Low-rank matrix recovery via smooth rank function and its application in image restoration
Low-rank matrix recovery via smooth rank function and its application in image restoration
复制标题
基于平滑秩函数的低秩矩阵恢复及其在图像恢复中的应用
DOI：
10.1007/s13042-017-0665-9
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发表时间：
2018
影响因子：
5.6
通讯作者：
Zeng Ming
中科院分区：
文献类型：
--
作者：
Wang Hengyou;Zhao Ruizhen;Cen Yigang;Liang Liequan;He Qiang;Zhang Fengzhen;Zeng Ming
近年来，由于光滑秩函数一般比现有方法更接近本质秩函数，因此被用来处理矩阵完备化问题。提出了一种基于光滑函数的低秩矩阵恢复问题的新方法。它不仅用一个光滑函数来逼近秩函数，而且用一个连续可微的函数来逼近-范数。此外，梯度下降的方法被用来解决最小化问题。最后，实验结果表明，我们提出的算法提供了一个较高的准确性，在大多数情况下，合理的运行时间。特别是对于加性高斯噪声、瑞利噪声以及高斯噪声和椒盐噪声的混合噪声，该方法具有更高的逼近性能。
Recently, due to smooth rank function generally lie much closer to essential rank function than existing methods, it was used to handle matrix completion problem. In this paper, a new approach for solving low-rank matrix recovery problem based on smooth function is proposed. It not only uses a smooth function to approximate the rank function, but also approximates the-norm with a continuous and differentiable function. In addition, gradient decreasing approach is used to solve the minimization problem. Finally, experimental results show that our proposed algorithm provides a higher accurate in most cases with reasonable running time. Especially, it has higher approximation performance than other methods for additive Gaussian noise, Rayleigh noise, and mixed noise of Gaussian and salt and pepper noise.