Optical wavelet matched filters

The wavelet transform decomposes a signal onto a set of basis wavelet functions that are dilated and shifted from the mother functions h(t), satisfying an admissible condition. This transform is compact in both time and frequency domains and is therefore efficient for time-dependent frequency analysis of the signal. We consider the wavelet transform as the correlations between the signal and a bank of wavelet filters, each having a fixed scale.1 Thus, the wavelet transform of a 1D signal is implemented in an optical correlator with multiple strip wavelet filters, and the wavelet transform of a 2D signal is implemented in a multichannel optical correlator. We make the matched filters recording the 4D wavelet transforms of a 2D input image for optical pattern recognition. With the isotropic Mexican-hat wavelets, the wavelet transform becomes the well known Laplacian-Gaussian operator for zero-crossing edge detection. However, we synthesize the filters by combining the wavelet transform filters and the conventional matched filters in the same Fourier plane for pattern recognition. The experimental results will be shown.