Uncertainty Quantification for Sparse Estimation of Spectral Lines

Line spectral estimation is an important problem that finds many useful applications in signal processing. Many high-performance methods have been proposed for solving this problem: they select the number of spectral lines and provide point estimates of the frequencies and amplitudes of such spectral lines. This paper studies the line spectral estimation problem from a different and equally important angle: uncertainty quantification. More precisely, this paper develops a novel method that provides an uncertainty measure for the number of spectral lines and also offers point estimates and confidence intervals for other parameters of interest. The proposed method is based on the generalized fiducial inference framework and is shown to possess desirable theoretical and empirical properties. It has also been numerically compared with existing methods in the literature and applied for the detection of exoplanets.