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
The trace norm of matrices plays an important role in quantum information and quantum computing. How to quantify it in today’s noisy intermediate scale quantum(NISQ) devices is a crucial task for information processi...The trace norm of matrices plays an important role in quantum information and quantum computing. How to quantify it in today’s noisy intermediate scale quantum(NISQ) devices is a crucial task for information processing. In this paper, we present three variational quantum algorithms on NISQ devices to estimate the trace norms corresponding to different situations.Compared with the previous methods, our means greatly reduce the requirement for quantum resources. Numerical experiments are provided to illustrate the effectiveness of our algorithms.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
The utilization of gradient operators is prevalent in image processing,as they effectively detect edges and provide directional information.However,these operators only differentiate the horizontal and vertical direct...The utilization of gradient operators is prevalent in image processing,as they effectively detect edges and provide directional information.However,these operators only differentiate the horizontal and vertical directions,ignoring details and causing loss of information in other directions.This paper introduces the shear gradient operator to overcome this limitation by capturing details accurately in multiple directions.It investigates the properties of the shear gradient operator and proposes the shear total variation(STV)norm for image deblurring.By combining non-convex regularization to avoid excessive penalty and retain image details,a novel deblurring model integrating the STV norm and the L_(1)/L_(2) minimization is proposed.The alternating direction method of multipliers(ADMM)algorithm is employed to solve this computationally challenging model,demonstrating exceptional performance in non-blind image deblurring through experiments.展开更多
经典三维/四维变分融合基于误差服从高斯分布,在极小化迭代时涉及到求解目标泛函梯度,若资料不连续则不可微,从而无法求解相应梯度,故理论要求所融合的资料必须具有"连续性"。采用扩展经典三维/四维变分融合方法,显式地基于L...经典三维/四维变分融合基于误差服从高斯分布,在极小化迭代时涉及到求解目标泛函梯度,若资料不连续则不可微,从而无法求解相应梯度,故理论要求所融合的资料必须具有"连续性"。采用扩展经典三维/四维变分融合方法,显式地基于L1范数把先验知识作为正则项约束项耦合到经典变分融合模型。在实施过程中把资料映射到小波域,采用新的融合模型在"小波空间"完成资料融合后,再采用小波逆变换映射回"观测空间"。通过线性平流扩散方程作为四维预报模式进行理想试验,试验设计融合背景和观测资料不连续,即在某些点左右导数不相等,试验结果表明文中采用的方法可行。进一步将该方法用于多源降水资料融合试验,采用基于GAMMA拟合函数的概率密度匹配法(Probability Density Function matching method,PDF)进行CMORPH反演降水资料订正,再将订正后的资料与地面站观测资料进行融合。通过与参考场结构相似性度量,得到该方法能更好地保留代表一些天气现象的"离群点"。该融合方法为不连续资料融合,尤其是"跳变点"的变分融合奠定了理论基础并提供了可借鉴的方法。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The trace norm of matrices plays an important role in quantum information and quantum computing. How to quantify it in today’s noisy intermediate scale quantum(NISQ) devices is a crucial task for information processing. In this paper, we present three variational quantum algorithms on NISQ devices to estimate the trace norms corresponding to different situations.Compared with the previous methods, our means greatly reduce the requirement for quantum resources. Numerical experiments are provided to illustrate the effectiveness of our algorithms.
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.
基金Supported by the National Natural Science Foundation of China(61701004)。
文摘The utilization of gradient operators is prevalent in image processing,as they effectively detect edges and provide directional information.However,these operators only differentiate the horizontal and vertical directions,ignoring details and causing loss of information in other directions.This paper introduces the shear gradient operator to overcome this limitation by capturing details accurately in multiple directions.It investigates the properties of the shear gradient operator and proposes the shear total variation(STV)norm for image deblurring.By combining non-convex regularization to avoid excessive penalty and retain image details,a novel deblurring model integrating the STV norm and the L_(1)/L_(2) minimization is proposed.The alternating direction method of multipliers(ADMM)algorithm is employed to solve this computationally challenging model,demonstrating exceptional performance in non-blind image deblurring through experiments.
文摘经典三维/四维变分融合基于误差服从高斯分布,在极小化迭代时涉及到求解目标泛函梯度,若资料不连续则不可微,从而无法求解相应梯度,故理论要求所融合的资料必须具有"连续性"。采用扩展经典三维/四维变分融合方法,显式地基于L1范数把先验知识作为正则项约束项耦合到经典变分融合模型。在实施过程中把资料映射到小波域,采用新的融合模型在"小波空间"完成资料融合后,再采用小波逆变换映射回"观测空间"。通过线性平流扩散方程作为四维预报模式进行理想试验,试验设计融合背景和观测资料不连续,即在某些点左右导数不相等,试验结果表明文中采用的方法可行。进一步将该方法用于多源降水资料融合试验,采用基于GAMMA拟合函数的概率密度匹配法(Probability Density Function matching method,PDF)进行CMORPH反演降水资料订正,再将订正后的资料与地面站观测资料进行融合。通过与参考场结构相似性度量,得到该方法能更好地保留代表一些天气现象的"离群点"。该融合方法为不连续资料融合,尤其是"跳变点"的变分融合奠定了理论基础并提供了可借鉴的方法。
