谱压缩感知的非凸低秩矩阵优化模型与方法综述

Spectral compressed sensing refers to the problem of recovering spectral-sparse signals and their continuous-valued frequency parameters from limited samples. It is an extension of the classical spectral analysis problem of signals and widely used in information technology fields such as array and radar signal processing and wireless communications. The classical methods for spectral compressed sensing and the convex relaxation methods of this century have limits in the scope of application，estimation accuracy or algorithm speed，which cannot satisfy the urgent demands for high accuracy and speed in technologies such as current 5G and future 6G wireless communications. Recently，a series of nonconvex optimization models based on structured low-rank matrices have been proposed. By characterizing the geometric structures of spectral sparse signals，the original highly non-convex optimization problem in the parameter domain is cast as a structured low-rank matrix recovery problem in the signal domain，which provides a novel solution for the spectral compressed sensing problem and brings a substantial improvement in the algorithm accuracy. In this paper，we systematically review the existing structured low-rank matrix recovery models and algorithms for three types of spectral sparse signals：single-channel，multichannel，and constant modulus，analyze commonalities and differences of these models；and point out possible future research directions.