Chaotic Analog-to-Information Conversion with Chaotic State Modulation

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.