Mallat算法的光学实现方法

现有的光学小波变换方法均基于连续小波变换，基于离散信号的小波变换算法（Mallat算法）的光学小波变换还没有出现，这阻碍了光学小波变换应用的发展。针对这一问题，分析利用光学4f系统实现Mallat算法的基本原理，提出Mallat算法的光学实现方法。针对空间光调制器只能实现非负的实函数，且CCD只能记录光的强度，给出一种应用于光学4f系统的光学小波滤波器的设计方法。使用该种光学小波滤波器，利用光学4f系统实现Mallat算法的小波分解部分，并通过数值计算实现Mallat算法的小波重构部分。仿真分析和光学实验结果验证了方法的正确性。

Optical Implementation Method of Mallat Algorithm

To expand optical wavelet transform method into the digital signal processing domain,the optical implementation method of discrete wavelet transform algorithm(Mallat algorithm) for optical 4f system is proposed.Because amplitude-only Spatial Light Modulator(SLM) can only implement non-negative real function and CCD can only record light intensity,a design method for optical wavelet filters used in optical 4f system is presented.According to the sampling spacing,the two-dimension wavelet filters are constructed with one-dimension coefficients of wavelet filter in terms of tensor product method.Then the frequency domain wavelet filters in the form of non-negative real function are constructed with splitting,Fourier transform and normalization.Finally,the corresponding optical wavelet transform post-processing method is given.With this kind of optical wavelet filter and its corresponding post-processing method,the wavelet decomposition is implemented by optical 4f system,and wavelet reconstruction by numerical computation in Mallat algorithm.The simulation experimental results show that the input images can be reconstructed theoretically by proposed method with high precision,the average reconstructed PSNR is 54.27 dB,even under the condition of introducing the optical device quantization error.Also,the input images with good quality can be reconstructed by optical experiment in actual optical 4f system.The simulation analysis and optical experimental results verify proposed method.