提出了Mallat算法的光学实现方法。针对振幅型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,提出一种应用于光学4f系统的光学小波滤波器的设计方法。根据采样间距,基于张量积方法由一维小波滤波器系数构造二维小波滤波函数。然后通过拆分、傅里叶变换与归一化,得到非负的实函数形式的频域小波滤波器。最后,给出相应的光学小波变换后处理方法。使用该种光学小波滤波器及其相应的后处理方法,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。仿真实验结果表明,通过本文提出的方法在理论上能够高精度地重构输入图像;在引入光学器件量化误差的条件下,平均重构PSNR为54.27 dB。利用实际的光学4f系统进行光学实验,也能以良好的质量重构输入图像。仿真分析和光学实验结果验证了方法的正确性。

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.