Forward Network
Since the forward neural network serves as a "standard' for measuring the performance of the feedback neural network scheme, it must be capable of accurately estimating the signal obtained from a variety of defect profiles. A wavelet basis function neural network is used for implementing the forward network. The structure of a wavelet basis function network is shown at right. The wavelet basis function neural network uses a multi-resolution function approximation.Hwang97] given by
The networks use a single hidden layer with sets of function nodes depending on the number of resolutions. A family of wavelets is used as the basis functions and the network is fully interconnected. Training of wavelet basis function neural networks involves determining the weights connecting the hidden layer nodes to the output layer nodes as well as the centers and spreads of the basis functions. Centers of the scaling functions at the coarse (or first) resolution are determined by using a K-means clustering algorithm while the centers of the wavelet functions at higher (or finer) resolutions are computed using a dyadic grid. The spreads of these functions are set proportional to the cluster sizes. The interconnection weights are then computed using a matrix inversion step. The network used in this study employs Mexican hat functions as the wavelet and a Gaussian function is employed as the scaling function. |
