Generalized Line Spectral Estimation via Convex Optimization
Abstract
Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we do not have access directly to such equispaced samples. Rather we only observe a severely undersampled version of these observations through linear measurements. This paper is about such generalized line spectral estimation problems. We reformulate these problems as sparse signal recovery problems over a continuously indexed dictionary which can be solved via a convex program. We prove that the frequencies and amplitudes of the components of the mixture can be recovered perfectly from a near-minimal number of observations via this convex program. This result holds provided the frequencies are sufficiently separated, and the linear measurements obey natural conditions that are satisfied in a variety of applications.
Cite
@article{arxiv.1609.08198,
title = {Generalized Line Spectral Estimation via Convex Optimization},
author = {Reinhard Heckel and Mahdi Soltanolkotabi},
journal= {arXiv preprint arXiv:1609.08198},
year = {2016}
}