  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.
