基于先验信息的Hankel矩阵完备的谱稀疏信号恢复
Spectrally Sparse Signal Recovery via Hankel Matrix Completion with Prior Information
摘要：
本文研究了利用先验信息，通过低秩Hankel矩阵完备化，从时域样本的随机子集重构谱稀疏信号的问题。利用提升域谱稀疏信号的低秩结构和信号与先验信息的相似性，提出了一种基于凸函数的欠采样谱稀疏信号恢复方法.该方法将期望信号与其先验信息在提升域的内积集成到香草Hankel矩阵完备中，最大化了信号与其先验信息之间的相关性。理论分析表明，在先验信息可靠的情况下，该方法比香草Hankel矩阵完备化方法具有更好的性能，其测量次数减少了一个对数因子。我们还开发了一个ADMM算法来解决相应的优化问题。数值结果验证了所提出的方法和相应的算法的性能。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
