  In this paper, we provide a method to recover off-the-grid frequencies of a
signal in two-dimensional (2-D) line spectral estimation. Most of the
literature in this field focuses on the case in which the only information is
spectral sparsity in a continuous domain and does not consider prior
information. However, in many applications such as radar and sonar, one has
extra information about the spectrum of the signal of interest. The common way
of accommodating prior information is to use weighted atomic norm minimization.
We present a new semidefinite program using the theory of positive
trigonometric polynomials that incorporate this prior information into 2-D line
spectral estimation. Specifically, we assume prior knowledge of 2-D frequency
subbands in which signal frequency components are located. Our approach
improves the recovery performance compared with the previous work that does not
consider prior information. Through numerical experiments, we find out that the
amount of this improvement depends on prior information we have about the
locations of the true frequencies.
