology in modern manufacturing systems and industry.In this paper,a multi-scale Convolutional Gated Recurrent Unit network(MCGRU)is proposed to address raw sensory data for tool wear prediction.At the bottom of MCGRU,six parallel and independent branches with different kernel sizes are designed to form a multi-scale convolutional neural network,which augments the adaptability to features of different time scales.These features of different scales extracted from raw data are then fed into a Deep Gated Recurrent Unit network to capture long-term dependencies and learn significant representations.At the top of the MCGRU,a fully connected layer and a regression layer are built for cutting tool wear prediction.Two case studies are performed to verify the capability and effectiveness of the proposed MCGRU network and results show that MCGRU outperforms several state-of-the-art baseline models. 展开更多
关键词 Tool wear prediction multi-scale convolutional neural networks Gated recurrent unit
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Multi-function terahertz wave manipulation utilizing Fourier convolution operation metasurface 被引量:2
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作者 Min Zhong Jiu-Sheng Li 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第5期350-354,共5页
We propose a novel metasurface based on a combined pattern of outer C-shaped ring and inner rectangular ring.By Fourier convolution operation to generating different predesigned sequences of metasurfaces,we realize va... We propose a novel metasurface based on a combined pattern of outer C-shaped ring and inner rectangular ring.By Fourier convolution operation to generating different predesigned sequences of metasurfaces,we realize various functionalities to flexible manipulate terahertz waves including vortex terahertz beam splitting,anomalous vortex terahertz wave deflection,vortex terahertz wave splitting and deflection simultaneously.The incident terahertz wave can be flexibly controlled in a single metasurface.The designed metasurface has an extensive application prospect in the field of future terahertz communication and sensing. 展开更多
关键词 Fourier convolution operation metasurface terahertz wave flexible manipulation
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A Lightweight Convolutional Neural Network with Hierarchical Multi-Scale Feature Fusion for Image Classification 被引量:2
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作者 Adama Dembele Ronald Waweru Mwangi Ananda Omutokoh Kube 《Journal of Computer and Communications》 2024年第2期173-200,共28页
Convolutional neural networks (CNNs) are widely used in image classification tasks, but their increasing model size and computation make them challenging to implement on embedded systems with constrained hardware reso... Convolutional neural networks (CNNs) are widely used in image classification tasks, but their increasing model size and computation make them challenging to implement on embedded systems with constrained hardware resources. To address this issue, the MobileNetV1 network was developed, which employs depthwise convolution to reduce network complexity. MobileNetV1 employs a stride of 2 in several convolutional layers to decrease the spatial resolution of feature maps, thereby lowering computational costs. However, this stride setting can lead to a loss of spatial information, particularly affecting the detection and representation of smaller objects or finer details in images. To maintain the trade-off between complexity and model performance, a lightweight convolutional neural network with hierarchical multi-scale feature fusion based on the MobileNetV1 network is proposed. The network consists of two main subnetworks. The first subnetwork uses a depthwise dilated separable convolution (DDSC) layer to learn imaging features with fewer parameters, which results in a lightweight and computationally inexpensive network. Furthermore, depthwise dilated convolution in DDSC layer effectively expands the field of view of filters, allowing them to incorporate a larger context. The second subnetwork is a hierarchical multi-scale feature fusion (HMFF) module that uses parallel multi-resolution branches architecture to process the input feature map in order to extract the multi-scale feature information of the input image. Experimental results on the CIFAR-10, Malaria, and KvasirV1 datasets demonstrate that the proposed method is efficient, reducing the network parameters and computational cost by 65.02% and 39.78%, respectively, while maintaining the network performance compared to the MobileNetV1 baseline. 展开更多
关键词 MobileNet Image Classification Lightweight convolutional Neural Network Depthwise Dilated Separable convolution Hierarchical multi-scale Feature Fusion
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Pedestrian attribute classification with multi-scale and multi-label convolutional neural networks
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作者 朱建清 Zeng Huanqiang +2 位作者 Zhang Yuzhao Zheng Lixin Cai Canhui 《High Technology Letters》 EI CAS 2018年第1期53-61,共9页
