| Due to its excellent performance, wavelet transform has been extensively applied to many fields, such as image processing , signal processing and image compression. However, its application is restricted by its computational complexity. Therefore, the optical method and wavelet transform are combined to implement optical wavelet transform, which can greatly reduce the time spent on wavelet transform and has good theoretical and practical value. At present, optical wavelet transform has been applied to many fields, such as edge extraction, feature extraction, pattern recognition, image segmentation as well as computer vision, and shows good prospects. But high precision reconstruction can not be implemented by the existing optical wavelet transform, which restricts its application in some fileds such as image compression. So, the fundamental theory and developments of wavelet transform were systematically described in this dissertation, with the characteristics of optical wavelet transform being analyzed in detail, the principle and optical implementation methods of multiresolution analysis being deeply studied.The image spatial frequency characteristic in optical 4f system was studied. The fundamental theory of spatial frequency was described. Then effects on the spatial frequency characteristic were analyzed which caused by way of image realization and image acquisition in optical 4f system, and researches on the relationship among the characteristic of energy concentration of image in frequency domain, radius of spatial filter and the qualities of the reconstructed image were carried out. The qualities of the reconstructed image with different input sizes were compared. The relevant calculational and analysis methods were given. The theoretical analysis, simulations and optical experiments have shown that the spatial filtering radius of optical wavelet transform applied to some fileds requiring high precision reconstruction such as image compression is restricted by the size of input images, the adaxial condition, the sampling characteristic of apparatus in optical 4f system, the characteristic of energy concentration of image in frequency domain and the system noise. The restrictive conditions on the sizes of input image were given.The optical implementation method of multiresolution analysis was studied. Connections between the scaling and wavelet functions and coefficients of wavelet filter were analyzed. Three algorithms on the computation of the scaling and wavelet function using coefficients of wavelet filter were introduced, and iterative convolution algorithm was improved, meanwhile the method of judging the convergence of iterative convolution was given. Principles of multiresolution analysis and optical 4f system were deeply analyzed, then the optical implementation method of multiresolution analysis based on continuous wavelet transform utilizing optical 4f system was studied. As CCD can only record light intensity, a design method of optical wavelet filters applied to optical 4f system and the relevant post-processing method were given, meanwhile the reconstruction method of multiresolution analysis by numerical computation utilizing computer was presented. Through simulations and theoretical analysis, the limitations on the optical implementation method of continuous wavelet transform were indicated.Optical implementation method of Mallat algorithm was proposed. Based on the theory of multiresolution analysis, the core principle of Mallat algorithm and optical 4f system were analyzed, and the feasibility on Mallat algorithm implemented by optical 4f system was demonstrated, meanwhile optical implementation method of Mallat algorithm was proposed. As amplitude-only SLM (Spatial Light Modulator) can only implement non-negative real function and CCD can only record light intensity, a design method of optical wavelet filters applied to optical 4f system was presented. Firstly, according to the sampling interval, the two-dimensional wavelet filters were constructed with one-dimensional coefficients of wavelet filter in terms of tensor product method. Then the frequency domain wavelet filters in the form of non-negative real function were constructed by splitting, Fourier transform and normalization. At last, the relevant post-processing method of optical wavelet transform was given. With this kind of optical wavelet filter and its relevant post-processing method, the wavelet decomposition in Mallat algorithm was implemented utilizing an optical 4f system, and the wavelet reconstruction in Mallat algorithm was implemented by numerical computation. Simulation results indicated that input images can almost be perfectly reconstructed by the presented method, and input images can be reconstructed with high precision under the conditions of quantization errors introduced by optical devices. Input images can also be reconstructed with good quality by optical experiment utilizing an actual optical 4f system. Furthermore, a method of hybrid optical wavelet transform was presented to eliminate coherent noise. The scale consistency of optical wavelet filter in both frequency and spacial domain as well as the relevant design method was studied. The low-pass filtering of wavelet decomposition in Mallat algorithm was implemented utilizing a defocus system, while the high-pass filtering of wavelet decomposition in Mallat algorithm was implemented utilizing an optical 4f system. The wavelet reconstruction in Mallat algorithm was implemented by numerical computation utilizing computer.The optimized design method on optical wavelet filter was studied. Through computer simulation, the quantization error of optical wavelet filter constructed by different wavelet bases was studied, the effect on quantization error due to the exchange of decomposition wavelets with reconstruction wavelets was compared, and the effect on quantization error due to different sampling frequencies in frequency domain was analyzed. According to the least quantization error criteria of optical wavelet filter both in spacial domain and frequency domain, an optimal wavelet base was constructed based on lifting algorithm.
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