Line Spectral Estimation Using a G-Filter: Atomic Norm Minimization with Multiple Output Vectors

TL;DR

This paper introduces an advanced atomic norm minimization method using a G-filter with multiple output vectors to improve frequency estimation accuracy in noisy signals, especially at low SNR.

Contribution

It extends previous G-filter ANM methods by incorporating multiple output vectors, enhancing data utilization and robustness in frequency estimation.

Findings

Outperforms standard ANM in frequency recovery accuracy

Significantly better in low SNR conditions

Reformulates the problem as a semidefinite program

Abstract

We propose an atomic norm minimization (ANM) estimator of frequencies in a noisy complex sinusoidal signal that integrates Georgiou's filter bank (G-filter) with multiple output vectors (MOV). Unlike our previous work on the G-filter version of ANM which is restricted to a single filtered output vector, the proposed method in this paper uses MOV to improve data utilization and robustness of the estimate. The ANM problem with MOV can be reformulated as a semidefinite program thanks to a Carath\'eodory--Fej\'er-type decomposition for output covariance matrices of the G-filter. Numerical simulations demonstrate that the proposed approach significantly outperforms the standard ANM and the G-filter version of ANM with a single output vector in recovering the correct number of frequency components when the frequencies fall within the band(s) selected by the G-filter, particularly in the low SNR regime.