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We discuss the possible usage of the compressive sampling for the earlydetection of rogue waves. One of the promising techniques for the earlydetection of the oceanic rogue waves is to measure the triangular Fourierspectra which begin to appear at the early stages of their development. For theearly detection of the rogue waves it is possible to treat such a spectrum as asparse signal since we would mainly be interested in the high amplitudetriangular region located at the central wavenumber. Therefore compressivesampling can be a very efficient tool for the rogue wave early warning systems.Compressed measurements can be acquired by remote sensing techniques such ascoherent SAR which measure the ocean surface envelope or by insitu techniquessuch as spectra measuring tools mounted on a ship hull or bottom mountedpressure gauges. By employing a numerical approach we show that triangularFourier spectra can be sensed by compressive measurements at the early stagesof the development of rogue waves such as those in the form of Peregrine andAkhmediev-Peregrine solitons. Our results may lead to development of the earlywarning hardware systems which use the compressive sampling thus the memoryrequirements for those systems can be greatly reduced.

Early Detection of Rogue Waves Using Compressive Sensing