论文标题
通过Hankel矩阵完成的光谱稀疏信号恢复，并提供先验信息
Spectrally Sparse Signal Recovery via Hankel Matrix Completion with Prior Information
论文作者
论文摘要
本文研究了通过借助先验信息的低率汉克尔矩阵完成，从一个小时的时域样本中重建稀疏的信号的问题。通过利用举升域中频谱稀疏信号的低排列结构以及信号及其先前信息之间的相似性，我们提出了一种凸方法来恢复频谱稀疏信号。所提出的方法将所需信号的内部产物及其在升力域中的先前信息集成到香草hankel矩阵完成中，从而最大程度地提高了信号及其先前信息之间的相关性。理论分析表明，当先验信息可靠时，提出的方法的性能要比汉克尔矩阵完成更好，这可以减少对数因子的测量数量。我们还开发了一种ADMM算法来解决相应的优化问题。提供数值结果以验证所提出的方法的性能和相应的算法。
This paper studies the problem of reconstructing spectrally sparse signals from a small random subset of time domain samples via low-rank Hankel matrix completion with the aid of prior information. By leveraging the low-rank structure of spectrally sparse signals in the lifting domain and the similarity between the signals and their prior information, we propose a convex method to recover the undersampled spectrally sparse signals. The proposed approach integrates the inner product of the desired signal and its prior information in the lift domain into vanilla Hankel matrix completion, which maximizes the correlation between the signals and their prior information. Theoretical analysis indicates that when the prior information is reliable, the proposed method has a better performance than vanilla Hankel matrix completion, which reduces the number of measurements by a logarithmic factor. We also develop an ADMM algorithm to solve the corresponding optimization problem. Numerical results are provided to verify the performance of proposed method and corresponding algorithm.
