Robust line spectral estimation

Line spectral estimation is a classical signal processing problem that finds numerous applications in array signal processing and speech analysis. We propose a robust approach for line spectral estimation based on atomic norm minimization that is able to recover the spectrum exactly even when the observations are corrupted by arbitrary but sparse outliers. The resulting optimization problem is reformulated as a semidefinite program. Our work extends previous work on robust uncertainty principles by allowing the frequencies to assume values in a continuum rather than a discrete set.