COHERENT OPTICAL-PROCESSING OF GABOR AND WAVELET EXPANSIONS OF ONE-DIMENSIONAL AND 2-DIMENSIONAL SIGNALS

Recent development in vision and image understanding related study reveals that a signal decomposition before processing may provide an enormous amount of useful information about the signal. Various signal decomposition models such as the Gabor and wavelet expansions have been proposed. While the Gabor signal expansion creates a fixed resolution space-frequency signal representation, the wavelet transform provides a multiresolution signal space-scale decomposition. Digital implementation of these expansions are computationally intensive both because of the nature of the coordinate-doubling of the transforms and because of the large quantity of convolution/correlation operations to be performed. Optics with its inherent parallel-processing capability has been applied to many useful linear signal and image transformations for feature analysis and extraction. We studied the suitability of using optical processing techniques for the signal Gabor and wavelet analysis. Gabor and wavelet expansions of both 1- and 2-D signals and images are discussed. System parameters and limitations are analyzed. Preliminary experimental results are presented.