In this paper, we propose a novel shear gradient operator by combining the shear and gradient operators. The shear gradient operator performs well to capture diverse directional information in the image gradient domai...In this paper, we propose a novel shear gradient operator by combining the shear and gradient operators. The shear gradient operator performs well to capture diverse directional information in the image gradient domain. Based on the shear gradient operator, we extend the total variation(TV) norm to the shear total variation(STV) norm by adding two shear gradient terms. Subsequently, we introduce a shear total variation deblurring model. Experimental results are provided to validate the ability of the STV norm to capture the detailed information. Leveraging the Block Circulant with Circulant Blocks(BCCB) structure of the shear gradient matrices, the alternating direction method of multipliers(ADMM) algorithm can be used to solve the proposed model efficiently. Numerous experiments are presented to verify the performance of our algorithm for non-blind image deblurring.展开更多
Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed poin...Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.展开更多
some properties of the inclusion variation and the disjoint variation of set functions on T∞-tribe are studied in detail.The absolute continuity and singularity of set functions on T∞-tribe are discussed.The triangu...some properties of the inclusion variation and the disjoint variation of set functions on T∞-tribe are studied in detail.The absolute continuity and singularity of set functions on T∞-tribe are discussed.The triangular norms T∞ and S∞ are considered as the operators of intersection and union between the fuzzy sets.As a result,some important conclusions about the variations and absolute continuity of set functions on T∞-tribe are obtained such as the superadditivity of inclusion variation,the relation between the variations and the equivalence proposition of absolute continuity of set functions on T∞-tribe.In addition,two small mistakes about T∞-measure are pointed out by the counterexamples and are revised.展开更多
The paper discusses the core parameters of the 3 D and 4 D variational merging based on L1 norm regularization,namely optimization characteristic correlation length of background error covariance matrix and regulariza...The paper discusses the core parameters of the 3 D and 4 D variational merging based on L1 norm regularization,namely optimization characteristic correlation length of background error covariance matrix and regularization parameter. Classical 3 D/4 D variational merging is based on the theory that error follows Gaussian distribution. It involves the solution of the objective functional gradient in minimization iteration,which requires the data to have continuity and differentiability. Classic 3 D/4 D-dimensional variational merging method was extended,and L1 norm was used as the constraint coupling to the classical variational merged model. Experiment was carried out by using linear advection-diffusion equation as four-dimensional prediction model,and parameter optimization of this method is discussed. Considering the strong temporal and spatial variation of water vapor,this method is further applied to the precipitable water vapor( PWV) merging by calculating reanalysis data and GNSS retrieval.Parameters were adjusted gradually to analyze the influence of background field on the merging result,and the experiment results show that the mathematical algorithm adopted in this paper is feasible.展开更多
为了实现对线性空间不变的模糊图像的盲复原,提出了一种基于稀疏性和平滑特性的多正则化约束的模糊图像盲复原方法.首先,根据自然图像边缘的稀疏特性,运用了一种权重的全变差范数(weighted total variation norm,简称WTV-norm)对复原图...为了实现对线性空间不变的模糊图像的盲复原,提出了一种基于稀疏性和平滑特性的多正则化约束的模糊图像盲复原方法.首先,根据自然图像边缘的稀疏特性,运用了一种权重的全变差范数(weighted total variation norm,简称WTV-norm)对复原图像进行正则化约束;然后,从运动模糊的点扩散函数(motion point spread function,简称MPSF)的特性出发,提出一种能够适用于多种模糊情况的多正则化约束;最后,提出了一种改进的变量分裂(modified variable splitting,简称MVS)方法来得到清晰的复原图像,同时准确地估计出相应的模糊退化函数.大量的实验结果表明,该方法能够较好地复原多种不同类型的模糊(例如运动模糊、高斯模糊、均匀模糊、圆盘模糊).与近几年提出来的一些具有代表性的模糊图像盲复原方法相比,该方法不仅主观的视觉效果得到了较为明显的改进,而且客观的信噪比增量也增加了1.20dB^4.22dB.展开更多
基金Supported by Open Fund of Key Laboratory of Anhui Higher Education Institutes (CS2021-07)the National Natural Science Foundation of China (61701004)Outstanding Young Talents Support Program of Anhui Province (gxyq2021178)。
文摘In this paper, we propose a novel shear gradient operator by combining the shear and gradient operators. The shear gradient operator performs well to capture diverse directional information in the image gradient domain. Based on the shear gradient operator, we extend the total variation(TV) norm to the shear total variation(STV) norm by adding two shear gradient terms. Subsequently, we introduce a shear total variation deblurring model. Experimental results are provided to validate the ability of the STV norm to capture the detailed information. Leveraging the Block Circulant with Circulant Blocks(BCCB) structure of the shear gradient matrices, the alternating direction method of multipliers(ADMM) algorithm can be used to solve the proposed model efficiently. Numerous experiments are presented to verify the performance of our algorithm for non-blind image deblurring.
