The distortion of a signal due to noise contamination can be overcome by using a decomposition of the signal in a base of wavelets. If the decomposition coefficients are small compared with the noise, the scene is dominated by the distortion. On the contrary, if they are bigger in absolute value, the signal is stronger that the noise. A way of reconstructing an image with a lower level of noise is accomplished neglecting the coefficients which values are lower than a threshold, and replacing them by zero. In this work we present a method that applies the thresholding of the wavelet coefficients in order to perform pattern recognition of noisy scenes. The method could be implemented in optical processing by using a Vander Lugt correlator architecture operating with liquid crystal displays. The function to be recognized is decomposed in sub-bands based on the Gabor decomposition, in the frequency plane. Hard thresholding is performed and the threshold is generated with accurate support functions in the filter plane. The criterion for the threshold selection is chosen to optimize the signal to noise ratio in the output plane. Numerical simulations results are shown and comparisons with other filters are made.
We propose here a method to optically perform multiple feature extraction using wavelet transforms. The method is based on obtaining the optical correlation by means of a Vander Lugt architecture, where the scene and the filter are displayed on spatial light modulators (SLM). Multiple phase filters containing the information about the features that we are interested on extracting are designed and then displayed on a SLM working in mostly phase mode. We have designed filters where edges and corners or different characteristic frequencies contained on the input scene are detected. Simulated and experimental results are shown.