Bayesian empirical likelihood is a semiparametric method that combines parametric priors and nonparametric likelihoods, that is, replacing the parametric likelihood function in Bayes theorem with a nonparametric empir...Bayesian empirical likelihood is a semiparametric method that combines parametric priors and nonparametric likelihoods, that is, replacing the parametric likelihood function in Bayes theorem with a nonparametric empirical likelihood function, which can be used without assuming the distribution of the data. It can effectively avoid the problems caused by the wrong setting of the model. In the variable selection based on Bayesian empirical likelihood, the penalty term is introduced into the model in the form of parameter prior. In this paper, we propose a novel variable selection method, L<sub>1/2</sub> regularization based on Bayesian empirical likelihood. The L<sub>1/2</sub> penalty is introduced into the model through a scale mixture of uniform representation of generalized Gaussian prior, and the posterior distribution is then sampled using MCMC method. Simulations demonstrate that the proposed method can have better predictive ability when the error violates the zero-mean normality assumption of the standard parameter model, and can perform variable selection.展开更多
压缩感知(compressed sensing,CS)是一种全新的信息采集与处理的理论框架,借助信号内在的稀疏性或可压缩性,可以从小规模的线性、非自适应的测量中通过求解非线性优化问题重构原信号.块稀疏信号是一种具有块结构的信号,即信号的非零元...压缩感知(compressed sensing,CS)是一种全新的信息采集与处理的理论框架,借助信号内在的稀疏性或可压缩性,可以从小规模的线性、非自适应的测量中通过求解非线性优化问题重构原信号.块稀疏信号是一种具有块结构的信号,即信号的非零元是成块出现的.受YIN Peng-hang,LOU Yi-fei,HE Qi等提出的l_1-2范数最小化方法的启发,将基于l_1-l_2范数的稀疏重构算法推广到块稀疏模型,证明了块稀疏模型下l_1-l_2范数的相关性质,建立了基于l_1-l_2范数的块稀疏信号精确重构的充分条件,并通过DCA(difference of convex functions algorithm)和ADMM(alternating direction method of multipliers)给出了求解块稀疏模型下l_1-l_2范数的迭代方法.数值实验表明,基于l_1-l_2范数的块稀疏重构算法比其他块稀疏重构算法具有更高的重构成功率.展开更多
针对图像重建过程中噪声去除问题,提出一种自适应加权编码L1/2正则化重建算法。首先,考虑到许多真实图像中不仅含有高斯噪声,而且含有拉普拉斯噪声,设计一种改进的L1-L2混合误差模型(IHEM)算法,该算法兼顾了L1范数与L2范数的各自优点;其...针对图像重建过程中噪声去除问题,提出一种自适应加权编码L1/2正则化重建算法。首先,考虑到许多真实图像中不仅含有高斯噪声,而且含有拉普拉斯噪声,设计一种改进的L1-L2混合误差模型(IHEM)算法,该算法兼顾了L1范数与L2范数的各自优点;其次,由于迭代过程中噪声分布会发生改变,设计一种自适应隶属度算法,该算法可以减少迭代次数和运算时间;利用一种自适应加权编码方法,该方法可以有效地去除含有重尾分布特性的拉普拉斯噪声;另外,设计一种L1/2正则化算法,该算法可以得到较稀疏的解。实验结果表明,相比IHEM算法,自适应L1/2正则化图像重建算法的峰值信噪比(PSNR)平均提高了3.46 d B,结构相似度(SSIM)平均提高了0.02,对含有多种噪声的图像处理具有比较理想的效果。展开更多
We derive a sharp nonasymptotic bound of parameter estimation of the L1/2 regularization. The bound shows that the solutions of the L1/2 regularization can achieve a loss within logarithmic factor of an ideal mean squ...We derive a sharp nonasymptotic bound of parameter estimation of the L1/2 regularization. The bound shows that the solutions of the L1/2 regularization can achieve a loss within logarithmic factor of an ideal mean squared error and therefore underlies the feasibility and effectiveness of the L1/2 regularization. Interestingly, when applied to compressive sensing, the L1/2 regularization scheme has exhibited a very promising capability of completed recovery from a much less sampling information. As compared with the Lp （0 〈 p 〈 1） penalty, it is appeared that the L1/2 penalty can always yield the most sparse solution among all the Lv penalty when 1/2 〈 p 〈 1, and when 0 〈 p 〈 1/2, the Lp penalty exhibits the similar properties as the L1/2 penalty. This suggests that the L1/2 regularization scheme can be accepted as the best and therefore the representative of all the Lp （0 〈 p 〈 1） regularization schemes.展开更多
The generative adversarial network(GAN)is first proposed in 2014,and this kind of network model is machine learning systems that can learn to measure a given distribution of data,one of the most important applications...The generative adversarial network(GAN)is first proposed in 2014,and this kind of network model is machine learning systems that can learn to measure a given distribution of data,one of the most important applications is style transfer.Style transfer is a class of vision and graphics problems where the goal is to learn the mapping between an input image and an output image.CYCLE-GAN is a classic GAN model,which has a wide range of scenarios in style transfer.Considering its unsupervised learning characteristics,the mapping is easy to be learned between an input image and an output image.However,it is difficult for CYCLE-GAN to converge and generate high-quality images.In order to