  This paper proposes a chaos-based analog-to-information conversion system for
the acquisition and reconstruction of sparse analog signals. The sparse signal
acts as an excitation term of a continuous-time chaotic system and the
compressive measurements are performed by sampling chaotic system outputs. The
reconstruction is realized through the estimation of the sparse coefficients
with principle of chaotic parameter estimation. With the deterministic
formulation, the analysis on the reconstructability is conducted via the
sensitivity matrix from the parameter identifiability of chaotic systems. For
the sparsity-regularized nonlinear least squares estimation, it is shown that
the sparse signal is locally reconstructable if the columns of the
sparsity-regularized sensitivity matrix are linearly independent. A Lorenz
system excited by the sparse multitone signal is taken as an example to
illustrate the principle and the performance.
