New low-rank optimization model and algorithms for spectral compressed sensing  

作　　者：Zai Yang Xunmeng Wu Zongben Xu 

机构地区：[1]School of Mathematics and Statistics,Xi'an Jiaotong University,Xi'an 710049,China

出　　处：《Science China Mathematics》2024年第10期2409-2432,共24页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 61977053 and 11922116)。

摘　　要：In this paper, we investigate the recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples within the framework of spectral compressed sensing and super-resolution. We show that the existing Hankel-based optimization methods suffer from the fundamental limitation that the prior knowledge of undampedness cannot be exploited. We propose a new low-rank optimization model partially inspired by forward-backward processing for line spectral estimation and show its capability to restrict the spectral poles to the unit circle. We present convex relaxation approaches with the model and show their provable accuracy and robustness to bounded and sparse noise. All our results are generalized from one-dimensional to arbitrary-dimensional spectral compressed sensing. Numerical simulations are provided to corroborate our analysis and show the efficiency of our model and the advantageous performance of our approach in terms of accuracy and resolution compared with the state-of-the-art Hankel and atomic norm methods.

关 键 词：low-rank double Hankel model doubly enhanced matrix completion line spectral estimation spectral compressed sensing Kronecker's theorem 

分 类 号：TN911.7[电子电信—通信与信息系统]