  Recent research in off-the-grid compressed sensing (CS) has demonstrated
that, under certain conditions, one can successfully recover a spectrally
sparse signal from a few time-domain samples even though the dictionary is
continuous. In this paper, we extend off-the-grid CS to applications where some
prior information about spectrally sparse signal is known. We specifically
consider cases where a few contributing frequencies or poles, but not their
amplitudes or phases, are known a priori. Our results show that equipping
off-the-grid CS with the known-poles algorithm can increase the probability of
recovering all the frequency components.
