We describe a new nonlinear discriminant analysis method for feature extraction. This method applies a nonsingular transform to the data such that the transformed data have a Gaussian distribution. Then a Bayes likelihood ratio is calculated for the transformed data. The nonsingular transform makes use of wavelet transforms and histogram matching techniques. Wavelet transforms are an effective tool in analyzing data structures. Histogram matching is applied to the wavelet coefficients and the ordinary image pixel values in order to create a transformed image that has the desired Gaussian statistics.