Compressive line spectrum estimation with clustering and interpolation

We consider the standard line spectral estimation problem when the number of observed samples is significantly lower than that prescribed by the Nyquist rate. Two families of sparsity-based methods have recently been proposed for this problem. The first one uses an atomic norm minimization algorithm where the atoms correspond to complex exponentials of varying frequencies. The second one defines the sparse coefficient vectors for the signals of interest by designing parametric dictionaries that can be leveraged by sparse approximation algorithms involving clustering and interpolation. This paper compares the performance of these two algorithm families. Experiments show their advantages and disadvantages in terms of precision and complexity.