Chaotic analogue-to-information conversion with chaotic state modulation

Chaotic compressive sensing is a non-linear framework for compressive sensing. Along the framework, this study proposes a chaotic analogue-to-information converter, `chaotic modulation´, to acquire and reconstruct band-limited sparse analogue signals at sub-Nyquist rate. In the chaotic modulation, the sparse signal is randomised 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 the principle of chaotic impulsive synchronisation and l_p-norm regularised non-linear 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 dynamic system is negative. As examples, the Lorenz system and the Liu system excited by sparse multi-tone signals are taken to illustrate the principle and the performance.