On Gridless Sparse Methods for Line Spectral Estimation From Complete and Incomplete Data
This addresses frequency estimation challenges in signal processing by providing more accurate gridless methods, though it appears incremental as it builds on existing atomic norm and SPICE approaches.
The paper tackles the problem of estimating continuous frequencies in line spectral estimation by developing gridless sparse methods that avoid grid mismatches, presenting gridless SPICE (GLS) for both complete and incomplete data without requiring noise level knowledge. It proves equivalence between GLS and atomic norm-based techniques under different noise assumptions and demonstrates performance through numerical simulations.
This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., $\ell_1$ optimization and SPICE, with an infinitely dense grid. We generalize AST (atomic-norm soft thresholding) to the case of nonconsecutively sampled data (incomplete data) inspired by recent atomic norm based techniques. We present a gridless version of SPICE (gridless SPICE, or GLS), which is applicable to both complete and incomplete data without the knowledge of noise level. We further prove the equivalence between GLS and atomic norm-based techniques under different assumptions of noise. Moreover, we extend GLS to a systematic framework consisting of model order selection and robust frequency estimation, and present feasible algorithms for AST and GLS. Numerical simulations are provided to validate our theoretical analysis and demonstrate performance of our methods compared to existing ones.