Grid selection for sparse estimation of spectral-line parameters is a critical problem that was in need of a satisfactory solution: assuming the usual case of a uniform spectral grid how should one select the number of grid points, $K?$ We first present a simple practical rule for choosing an initial value (or initial values) of $K$ in a given situation. Then, we go on to explain how the estimation results corresponding to different values of $K$ can be compared with one another and therefore how to select the “best” value of $K$ among those considered. Furthermore, we introduce a method for detecting when a grid is “too rough” and for obtaining refined parameter estimates in such a case.

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