文摘Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.
基金Sponsored by the National Natural Science Foundation of China(70471063,70771010)Youth Foundation of Henan University of Science and Technology(2007QN051)
文摘some properties of the inclusion variation and the disjoint variation of set functions on T∞-tribe are studied in detail.The absolute continuity and singularity of set functions on T∞-tribe are discussed.The triangular norms T∞ and S∞ are considered as the operators of intersection and union between the fuzzy sets.As a result,some important conclusions about the variations and absolute continuity of set functions on T∞-tribe are obtained such as the superadditivity of inclusion variation,the relation between the variations and the equivalence proposition of absolute continuity of set functions on T∞-tribe.In addition,two small mistakes about T∞-measure are pointed out by the counterexamples and are revised.
基金Supported by Open Foundation Project of Shenyang Institute of Atmospheric Environment,China Meteorological Administration(2016SYIAE14)Natural Science Foundation of Anhui Province,China(1708085QD89)National Natural Science Foundation of China(41805080)
文摘The paper discusses the core parameters of the 3 D and 4 D variational merging based on L1 norm regularization,namely optimization characteristic correlation length of background error covariance matrix and regularization parameter. Classical 3 D/4 D variational merging is based on the theory that error follows Gaussian distribution. It involves the solution of the objective functional gradient in minimization iteration,which requires the data to have continuity and differentiability. Classic 3 D/4 D-dimensional variational merging method was extended,and L1 norm was used as the constraint coupling to the classical variational merged model. Experiment was carried out by using linear advection-diffusion equation as four-dimensional prediction model,and parameter optimization of this method is discussed. Considering the strong temporal and spatial variation of water vapor,this method is further applied to the precipitable water vapor( PWV) merging by calculating reanalysis data and GNSS retrieval.Parameters were adjusted gradually to analyze the influence of background field on the merging result,and the experiment results show that the mathematical algorithm adopted in this paper is feasible.
文摘为了实现对线性空间不变的模糊图像的盲复原,提出了一种基于稀疏性和平滑特性的多正则化约束的模糊图像盲复原方法.首先,根据自然图像边缘的稀疏特性,运用了一种权重的全变差范数(weighted total variation norm,简称WTV-norm)对复原图像进行正则化约束;然后,从运动模糊的点扩散函数(motion point spread function,简称MPSF)的特性出发,提出一种能够适用于多种模糊情况的多正则化约束;最后,提出了一种改进的变量分裂(modified variable splitting,简称MVS)方法来得到清晰的复原图像,同时准确地估计出相应的模糊退化函数.大量的实验结果表明,该方法能够较好地复原多种不同类型的模糊(例如运动模糊、高斯模糊、均匀模糊、圆盘模糊).与近几年提出来的一些具有代表性的模糊图像盲复原方法相比,该方法不仅主观的视觉效果得到了较为明显的改进,而且客观的信噪比增量也增加了1.20dB^4.22dB.
