When atomic norm meets the G-filter: A general framework for line spectral estimation

TL;DR

This paper introduces a unified framework combining G-filter and atomic norm minimization for improved line spectral estimation, demonstrating superior performance over standard ANM especially at moderate noise levels.

Contribution

It develops a new approach that integrates G-filter with atomic norm minimization, including a covariance decomposition and semidefinite programming formulation.

Findings

Outperforms standard ANM in spectral line recovery at SNR ≥ 0 dB.

Uses a Carathéodory-Fejér-type decomposition for covariance matrices.

Framework generalizes existing spectral estimation methods.

Abstract

This paper proposes a novel approach for line spectral estimation which combines Georgiou's filter bank (G-filter) with atomic norm minimization (ANM). A key ingredient is a Carath\'{e}odory--Fej\'{e}r-type decomposition for the covariance matrix of the filter output. The resulting optimization problem can be characterized via semidefinite programming and contains the standard ANM for line spectral estimation as a special case. Simulations show that our approach outperforms the standard ANM in terms of recovering the number of spectral lines when the signal-to-noise ratio is no lower than 0 dB and the G-filter is suitably designed.