A Theory of Computational Resolution Limit for Line Spectral Estimation

Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their which contaminated by deterministic or random noise. Despite large body of research on this subject, theoretical understanding still elusive. In paper, we introduce and quantitatively characterize two resolution limits for under noise: one minimum separation distance between required exact detection number, other stable recovery supports. The quantitative results imply phase transition phenomenon in each problems, also subtle difference two. We further propose sweeping singular-value-thresholding algorithm number conduct numerical experiments. confirm problem.