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基于l-模的Hankel矩阵填充的保结构阈值算法

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基于l-模的Hankel矩阵填充的保结构阈值算法 张江梅, 王川龙太原师范学院工程科学计算山西省高等学校重点实验室, 晋中 030619 Structure-preserving Thresholding Algorithm Based on l-norm for Hankel Matrix Completion ZHANG Jiangmei, WANG ChuanlongHigher 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l-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加速邻近梯度算法、阈值的增广Lagrange乘子算法以及基于F-模的Hankel矩阵填充的保结构阈值算法更有效.
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收稿日期: 2017-09-21
PACS:O241.5
基金资助:国家自然科学基金(11371275)资助项目.

引用本文:
张江梅, 王川龙. 基于l-模的Hankel矩阵填充的保结构阈值算法[J]. 应用数学学报, 2019, 42(1): 55-70. ZHANG Jiangmei, WANG Chuanlong. Structure-preserving Thresholding Algorithm Based on l-norm for Hankel Matrix Completion. Acta Mathematicae Applicatae Sinica, 2019, 42(1): 55-70.
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