Gridless compressive-sensing methods for frequency estimation: Points of tangency and links to basics

The gridless compressive-sensing methods form the most recent class of approaches that have been proposed for estimating the frequencies of sinusoidal signals from noisy measurements. In this paper we review these methods with the main goal of providing new insights into the relationships between them and their links to the basic approach of nonlinear least squares (NLS).We show that a convex relaxation of penalized NLS leads to the atomic-norm minimization method. This method in turn can be approximated by a gridless version of the SPICE method, for which the dual problem is shown to be equivalent to the global matched filter method.