solve this problem,spectral normalization is introduced into each convolutional kernel of the discriminator.Every convolutional kernel reaches Lipschitz stability constraint with adding spectral normalization and the value of the convolutional kernel is limited to[0,1],which promotes the training process of the proposed model.Besides,we use pretrained model(VGG16)to control the loss of image content in the position of l1 regularization.To avoid overfitting,l1 regularization term and l2 regularization term are both used in the object loss function.In terms of Frechet Inception Distance(FID)score evaluation,our proposed model achieves outstanding performance and preserves more discriminative features.Experimental results show that the proposed model converges faster and achieves better FID scores than the state of the art.展开更多
Compared with traditional learning methods such as the back propagation(BP)method,extreme learning machine provides much faster learning speed and needs less human intervention,and thus has been widely used.In this pa...Compared with traditional learning methods such as the back propagation(BP)method,extreme learning machine provides much faster learning speed and needs less human intervention,and thus has been widely used.In this paper we combine the L1/2regularization method with extreme learning machine to prune extreme learning machine.A variable learning coefcient is employed to prevent too large a learning increment.A numerical experiment demonstrates that a network pruned by L1/2regularization has fewer hidden nodes but provides better performance than both the original network and the network pruned by L2regularization.展开更多
The traditional compressed sensing method for improving resolution is realized in the frequency domain.This method is aff ected by noise,which limits the signal-to-noise ratio and resolution,resulting in poor inversio...The traditional compressed sensing method for improving resolution is realized in the frequency domain.This method is aff ected by noise,which limits the signal-to-noise ratio and resolution,resulting in poor inversion.To solve this problem,we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics.Moreover,the reconstruction of the sparse refl ection coeffi cient is implemented by the mixed L1_L2 norm algorithm,which converts the L0 norm problem into an L1 norm problem.Additionally,a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error.The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods.It not only has better denoising and smoothing eff ects but also improves the recognition accuracy of thin interbeds.The actual data application also shows that the new method can eff ectively expand the seismic frequency band and improve seismic data resolution,so the method is conducive to the identifi cation of thin interbeds for beach-bar sand reservoirs.展开更多
文摘Bayesian empirical likelihood is a semiparametric method that combines parametric priors and nonparametric likelihoods, that is, replacing the parametric likelihood function in Bayes theorem with a nonparametric empirical likelihood function, which can be used without assuming the distribution of the data. It can effectively avoid the problems caused by the wrong setting of the model. In the variable selection based on Bayesian empirical likelihood, the penalty term is introduced into the model in the form of parameter prior. In this paper, we propose a novel variable selection method, L<sub>1/2</sub> regularization based on Bayesian empirical likelihood. The L<sub>1/2</sub> penalty is introduced into the model through a scale mixture of uniform representation of generalized Gaussian prior, and the posterior distribution is then sampled using MCMC method. Simulations demonstrate that the proposed method can have better predictive ability when the error violates the zero-mean normality assumption of the standard parameter model, and can perform variable selection.
文摘压缩感知(compressed sensing,CS)是一种全新的信息采集与处理的理论框架,借助信号内在的稀疏性或可压缩性,可以从小规模的线性、非自适应的测量中通过求解非线性优化问题重构原信号.块稀疏信号是一种具有块结构的信号,即信号的非零元是成块出现的.受YIN Peng-hang,LOU Yi-fei,HE Qi等提出的l_1-2范数最小化方法的启发,将基于l_1-l_2范数的稀疏重构算法推广到块稀疏模型,证明了块稀疏模型下l_1-l_2范数的相关性质,建立了基于l_1-l_2范数的块稀疏信号精确重构的充分条件,并通过DCA(difference of convex functions algorithm)和ADMM(alternating direction method of multipliers)给出了求解块稀疏模型下l_1-l_2范数的迭代方法.数值实验表明,基于l_1-l_2范数的块稀疏重构算法比其他块稀疏重构算法具有更高的重构成功率.