Pedestrian attribute classification from a pedestrian image captured in surveillance scenarios is challenging due to diverse clothing appearances,varied poses and different camera views. A multiscale and multi-label c... Pedestrian attribute classification from a pedestrian image captured in surveillance scenarios is challenging due to diverse clothing appearances,varied poses and different camera views. A multiscale and multi-label convolutional neural network( MSMLCNN) is proposed to predict multiple pedestrian attributes simultaneously. The pedestrian attribute classification problem is firstly transformed into a multi-label problem including multiple binary attributes needed to be classified. Then,the multi-label problem is solved by fully connecting all binary attributes to multi-scale features with logistic regression functions. Moreover,the multi-scale features are obtained by concatenating those featured maps produced from multiple pooling layers of the MSMLCNN at different scales. Extensive experiment results show that the proposed MSMLCNN outperforms state-of-the-art pedestrian attribute classification methods with a large margin. 展开更多
关键词 PEDESTRIAN ATTRIBUTE CLASSIFICATION multi-scale features MULTI-LABEL CLASSIFICATION convolutional NEURAL network (CNN)
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Identification of Key Links in Electric Power Operation Based-Spatiotemporal Mixing Convolution Neural Network
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作者 Lei Feng Bo Wang +2 位作者 Fuqi Ma Hengrui Ma Mohamed AMohamed 《Computer Systems Science & Engineering》 SCIE EI 2023年第8期1487-1501,共15页
As the scale of the power system continues to expand,the environment for power operations becomes more and more complex.Existing risk management and control methods for power operations can only set the same risk dete... As the scale of the power system continues to expand,the environment for power operations becomes more and more complex.Existing risk management and control methods for power operations can only set the same risk detection standard and conduct the risk detection for any scenario indiscriminately.Therefore,more reliable and accurate security control methods are urgently needed.In order to improve the accuracy and reliability of the operation risk management and control method,this paper proposes a method for identifying the key links in the whole process of electric power operation based on the spatiotemporal hybrid convolutional neural network.To provide early warning and control of targeted risks,first,the video stream is framed adaptively according to the pixel changes in the video stream.Then,the optimized MobileNet is used to extract the feature map of the video stream,which contains both time-series and static spatial scene information.The feature maps are combined and non-linearly mapped to realize the identification of dynamic operating scenes.Finally,training samples and test samples are produced by using the whole process image of a power company in Xinjiang as a case study,and the proposed algorithm is compared with the unimproved MobileNet.The experimental results demonstrated that the method proposed in this paper can accurately identify the type and start and end time of each operation link in the whole process of electric power operation,and has good real-time performance.The average accuracy of the algorithm can reach 87.8%,and the frame rate is 61 frames/s,which is of great significance for improving the reliability and accuracy of security control methods. 展开更多
关键词 Security risk management key links identifications electric power operation spatiotemporal mixing convolution neural network MobileNet network
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MSSTNet:Multi-scale facial videos pulse extraction network based on separable spatiotemporal convolution and dimension separable attention
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作者 Changchen ZHAO Hongsheng WANG Yuanjing FENG 《Virtual Reality & Intelligent Hardware》 2023年第2期124-141,共18页
Background The use of remote photoplethysmography(rPPG)to estimate blood volume pulse in a noncontact manner has been an active research topic in recent years.Existing methods are primarily based on a singlescale regi... Background The use of remote photoplethysmography(rPPG)to estimate blood volume pulse in a noncontact manner has been an active research topic in recent years.Existing methods are primarily based on a singlescale region of interest(ROI).However,some noise signals that are not easily separated in a single-scale space can be easily separated in a multi-scale space.Also,existing spatiotemporal networks mainly focus on local spatiotemporal information and do not emphasize temporal information,which is crucial in pulse extraction problems,resulting in insufficient spatiotemporal feature modelling.Methods Here,we propose a multi-scale facial video pulse extraction network based on separable spatiotemporal convolution(SSTC)and dimension separable attention(DSAT).First,to solve the problem of a single-scale ROI,we constructed a multi-scale feature space for initial signal separation.Second,SSTC and DSAT were designed for efficient spatiotemporal correlation modeling,which increased the information interaction between the long-span time and space dimensions;this placed more emphasis on temporal features.Results The signal-to-noise ratio(SNR)of the proposed network reached 9.58dB on the PURE dataset and 6.77dB on the UBFC-rPPG dataset,outperforming state-of-the-art algorithms.Conclusions The results showed that fusing multi-scale signals yielded better results than methods based on only single-scale signals.The proposed SSTC and dimension-separable attention mechanism will contribute to more accurate pulse signal extraction. 展开更多
