# A Tomographic Approach For the Early Detection of 2D Rogue Waves

## TL;DR

This paper introduces a tomographic method utilizing Radon transforms and compressed sensing to detect 2D rogue waves early by identifying their characteristic conical spectral features before they become visually apparent.

## Contribution

The paper presents a novel tomographic approach combining Radon transforms, compressed sensing, and filtered back projection to detect 2D rogue waves early based on their spectral signatures.

## Key findings

- Efficient detection of conical spectra of rogue waves before they are visible.
- Successful modeling using Peregrine and Akhmediev-Peregrine solitons.
- Potential for early warning systems in oceanography.

## Abstract

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.