基于F-模的Hankel矩阵填充的保结构阈值算法

STRUCTURE-PRESERVING THRESHOLDING ALGORITHM BASED ON F-NORM FOR HANKEL MATRIX COMPLETION

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.

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.