数值计算与计算机应用
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数值计算与计算机应用  2018, Vol. 39 Issue (1): 60-72    DOI:
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基于F-模的Hankel矩阵填充的保结构阈值算法
王川龙, 张江梅
工程科学计算山西省高等学校重点实验室, 太原师范学院, 晋中 030619
STRUCTURE-PRESERVING THRESHOLDING ALGORITHM BASED ON F-NORM FOR HANKEL MATRIX COMPLETION
Wang Chuanlong, Zhang Jiangmei
Higher Education Key Laboratory of Engineering and Scientific Computing in Shanxi Province, Taiyuan Normal University, Jinzhong 030619, China
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摘要 文章基于F-范数的性质及奇异值阈值方法,提出Hankel矩阵填充的一种算法.该算法保证每次迭代产生的填充矩阵是可行的Hankel矩阵,不仅减少了奇异值分解所用的时间,而且获得更精确的填充矩阵.同时,讨论了新算法的收敛性.最后通过数值实验以及简单的图像修复证明新算法比阈值的增广Lagrange乘子算法更有效.
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关键词F-模   保结构   矩阵填充   Hankel矩阵     
Abstract: In this paper, based on the property of the F-norm and the method of the singular value threshold, we present an algorithm for Hankel matrix completion. The proposed algorithm ensures each iterative matrix is feasible Hankel structure, which not only decreases the computation of SVD but also gains more effective approximation to solution in precision. Meanwhile, the convergence of the new algorithm is established. Finally, the numerical examples and inpainted images show that the proposed algorithm is more effective than the ALM (augmented Lagrange multiplier) algorithm for Hankel matrix completion.
Key wordsF-norm   structure-preserving   matrix completion   Hankel matrix   
收稿日期: 2017-04-18;
基金资助:

国家自然科学基金(11371275);山西省自然科学基金(201601D011004).

引用本文:   
. 基于F-模的Hankel矩阵填充的保结构阈值算法[J]. 数值计算与计算机应用, 2018, 39(1): 60-72.
. STRUCTURE-PRESERVING THRESHOLDING ALGORITHM BASED ON F-NORM FOR HANKEL MATRIX COMPLETION[J]. Journal of Numerical Methods and Computer Applicat, 2018, 39(1): 60-72.
 
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