关键词 Remote photoplethysmography Heart rate Separable spatiotemporal convolution Dimension separable attention multi-scale Neural network
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M2ANet:Multi-branch and multi-scale attention network for medical image segmentation 被引量:1
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作者 Wei Xue Chuanghui Chen +3 位作者 Xuan Qi Jian Qin Zhen Tang Yongsheng He 《Chinese Physics B》 2025年第8期547-559,共13页
Convolutional neural networks(CNNs)-based medical image segmentation technologies have been widely used in medical image segmentation because of their strong representation and generalization abilities.However,due to ... Convolutional neural networks(CNNs)-based medical image segmentation technologies have been widely used in medical image segmentation because of their strong representation and generalization abilities.However,due to the inability to effectively capture global information from images,CNNs can easily lead to loss of contours and textures in segmentation results.Notice that the transformer model can effectively capture the properties of long-range dependencies in the image,and furthermore,combining the CNN and the transformer can effectively extract local details and global contextual features of the image.Motivated by this,we propose a multi-branch and multi-scale attention network(M2ANet)for medical image segmentation,whose architecture consists of three components.Specifically,in the first component,we construct an adaptive multi-branch patch module for parallel extraction of image features to reduce information loss caused by downsampling.In the second component,we apply residual block to the well-known convolutional block attention module to enhance the network’s ability to recognize important features of images and alleviate the phenomenon of gradient vanishing.In the third component,we design a multi-scale feature fusion module,in which we adopt adaptive average pooling and position encoding to enhance contextual features,and then multi-head attention is introduced to further enrich feature representation.Finally,we validate the effectiveness and feasibility of the proposed M2ANet method through comparative experiments on four benchmark medical image segmentation datasets,particularly in the context of preserving contours and textures. 展开更多
关键词 medical image segmentation convolutional neural network multi-branch attention multi-scale feature fusion
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Deep Multi-Scale and Attention-Based Architectures for Semantic Segmentation in Biomedical Imaging
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作者 Majid Harouni Vishakha Goyal +2 位作者 Gabrielle Feldman Sam Michael Ty C.Voss 《Computers, Materials & Continua》 2025年第10期331-366,共36页
Semantic segmentation plays a foundational role in biomedical image analysis, providing precise information about cellular, tissue, and organ structures in both biological and medical imaging modalities. Traditional a... Semantic segmentation plays a foundational role in biomedical image analysis, providing precise information about cellular, tissue, and organ structures in both biological and medical imaging modalities. Traditional approaches often fail in the face of challenges such as low contrast, morphological variability, and densely packed structures. Recent advancements in deep learning have transformed segmentation capabilities through the integration of fine-scale detail preservation, coarse-scale contextual modeling, and multi-scale feature fusion. This work provides a comprehensive analysis of state-of-the-art deep learning models, including U-Net variants, attention-based frameworks, and Transformer-integrated networks, highlighting innovations that improve accuracy, generalizability, and computational efficiency. Key architectural components such as convolution operations, shallow and deep blocks, skip connections, and hybrid encoders are examined for their roles in enhancing spatial representation and semantic consistency. We further discuss the importance of hierarchical and instance-aware segmentation and annotation in interpreting complex biological scenes and multiplexed medical images. By bridging methodological developments with diverse application domains, this paper outlines current trends and future directions for semantic segmentation, emphasizing its critical role in facilitating annotation, diagnosis, and discovery in biomedical research. 展开更多
关键词 Biomedical semantic segmentation multi-scale feature fusion fine-and coarse-scale features convolution operations shallow and deep blocks skip connections
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Hybrid Efficient Convolution Operators for Visual Tracking 被引量:1
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作者 Yu Wang 《Journal on Artificial Intelligence》 2021年第2期63-72,共10页
