A TOMOGRAPHIC APPROACH FOR THE EARLY DETECTION OF 2D ROGUE WAVES

A TOMOGRAPHIC APPROACH FOR THE EARLY DETECTION OF 2D ROGUE WAVES

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Abstract

In this paper we propose an ecient 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 specically, the proposed method is based on constructing the 1D Radon transforms of the emerging conical 2D spectra of the waveeld using compressive sampling (CS) and then constructing 2D spectra from those projections using ltered 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 eciently by the proposed method.

Keywords

2D rogue waves, Early detection, Tomography, Compressive sensing.