A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inne...A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.展开更多
图像修复问题中,局部细节特征的辨识修复和全局特征的保护是至关重要的。基于分数阶偏微分方程的模型具有丰富的演化行为能力,在图像修复中能较好地理解图像细节并兼具一定的锐化作用,但也易出现不能准确辨识较大尺度特征和过度锐化等...图像修复问题中,局部细节特征的辨识修复和全局特征的保护是至关重要的。基于分数阶偏微分方程的模型具有丰富的演化行为能力,在图像修复中能较好地理解图像细节并兼具一定的锐化作用,但也易出现不能准确辨识较大尺度特征和过度锐化等问题。为此提出以图像整体特征的总变差能量为目标函数,空间分数阶向量值Cahn-Hilliard方程为约束的最优控制模型,以达到局部细节修复和整体特征保持的均衡效果。通过L_(2)梯度流、H^(-1)梯度流和凸分裂设计非凸约束条件的数值计算格式,再结合分裂Bregman方法优化目标函数,并引入灰度级动态调整策略,保持灰度辨识能力的同时,进一步提升计算效率。数值实验表明,新模型修复结果的峰值信噪比(peak signal to noise ratio,PSNR)相较其他方法提升0.3718~9.9352 dB,结构相似指数(structural similarity,SSIM)表现出较强的竞争力,且在碎片破损的图像上更具效用;相较传统的分数阶方程模型,计算时间减少49.50%~52.91%。展开更多
The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces....The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces.The strong convergence result for our method is established under some standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping.Several numerical experiments are provided to verify the advantages and efficiency of proposed algorithms.展开更多
针对非光滑非凸–强拟凹鞍点问题,本文利用Bregman距离建立了Bregman近端梯度上升下降算法。对Bregman近端梯度上升迭代算法中,得到内部最大化问题函数差值不等式,从而得到近端梯度上升迭代点之间的不等式关系。对于非凸非光滑问题,引...针对非光滑非凸–强拟凹鞍点问题,本文利用Bregman距离建立了Bregman近端梯度上升下降算法。对Bregman近端梯度上升迭代算法中,得到内部最大化问题函数差值不等式,从而得到近端梯度上升迭代点之间的不等式关系。对于非凸非光滑问题,引入扰动类梯度下降序列,得到算法的次收敛性,当目标函数为半代数时,得到算法的全局收敛性。For the nonsmooth nonconvex-strongly quasi-concave saddle point problems, this paper establishes the Bregman proximal gradient ascent-descent algorithm by using the Bregman distance. In the Bregman proximal gradient ascent iterative algorithm, the difference inequality of the internal maximization problem function is obtained, and thus the inequality relationship between the proxi-mal gradient ascent iterative points is derived. For nonconvex and nonsmooth problems, a perturbed gradient-like descent sequence is introduced to obtain the sub-convergence of the algorithm. When the objective function is semi-algebraic, the global convergence of the algorithm is obtained.展开更多
基金The National Natural Science Foundation of China (No.61362001,61102043,61262084,20132BAB211030,20122BAB211015)the Basic Research Program of Shenzhen(No.JC201104220219A)
文摘A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.
文摘图像修复问题中,局部细节特征的辨识修复和全局特征的保护是至关重要的。基于分数阶偏微分方程的模型具有丰富的演化行为能力,在图像修复中能较好地理解图像细节并兼具一定的锐化作用,但也易出现不能准确辨识较大尺度特征和过度锐化等问题。为此提出以图像整体特征的总变差能量为目标函数,空间分数阶向量值Cahn-Hilliard方程为约束的最优控制模型,以达到局部细节修复和整体特征保持的均衡效果。通过L_(2)梯度流、H^(-1)梯度流和凸分裂设计非凸约束条件的数值计算格式,再结合分裂Bregman方法优化目标函数,并引入灰度级动态调整策略,保持灰度辨识能力的同时,进一步提升计算效率。数值实验表明,新模型修复结果的峰值信噪比(peak signal to noise ratio,PSNR)相较其他方法提升0.3718~9.9352 dB,结构相似指数(structural similarity,SSIM)表现出较强的竞争力,且在碎片破损的图像上更具效用;相较传统的分数阶方程模型,计算时间减少49.50%~52.91%。
基金Supported by NSFC(No.12171062)the Natural Science Foundation of Chongqing(No.CSTB2022NSCQ-JQX0004)+1 种基金the Chongqing Talent Support Program(No.cstc2024ycjh-bgzxm0121)Science and Technology Project of Chongqing Education Committee(No.KJZD-M202300503)。
文摘The purpose of this article is to introduce a new method with a self-adaptive stepsize for approximating a common solution of monotone inclusion problems and variational inequality problems in reflexive Banach spaces.The strong convergence result for our method is established under some standard assumptions without any requirement of the knowledge of the Lipschitz constant of the mapping.Several numerical experiments are provided to verify the advantages and efficiency of proposed algorithms.
文摘针对非光滑非凸–强拟凹鞍点问题,本文利用Bregman距离建立了Bregman近端梯度上升下降算法。对Bregman近端梯度上升迭代算法中,得到内部最大化问题函数差值不等式,从而得到近端梯度上升迭代点之间的不等式关系。对于非凸非光滑问题,引入扰动类梯度下降序列,得到算法的次收敛性,当目标函数为半代数时,得到算法的全局收敛性。For the nonsmooth nonconvex-strongly quasi-concave saddle point problems, this paper establishes the Bregman proximal gradient ascent-descent algorithm by using the Bregman distance. In the Bregman proximal gradient ascent iterative algorithm, the difference inequality of the internal maximization problem function is obtained, and thus the inequality relationship between the proxi-mal gradient ascent iterative points is derived. For nonconvex and nonsmooth problems, a perturbed gradient-like descent sequence is introduced to obtain the sub-convergence of the algorithm. When the objective function is semi-algebraic, the global convergence of the algorithm is obtained.
