  Chaotic compressive sensing is a nonlinear framework for compressive sensing.
Along the framework, this paper proposes a chaotic analog-to-information
converter, chaotic modulation, to acquire and reconstruct band-limited sparse
analog signals at sub-Nyquist rate. In the chaotic modulation, the sparse
signal is randomized through state modulation of continuous-time chaotic system
and one state output is sampled as compressive measurements. The reconstruction
is achieved through the estimation of the sparse coefficients with principle of
chaotic impulsive synchronization and Lp-norm regularized nonlinear least
squares. The concept of supreme local Lyapunov exponents (SLLE) is introduced
to study the reconstructablity. It is found that the sparse signals are
reconstructable, if the largest SLLE of the error dynamical system is negative.
As examples, the Lorenz system and Liu system excited by the sparse multi-tone
signals are taken to illustrate the principle and the performance.
