A computationally efficient neural network-based scheme for wavefront reconstruction and restoration of turbulence-degraded imagery in Adaptive Optics (AO)-based telescopes is described in this paper. Currently popular methods for the estimation of turbulence-generated distortions suffer from high computational complexity that preclude real-time implementations. For overcoming this "curse of dimensionality", a discrete cosine transform (DCT)-based feature extraction scheme that provides a reduced set of features to train a neural network estimator is described in this work. A dimensionality reduction of up to two orders of magnitude, accompanied by a relatively insignificant loss of overall information, and consequently in the overall performance, is achieved by the proposed scheme. Two neural network architectures, Multilayer Perceptron (MLP) and Radial Basis Function (RBF), trained to estimate wavefront parameters are described and their relative performance in AO implementations is outlined. Performance differences measured in terms of specific quantities of interest, such as Strehl ratio, point to the architectural differences and training methods for these two neural networks. The present work represents a novel application of the power of neural networks in facilitating real-time implementation of these systems.