Visual tracking is a classical computer vision problem with many applications.Efficient convolution operators(ECO)is one of the most outstanding visual tracking algorithms in recent years,it has shown great performanc... Visual tracking is a classical computer vision problem with many applications.Efficient convolution operators(ECO)is one of the most outstanding visual tracking algorithms in recent years,it has shown great performance using discriminative correlation filter(DCF)together with HOG,color maps and VGGNet features.Inspired by new deep learning models,this paper propose a hybrid efficient convolution operators integrating fully convolution network(FCN)and residual network(ResNet)for visual tracking,where FCN and ResNet are introduced in our proposed method to segment the objects from backgrounds and extract hierarchical feature maps of objects,respectively.Compared with the traditional VGGNet,our approach has higher accuracy for dealing with the issues of segmentation and image size.The experiments show that our approach would obtain better performance than ECO in terms of precision plot and success rate plot on OTB-2013 and UAV123 datasets. 展开更多
关键词 Visual tracking deep learning convolutional neural network hybrid convolution operator
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Magnetic Resonance Image Super-Resolution Based on GAN and Multi-Scale Residual Dense Attention Network
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作者 GUAN Chunling YU Suping +1 位作者 XU Wujun FAN Hong 《Journal of Donghua University(English Edition)》 2025年第4期435-441,共7页
The application of image super-resolution(SR)has brought significant assistance in the medical field,aiding doctors to make more precise diagnoses.However,solely relying on a convolutional neural network(CNN)for image... The application of image super-resolution(SR)has brought significant assistance in the medical field,aiding doctors to make more precise diagnoses.However,solely relying on a convolutional neural network(CNN)for image SR may lead to issues such as blurry details and excessive smoothness.To address the limitations,we proposed an algorithm based on the generative adversarial network(GAN)framework.In the generator network,three different sizes of convolutions connected by a residual dense structure were used to extract detailed features,and an attention mechanism combined with dual channel and spatial information was applied to concentrate the computing power on crucial areas.In the discriminator network,using InstanceNorm to normalize tensors sped up the training process while retaining feature information.The experimental results demonstrate that our algorithm achieves higher peak signal-to-noise ratio(PSNR)and structural similarity index measure(SSIM)compared to other methods,resulting in an improved visual quality. 展开更多
关键词 magnetic resonance(MR) image super-resolution(SR) attention mechanism generative adversarial network(GAN) multi-scale convolution
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PROPERTIES OF THE CONVOLUTION WITH PRESTARLIKE FUNCTIONS
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作者 Jacek DZIOK 《Acta Mathematica Scientia》 SCIE CSCD 2013年第6期1685-1694,共10页
In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known clas... In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known classes of functions defined by linear operators are also considered. 展开更多
关键词 analytic functions prestarlike functions starlike functions linear operator convolution
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ASYMPTOTIC FORMULAE FOR BIVARIATE MELLIN CONVOLUTION OPERATORS
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作者 C. Bardaro I. Mantellini 《Analysis in Theory and Applications》 2008年第4期377-394,共18页
In this paper some Voronovskaya approximation formulae for a class of Mellin convolution operators of the type (Twf)(x,y)=∫R^2+Kw(tx^-1,vy^-1)f(t,v)dtdv/tv are given. Moreover, various examples are discussed.
关键词 Mellin convolution operator local moment Voronovskaya formula
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A NOTE ON CONVOLUTION-TYPE CALDERóN-ZYGMUND OPERATORS 被引量:1
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作者 杨占英 杨奇祥 《Acta Mathematica Scientia》 SCIE CSCD 2009年第5期1341-1350,共10页
For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Trieb... For convolution-type Calderon-Zygmund operators, by the boundedness on Besov spaces and Hardy spaces, applying interpolation theory and duality, it is known that H5rmander condition can ensure the boundedness on Triebel-Lizorkin spaces Fp^0,q (1 〈 p,q 〈 ∞) and on a party of endpoint spaces FO,q (1 ≤ q ≤ 2), hut this idea is invalid for endpoint Triebel-Lizorkin spaces F1^0,q (2 〈 q ≤ ∞). In this article, the authors apply wavelets and interpolation theory to establish the boundedness on F1^0,q (2 〈 q ≤ ∞) under an integrable condition which approaches HSrmander condition infinitely. 展开更多
关键词 convolution-type CalderSn-Zygmund operators Triebel-Lizorkin spaces wavelets atomic decomposition
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On Fatou Type Convergence of Convolution Type Double Singular Integral Operators
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作者 Harun Karsli 《Analysis in Theory and Applications》 CSCD 2015年第3期307-320,共14页
In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,... In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15]. 展开更多
关键词 Fatou-type convergence convolution type double singular integral operators μgeneralized Lebesgue point
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The Hypoellipticity for a Class of Nonhomogeneous Convolution Operator on the Nilpotent Lie Group H^n×R^k
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作者 郑驻军 《Chinese Quarterly Journal of Mathematics》 CSCD 1993年第3期76-81,共6页
In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.
关键词 HYPOELLIPTICITY nonhomogeneous convolution operator NILPOTENT
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