Effectiveness of the tail-atomic norm in gridless spectrum estimation

An effective tail-atomic norm methodology and algorithms for gridless spectral estimations are developed with a tail-minimization mechanism. We prove that the tail-atomic norm can be equivalently reformulated as a positive semi-definite programming (PSD) problem as well. Some delicate and critical weighting constraints are derived. Iterative tail-minimization algorithms based on PSD programming are also derived and implemented. Extensive simulation results demonstrate that the tail-atomic norm mechanism substantially outperforms state-of-the-art gridless spectral estimation techniques. Numerical studies also show that the tail-atomic norm approach is more robust to noisy measurements than other known related atomic norm methodologies.