【作者】 韩亮；

【导师】 田逢春；

【作者基本信息】 重庆大学 ， 电路与系统， 2008， 博士

【摘要】 由于其良好的性能,小波变换在图像处理、信号处理以及图像压缩等领域中得到了广泛的应用,然而其庞大的计算量制约了小波变换应用的进一步推广。因此,将光学方法与小波变换结合起来,形成光学小波变换方法,可以极大地减少小波变换所花的时间,这是很有理论和实用价值的。目前,光学小波变换已经被应用于边缘提取、特征提取、模式识别、图像分割、机器视觉等领域,显示出很好的应用前景。但是,现有的光学小波变换方法无法通过数值计算进行高精度的重构,这限制了它在图像压缩等领域中的应用。为此,本论文全面系统地阐述了小波变换的发展动态和基本理论,详细分析了光学小波变换的特性,深入研究了多分辨率分析的原理和光学实现方法。研究光学4f系统的图像空间频率特性。阐述空间频率的基本理论,分析光学4f系统中图像实现方式和图像采集方式对图像空间频率特性的影响,研究输入图像频域能量集中度与对应图像重建质量及空间滤波半径的关系,比较不同尺寸的输入图像空间滤波后的图像重建质量的差异,给出关于光学4f系统中图像空间频率特性的计算和分析方法。通过理论分析、仿真计算和光学实验,表明用于图像压缩等需要高精度重构的领域的光学小波变换在频谱面上的空间滤波范围受到输入图像尺寸、近轴条件、光学4f系统的器件采样特性、图像频域能量集中度以及系统噪声的影响,并给出了输入图像尺寸的约束条件。研究多分辨率分析的光学实现方法。分析小波滤波器系数与尺度函数和小波函数的关系,介绍由小波滤波器系数求尺度函数和小波函数的三种常用算法,并对其中的迭代卷积算法进行改进,同时给出其相应的收敛判定方法。深入分析多分辨率分析和光学4f系统的基本原理,研究利用光学4f系统实现基于连续小波变换的多分辨率分析的方法。针对CCD(Charge Coupled Device)只能直接记录光的强度,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及其后处理方法,并给出利用计算机通过数值计算实现光学多分辨率分析的重构方法。通过仿真实验和理论分析,说明连续小波变换的光学实现方法的局限性。提出Mallat算法的光学实现方法。从多分辨率分析理论出发,分析Mallat算法的核心思想和光学4f系统的基本原理,论证利用光学4f系统实现Mallat算法的可行性,提出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只能直接记录光的强度,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。首先,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,通过该方法能够极好地重构输入图像;在引入光学器件量化误差的条件下,通过该方法仍然能够高精度地重构输入图像。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。此外,针对相干噪声问题,还实现了一种混合光学小波变换。研究空域和频域形式的光学小波滤波器的尺度一致性及其相应的设计方法,利用散焦系统实现Mallat算法的小波低通分解部分,利用光学4f系统实现Mallat算法的小波高通分解部分,并利用计算机通过数值计算实现Mallat算法的小波重构部分。研究光学小波滤波器的优化设计方法。通过仿真实验,研究不同小波基构造频域形式光学小波滤波器的量化误差,比较将分解和重构滤波器交换对频域形式光学小波滤波器的量化误差的影响,并分析频域上的不同采样频率对光学小波滤波器的量化误差的影响。利用提升算法,基于空域和频域量化误差最小的原则构造出最优小波。更多还原

【Abstract】 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.更多还原