  This paper proposes a compressed sensing (CS) framework for the acquisition
and reconstruction of frequency-sparse signals with chaotic dynamical systems.
The sparse signal is acting as an excitation term of a discrete-time chaotic
system and the compressed measurement is obtained by downsampling the system
output. The reconstruction is realized through the estimation of the excitation
coefficients with principle of impulsive chaos synchronization. The -norm
regularized nonlinear least squares is used to find the estimation. The
proposed framework is easily implementable and creates secure measurements. The
Henon map is used as an example to illustrate the principle and the
performance.
