# Efficient Measurement of the Vibrational Rogue Waves by Compressive Sampling Based Wavelet Analysis

## TL;DR

This paper presents a novel approach using compressive sampling and wavelet analysis to efficiently detect and measure vibrational rogue waves early, reducing memory needs and enabling practical sensing systems.

## Contribution

It introduces a method combining compressive sampling with wavelet analysis for early detection of vibrational rogue waves, which is more efficient than traditional techniques.

## Key findings

- Triangular wavelet spectra can be detected early in rogue wave development.
- Compressive measurements can reconstruct wave spectra with reduced data.
- Potential for developing low-memory rogue wave sensing systems.

## Abstract

In this paper we discuss the possible usage of the compressive sampling based wavelet analysis for the efficient measurement and for the early detection of one dimensional (1D) vibrational rogue waves. We study the construction of the triangular (V-shaped) wavelet spectra using compressive samples of rogue waves that can be modeled as Peregrine and Akhmediev-Peregrine solitons. We show that triangular wavelet spectra can be sensed by compressive measurements at the early stages of the development of vibrational rogue waves. Our results may lead to development of the efficient vibrational rogue wave measurement and early sensing systems with reduced memory requirements which use the compressive sampling algorithms. In typical solid mechanics applications, compressed measurements can be acquired by randomly positioning single sensor and multisensors.

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Source: https://tomesphere.com/paper/1706.01972