  In this paper we propose an efficient tomographic approach for the early
detection of 2D rogue waves. The method relies on the principle of detecting
conical spectral features before rogue wave becomes evident in time. More
specifically, the proposed method is based on constructing the 1D Radon
transforms of the emerging conical 2D spectra of the wavefield using
compressive sampling (CS) and then constructing 2D spectra from those
projections using filtered back projection (FBP) algorithm. For the 2D rogue
wave models we use the radially symmetric Peregrine soliton and
Akhmediev-Peregrine soliton solutions of the nonlinear Schrodinger equation,
which can model characteristics of the peaked structure of 2D rogue waves and
their conical spectra which may be treated as a sparse signal. We show that
emerging conical spectra of 2D rogue waves before they become evident in time
can be acquired efficiently by the proposed method.
