Matrix completion is about recovering a matrix from its partial revealed entries, and it can often be achieved by exploiting the inherent simplicity or low dimensional structure of the target matrix. For instance, a typical notion of matrix simplicity is low rank. In this paper we study matrix completion based on another low dimensional structure, namely the low rank Hankel structure in the Fourier domain. It is shown that matrices with this structure can be exactly recovered by solving a convex optimization program provided the sampling complexity is nearly optimal. Empirical results are also presented to justify the effectiveness of the convex method.

中文翻译：

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傅里叶域中基于低秩Hankel结构的精确矩阵完成

矩阵完成是关于从其部分显示的条目中恢复矩阵，并且通常可以通过利用目标矩阵固有的简单性或低维结构来实现。例如，矩阵简单性的典型概念是低等级。在本文中，我们研究基于另一个低维结构的矩阵完成，即傅立叶域中的低秩汉克尔结构。结果表明，只要采样复杂度几乎最佳，就可以通过求解凸优化程序来精确恢复具有这种结构的矩阵。实验结果也证明了凸方法的有效性。