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arXiv · 1609.08198

Generalized Line Spectral Estimation via Convex Optimization

Reinhard Heckel·Mahdi Soltanolkotabi
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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.

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Reinhard Heckel, Mahdi Soltanolkotabi. 2016-09-26. Generalized Line Spectral Estimation via Convex Optimization. https://arxiv.org/abs/1609.08198

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