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This paper addresses the problem of reconstructing a slowly-varying information-bearing signal from a parametrically modulated, nonstationary dynamical signal. A chaotic electronic oscillator model characterized by one control parameter and a double-scroll-like attractor is used throughout the study. Wavelet transforms are used to extract features of the chaotic signal resulting from parametric modulation of the control parameter by the useful signal. The vector of feature coefficients is fed into a feed-forward neural network that recovers the embedded information-bearing signal. The performance of the developed method is cross-validated through reconstruction of randomly-generated control parameter patterns. This method is applied to the reconstruction of speech signals, thus demonstrating its potential utility for secure communication applications. Our results are validated via numerical simulations. [ABSTRACT FROM AUTHOR]