Many traditional denoising methods,such as Gaussian fi ltering,tend to blur and lose details or edge information while reducing noise.The stationary wavelet packet transform is a multi-scale and multi-band analysis to...Many traditional denoising methods,such as Gaussian fi ltering,tend to blur and lose details or edge information while reducing noise.The stationary wavelet packet transform is a multi-scale and multi-band analysis tool.Compared with the stationary wavelet transform,it can suppress high-frequency noise while preserving more edge details.Deep learning has signifi cantly progressed in denoising applications.DnCNN,a residual network;FFDNet,an effi cient,fl exible network;U-NET,a codec network;and GAN,a generative adversative network,have better denoising effects than BM3D,the most popular conventional denoising method.Therefore,SWP_hFFDNet,a random noise attenuation network based on the stationary wavelet packet transform(SWPT)and modified FFDNet,is proposed.This network combines the advantages of SWPT,Huber norm,and FFDNet.In addition,it has three characteristics:First,SWPT is an eff ective featureextraction tool that can obtain low-and high-frequency features of different scales and frequency bands.Second,because the noise level map is the input of the network,the noise removal performance of diff erent noise levels can be improved.Third,the Huber norm can reduce the sensitivity of the network to abnormal data and enhance its robustness.The network is trained using the Adam algorithm and the BSD500 dataset,which is augmented,noised,and decomposed by SWPT.Experimental and actual data processing results show that the denoising eff ect of the proposed method is almost the same as those of BM3D,DnCNN,and FFDNet networks for low noise.However,for high noise,the proposed method is superior to the aforementioned networks.展开更多
The DeGroot model is one of the most classical models in the field of opinion dynamics. The standard DeGroot model assumes that agents are homogeneous and update their opinions in the direction of a weighted average o...The DeGroot model is one of the most classical models in the field of opinion dynamics. The standard DeGroot model assumes that agents are homogeneous and update their opinions in the direction of a weighted average of their neighbors'opinions.One natural question is whether a second type of agents could significantly change the main properties of the model.The authors address this question by introducing rebels,who update their opinions toward the opposite of their neighbors' weighted average.The authors find that the existence of rebels remarkably affects the opinion dynamics. Under certain mild conditions,the existence of a few rebels will lead the group opinion to the golden mean,regardless of the initial opinions of the agents and the structure of the learning network.This result is completely different from that of the standard DeGroot model,where the final consensus opinion is determined by both the initial opinions and the learning topology.The study then provides new insights into understanding how heterogeneous individuals in a group reach consensus and why the golden mean is so common in human society.展开更多
文摘Many traditional denoising methods,such as Gaussian fi ltering,tend to blur and lose details or edge information while reducing noise.The stationary wavelet packet transform is a multi-scale and multi-band analysis tool.Compared with the stationary wavelet transform,it can suppress high-frequency noise while preserving more edge details.Deep learning has signifi cantly progressed in denoising applications.DnCNN,a residual network;FFDNet,an effi cient,fl exible network;U-NET,a codec network;and GAN,a generative adversative network,have better denoising effects than BM3D,the most popular conventional denoising method.Therefore,SWP_hFFDNet,a random noise attenuation network based on the stationary wavelet packet transform(SWPT)and modified FFDNet,is proposed.This network combines the advantages of SWPT,Huber norm,and FFDNet.In addition,it has three characteristics:First,SWPT is an eff ective featureextraction tool that can obtain low-and high-frequency features of different scales and frequency bands.Second,because the noise level map is the input of the network,the noise removal performance of diff erent noise levels can be improved.Third,the Huber norm can reduce the sensitivity of the network to abnormal data and enhance its robustness.The network is trained using the Adam algorithm and the BSD500 dataset,which is augmented,noised,and decomposed by SWPT.Experimental and actual data processing results show that the denoising eff ect of the proposed method is almost the same as those of BM3D,DnCNN,and FFDNet networks for low noise.However,for high noise,the proposed method is superior to the aforementioned networks.
基金supported by the National Natural Science Foundation of China under Grant Nos.71771026,71701058,11471326
文摘The DeGroot model is one of the most classical models in the field of opinion dynamics. The standard DeGroot model assumes that agents are homogeneous and update their opinions in the direction of a weighted average of their neighbors'opinions.One natural question is whether a second type of agents could significantly change the main properties of the model.The authors address this question by introducing rebels,who update their opinions toward the opposite of their neighbors' weighted average.The authors find that the existence of rebels remarkably affects the opinion dynamics. Under certain mild conditions,the existence of a few rebels will lead the group opinion to the golden mean,regardless of the initial opinions of the agents and the structure of the learning network.This result is completely different from that of the standard DeGroot model,where the final consensus opinion is determined by both the initial opinions and the learning topology.The study then provides new insights into understanding how heterogeneous individuals in a group reach consensus and why the golden mean is so common in human society.
