矩阵补全算法研究进展

Research Progress in Matrix Completion Algorithms

作为压缩感知理论的重要发展,矩阵补全与恢复已成为信号与图像处理的一种新的强有力的工具。综述了矩阵补全算法的最新研究进展。首先分析了核范数最小化模型的几种主要的矩阵补全算法,并对这些算法的迭代过程及原理进行了详细的阐述。其次讨论了矩阵补全的低秩矩阵分解模型,并列出了近年来出现的求解此模型的新算法。然后补充了上述两种模型的衍生版本,指出了相应的求解方法。在数值实验中,对文中所讨论的主要矩阵补全算法的性能进行了比较。最后给出了矩阵补全算法的未来研究方向及重点。

As an important development of compressed sensing theory,matrix completion and recovery has been a new and remarkable technique for signal and image processing.This paper made a survey on the latest research progress in matrix completion algorithms.Firstly,it analyzed several main algorithms to nuclear norm minimization model,and elaborated their iterative procedure and principle.Secondly,it discussed low-rank matrix factorization model of matrix completion and listed the corresponding new algorithms emerged in recent years.Then it complemented other versions derived from the above two models and pointed out the solving methods.In numerical experiments,performance comparisons were made on the main algorithms to matrix completion.Finally,it gave future research direction and focus for matrix completion algorithms.