Maximum Likelihood Line Spectral Estimation in the Signal Domain: A Rank-Constrained Structured Matrix Recovery Approach

作     者：Wu, Xunmeng Yang, Zai Stoica, Petre Xu, Zongben 

作者机构：Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Peoples R China Uppsala Univ Dept Informat Technol S-75105 Uppsala Sweden 

出 版 物：《IEEE TRANSACTIONS ON SIGNAL PROCESSING》 (IEEE Trans Signal Process)

年 卷 期：2022年第70卷

页      面：4156-4169页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 

基　　金：National Natural Science Foundation of China [11922116, 61977053, 61721002] Major Project of Natural Science Foundation of China [U1811461] Swedish Research Council VR [2017-04610, 2016-06079] Swedish Research Council [2017-04610] Funding Source: Swedish Research Council 

主　　题：Maximum likelihood estimation Signal processing algorithms Convex functions Noise measurement Frequency estimation Convergence Optimization methods Line spectral estimation maximum likelihood estimation Hankel-Toeplitz optimization model rank-constrained structured matrix recovery ADMM nonconvex optimization 

摘      要：Maximum likelihood estimation (MLE) provides a well-known benchmark for line spectral estimation and has been extensively studied in the parameter domain using a variety of optimization algorithms. To overcome the sensitivity of these algorithms to parameter initialization, in this paper we study the MLE in the signal domain. We formulate the MLE as an equivalent rank-constrained structured matrix recovery problem that admits a unique matrix solution containing the signal, from which the parameters of interest are uniquely retrieved. The alternating direction method of multipliers (ADMM) is used to solve the rank-constrained problem and it is shown to have a good convergence behavior. The proposed approach is generalized to the case of missing data and arbitrary-dimensional line spectral estimation. Extensive numerical results are provided that corroborate our analysis and confirm that the proposed approach globally solves the MLE problem and outperforms state-of-the-art algorithms.