【作者】 张莉；

【导师】 汪西莉；

【作者基本信息】 陕西师范大学 ， 计算机软件与理论， 2006， 硕士

【摘要】 20世纪80年代后期发展起来的小波变换因其在处理非平稳信号方面的独特优势而成为信号去噪领域中的一个重要研究方向。近年来,随着小波理论的不断完善,小波变换在图像去噪领域也得到了广泛的应用,并提出了许多小波图像去噪方法。离散小波变换虽然广泛用于图像去噪中,但离散小波变换存在两个缺点: 1、缺乏平移不变性,这意味着信号的微小平移将导致各尺度上的小波系数的能量分布的较大变化。 2、缺乏方向敏感性,可分离的二维小波变换只有三个方向的高频信息即水平、垂直和对角。 利用对偶树复小波变换进行图像去噪,可以克服上述离散小波变换的不足。本论文主要围绕对偶树复小波变换及其在图像处理中的应用来进行研究。主要进行了以下几个方面的工作: (1)对常用的小波变换图像去噪方法进行了研究,并在此基础上提出利用对偶树复小波变换进行图像去噪。 (2)介绍了对偶树复小波变换的原理和特性。对偶树复小波变换具有近似的平移不变性、良好的方向选择性,与此同时,它还具有完全重构特性。对偶树复小波变换在每一层产生六个具有方向选择性的子带,分别指向±15°,±45°,±75°。将对偶树复小波变换应用于图像去噪,可以更好地表示图像的边缘和纹理特征,从而得到较小波更好的去噪效果。 (3)提出对偶树复小波变换和贝叶斯估计确定阈值相结合的图像去噪方法。与常用的离散小波变换相比,该方法具有逼近的移不变性和更多的方向选择性,有利于特征的跟踪、定位和保留。结合贝叶斯估计技术和自适应分布参数确定方法,给出了有效的图像去噪算法。结果表明,该方法去除噪声彻底,边界、纹理等特征保留较好。 (4)在图像去噪中目前经常使用的模型假设系数是独立分布的,但是这些简单的分布作为自然图像小波分解系数的模型是不够准确的,因为它们忽略了系数之间的相关性。本论文进一步分析层内和层间相关性,提出了一种双变量模型。在该模型下将对偶树复小波变换与双变量收缩函数相结合进行图像去噪,实验结果表明,该算法比传统算法有更好的去噪效果。更多还原

【Abstract】 In the 1980s, wavelets have been found applications in image processing due to the time-frequency localization and multiscale decomposition property. In recent years, with the development of the wavelet theory, discrete wavelet transform (DWT) has been widely used in image denoising. Although DWT is a powerful signal-processing tool, it has two disadvantages that undermine its usage in many applications. First, DWT is shift sensitive because input-signal shifts generate unpredictable changes in DWT coefficients. Second, the DWT suffers from poor directionality because discrete wavelet transform coefficients reveal only three spatial orientations.In order to overcome the shortcoming of the commonly-used denoisng methods, the image denoising method based on dual tree complex wavelet transform (DT-CWT) is proposed. Dual tree complex wavelet transform and its application in image processing are investigated in detail in this dissertation. The main work can be summarized as follows:(1) Many literatures of wavelet denoising methods have been studied, on which dual tree complex wavelet denoising method is proposed.(2) The basic principles and characteristics of dual tree complex wavelet transform are discussed. The dual tree complex wavelet transform has the properties of approximate shift invariance, good directional selectivity and perfect reconstruction. It has six subbands corresponding to six spatial orientations: +15°, +45°, +75°, - 75°,- 45°, - 15°. The image denoising method is proposed based on dual tree complex wavelet transform, which can do better both in features preserving and noise removing.(3) The image denoising method is proposed based on dual tree complex wavelet transform and Bayesian estimation. Compared with the traditional discrete wavelet transform, the dual tree complex wavelet transform has the properties of approximate shift invariance and more directionality. These properties are good for tracing, locating and preserving image features. Combined with statistical based Bayesian estimation and adaptive distribution parameter estimation, an effective denoising algorithm is gained. The experiment results show the method not only removes most noises but also preserves features better.(4) We have proposed a simple non-Gaussian bivariate probability distribution functions to model the statistics of wavelet coefficients of natural images. The model captures the dependence between a wavelet coefficient and its parents. The shrinkage function, which depends on both the coefficient and its parent, yields improved results for wavelet-based image denoising. The theoretical analysis and experimental results presented in this paper show that, compared with the commonly-used wavelet threshold denoising methods, our denoising method can improve the denoising results.更多还原