A Nonconvex Approach for Line Spectral Estimation

As a significant problem in statistic signal processing, line spectral estimation has wide applications in radar, sonar and wireless communications. In this paper, we propose a novel nonconvex approach for estimating the frequency parameters of a superposition of complex sinusoids from noisy samples. By assuming that the number of frequencies is known, we formulate frequency estimation as a rank-constrained nonconvex optimization problem based on the double Hankel model that we proposed recently, and then resolve it using the alternating direction method of multipliers (ADMM). Numerical results are conducted that demonstrate the superior performance of our approach in improving the estimation accuracy compared with the existing method.