A non-linear training set superposition filter derived by neural network training methods for implementation in a shift invariant optical correlator

The various types of synthetic discriminant function (sdf) filter result in a weighted linear superposition of the training set images. Neural network training procedures result in a non-linear superposition of the training set images or, effectively, a feature extraction process, which leads to better interpolation properties than achievable with the sdf filter. However, generally, shift invariance is lost since a data dependant non-linear weighting function is incorporated in the input data window. As a compromise, we train a non-linear superposition filter via neural network methods with the constraint of a linear input to allow for shift invariance. The filter can then be used in a frequency domain based optical correlator. Simulation results are presented that demonstrate the improved training set interpolation achieved by the non-linear filter as compared to a linear superposition filter.