The Applications In The Optical Information Processing Of Wavelet Transform

The paper introduces the fundamental theories and characters of wavelet transform, especially the multi-resolution analysis and band-pass filtering characters, puts forward the optical realization of wavelet transform of 1-D and 2-D signals, analyzes the optical filter systems with wavelet transform, improves the feasibility and advantages of wavelet transform used into optical information processing. As a practical and typical application of optical-wavelet-transform in the field of optical information processing, the paper makes a fairly detailed study on the special information extraction of an optical image with a wavelet-filtering system.The paper is composed of the following parts:1 -The fundamental theory of wavelet analysis. In this part, the paper mainly introduces the definition and characters of wavelet transform. Wavelet analysis is one of the time-frequency analysis (as for space-frequency signals, it's a spatial-frequency analysis). Differing from the traditional Fourier transform, which is an overall-domain transform, wavelet transform is one that has the partial domain property both in time/space and frequency domains. The function family which deduces from an elementary function (the mother wavelet) by translations and dilatations are the base function of wavelet analysis. The type of the base function of wavelet analysis is not single, while the FT has only the sine (or cosine) function or exponential function. Wavelet transformation has the character of multi-resolution analysis. Wavelet transformation can analyze the signal in any precision (resolution) at any part of time and frequency according to the different translation factors and dilatation factors.2.The similarity between the phenomenon of light diffraction and the wavelettransformation. The theory of diffraction is the fundamention of optical information processing, in fact, is a light propagation law. hi this part, we analyze the feature showed in the light propagation process, contrast with the wavelet transform, they have much similarity. And the normal conception of wavelet transform is developed, a generalized wavelet transform argument is put forward.S.The optical information processing with wavelet transform. In this part, the optical realization of 1-D and 2-D wavelet transform is introduced. As analyzing the optical spatial filter and frequency domain filter with wavelet transform, the space variable processing > matched filtering and imagery system are the examples. All of these confirm the feasibility of wavelet transform applied in optical information processing.4. Special information extraction of optical image based on wavelet filter system. The information we interested can be any frequency part of an image. So, in this section, a double-passage 4f wavelet filtering optical system is put forward, combining with the visual computation theory. The DOG wavelet function is selected in the filter system, and the output images are just the expected, hi this part, an optical-electrical mixed system model is also mentioned, which has the advantages both in optical processing and digital processing system, such as real-time > intelligence.