文摘针对图像重建过程中噪声去除问题,提出一种自适应加权编码L1/2正则化重建算法。首先,考虑到许多真实图像中不仅含有高斯噪声,而且含有拉普拉斯噪声,设计一种改进的L1-L2混合误差模型(IHEM)算法,该算法兼顾了L1范数与L2范数的各自优点;其次,由于迭代过程中噪声分布会发生改变,设计一种自适应隶属度算法,该算法可以减少迭代次数和运算时间;利用一种自适应加权编码方法,该方法可以有效地去除含有重尾分布特性的拉普拉斯噪声;另外,设计一种L1/2正则化算法,该算法可以得到较稀疏的解。实验结果表明,相比IHEM算法,自适应L1/2正则化图像重建算法的峰值信噪比(PSNR)平均提高了3.46 d B,结构相似度(SSIM)平均提高了0.02,对含有多种噪声的图像处理具有比较理想的效果。
基金supported by National Natural Science Foundation of China(Grant Nos.11171212 and60975036)supported by National Natural Science Foundation of China(Grant No.6175054)
文摘We derive a sharp nonasymptotic bound of parameter estimation of the L1/2 regularization. The bound shows that the solutions of the L1/2 regularization can achieve a loss within logarithmic factor of an ideal mean squared error and therefore underlies the feasibility and effectiveness of the L1/2 regularization. Interestingly, when applied to compressive sensing, the L1/2 regularization scheme has exhibited a very promising capability of completed recovery from a much less sampling information. As compared with the Lp （0 〈 p 〈 1） penalty, it is appeared that the L1/2 penalty can always yield the most sparse solution among all the Lv penalty when 1/2 〈 p 〈 1, and when 0 〈 p 〈 1/2, the Lp penalty exhibits the similar properties as the L1/2 penalty. This suggests that the L1/2 regularization scheme can be accepted as the best and therefore the representative of all the Lp （0 〈 p 〈 1） regularization schemes.
基金This work is supported by the National Natural Science Foundation of China(No.61702226)the 111 Project(B12018)+1 种基金the Natural Science Foundation of Jiangsu Province(No.BK20170200)the Fundamental Research Funds for the Central Universities(No.JUSRP11854).
文摘The generative adversarial network(GAN)is first proposed in 2014,and this kind of network model is machine learning systems that can learn to measure a given distribution of data,one of the most important applications is style transfer.Style transfer is a class of vision and graphics problems where the goal is to learn the mapping between an input image and an output image.CYCLE-GAN is a classic GAN model,which has a wide range of scenarios in style transfer.Considering its unsupervised learning characteristics,the mapping is easy to be learned between an input image and an output image.However,it is difficult for CYCLE-GAN to converge and generate high-quality images.In order to solve this problem,spectral normalization is introduced into each convolutional kernel of the discriminator.Every convolutional kernel reaches Lipschitz stability constraint with adding spectral normalization and the value of the convolutional kernel is limited to[0,1],which promotes the training process of the proposed model.Besides,we use pretrained model(VGG16)to control the loss of image content in the position of l1 regularization.To avoid overfitting,l1 regularization term and l2 regularization term are both used in the object loss function.In terms of Frechet Inception Distance(FID)score evaluation,our proposed model achieves outstanding performance and preserves more discriminative features.Experimental results show that the proposed model converges faster and achieves better FID scores than the state of the art.
基金Project supported by the National Natural Science Foundation of China(No.11171367)the Fundamental Research Funds for the Central Universities,China
文摘Compared with traditional learning methods such as the back propagation(BP)method,extreme learning machine provides much faster learning speed and needs less human intervention,and thus has been widely used.In this paper we combine the L1/2regularization method with extreme learning machine to prune extreme learning machine.A variable learning coefcient is employed to prevent too large a learning increment.A numerical experiment demonstrates that a network pruned by L1/2regularization has fewer hidden nodes but provides better performance than both the original network and the network pruned by L2regularization.
基金National Science and Technology Major Project(No.2016ZX05006-002 and 2017ZX05072-001).
文摘The traditional compressed sensing method for improving resolution is realized in the frequency domain.This method is aff ected by noise,which limits the signal-to-noise ratio and resolution,resulting in poor inversion.To solve this problem,we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics.Moreover,the reconstruction of the sparse refl ection coeffi cient is implemented by the mixed L1_L2 norm algorithm,which converts the L0 norm problem into an L1 norm problem.Additionally,a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error.The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods.It not only has better denoising and smoothing eff ects but also improves the recognition accuracy of thin interbeds.The actual data application also shows that the new method can eff ectively expand the seismic frequency band and improve seismic data resolution,so the method is conducive to the identifi cation of thin interbeds for beach-bar sand reservoirs.
