【作者】 田勇；

【导师】 马义德；

【作者基本信息】 兰州大学 ， 无线电物理， 2009， 博士

【摘要】 图像去噪是图像分割、编码、模式识别等图像处理应用研究的基础，去噪效果的好坏直接影响这些应用研究的结果，因此去噪算法的研究一直受到了广泛关注。图像去噪的主要方法分为空间域和变换域两类：在空间域处理方法中，主要是利用相邻像素之间的相似性，采用均值滤波、中值滤波、维纳滤波和马尔科夫随机场模型等方法；在变换域处理法方法中，主要是利用傅立叶变换、小波变换和滤波器组分解等工具将图像投影到变换域，然后对变换域的系数进行处理以达到去噪的目的。小波变换和滤波器组分解因为其具有多分辨率分析及去高阶相关的特性，已成为图像去噪算法研究的主流方向。本文的主要工作和贡献如下：第一，小波系数的边缘分布为对称非高斯分布且具有尺度内聚簇性和尺度间继承性，因此对小波系数的边缘分布和条件分布的分析是建立图像去噪统计模型的基础。传统HMT模型较少考虑到尺度内系数之间的相关性，本文在定性分析了小波系数的边缘分布及条件分布的基础上，利用基于模糊理论的随机场方法，在隐马尔可夫树模型训练过程中，为该模型引入了聚簇约束，从而有效地提高了模型近似的精度。第二，不可分离方向性滤波器组能够将图像分解为多分辨率形式，并能更有效地提取图像的方向性信息。本文使用直方图方法，定性分析了分解系数的联合分布及条件分布，在此基础上利用方向性滤波器组的多尺度结构，为其系数建立了隐马尔可夫树模型。在实验中通过与DB4小波变换隐马尔可夫树模型的去噪效果对比，表明该模型去噪性能优异，尤其是在处理纹理信息丰富的图像时，该模型的去噪效果更加明显。第三，M带小波具有比2带小波更精细的频带划分，当前基于M带小波变换的图像去噪算法多为阈值方法。考虑到其尺度间的系数构成了十六叉树结构，条件分布和联合分布的定性分析也表明尺度内系数之间具有很强的相关性，适合采用多尺度随机场模型来处理。传统多尺度随机场模型多为各向同性，不能表达M带小波系数在同一尺度下不同子带的相关性，且随机场模型参数的精确估计需要消耗大量的计算时间和存储。本文借鉴基于模糊逻辑的随机场参数估计方法，为M带小波系数构建了一种自适应的多尺度隐马尔可夫随机场模型，采用伪似然方法计算似然函数，模型参数估计采用了EM-MAP算法。实验结果表明，与基于M带的阈值方法去噪效果相比，该模型的去噪效果在大噪声场合的表现非常优异。更多还原

【Abstract】 Image denoising is the foundation of high level image processing,such as imagesegmentation,coding,pattern recognition,etc.The research for image denoising algorithm hasreceived extensive attention because the applications of these high level image processingtechniques are directly influnced by the denoising results.There are two different ways of imagedenoising: spatial domain algorithm and transform domain algorithm.The main methods in spatialdomain include mean filter,median filter,wiener filter,and Markov Random Field Model.Allthese methods are mainly based on the similarity of neighboring pixcels.The methods intransform domain first transform the image using Fourier transform,wavelet transform and filterbanks decomposition,then images are denoised by.adjusting these coefficients.The researchs forimage denoising are mainly concerntrated on wavelet transform and filter bank decomposition inresent years,because the coefficients have the characteristics of multiresolution analysis and highorder decorrelation,.The main work and contribution in this thesis include:The wavelet coefficients have a non-gaussian symmetric marginal distribution,and haveproperties of intra-scale clustering and inter-scale persistence.So it is the foundation for theconstruction of statistical image processing models to analysis the marginal and conditionaldistribution of wavelet coefficients.In traditional Hidden Markov Tree model,the clusteringproperty of coefficients is less take into account.In this thesis,based on the qualitative analysis ofthe marginal and conditional distribution of wavelet coefficients,and using random field that isbased on the fuzzy logic,the clustering constraints are take account into the training process ofhidden markov tree model to efficiently enhance the precision of parameter estimation.Non seperable directional filter bank can decompose an image into multiresolution structureand can efficiently extract directional information.In this thesis,using histogram technique,aqualitative analysis of the marginal and conditional distribution is implemented.Then weconstructed a hidden markov tree model for the coefficients,and used this model for imagedenoising.Compared with the denoising results based on DB4 wavelet transform,it can be seenthat the model based on directional filter bank has very excellent denoising performance,especially for the images having rich textual information.Compared with 2-band wavelet transform,M-band wavelet transform can partition thefrequency domain with finer structure and its interscale coefficients have a structure ofhexadecimal tree.Currentely,the M-Band based image denoising algorithms are mainlythreadsholding methods,Through qualitative analysis of conditional and joint distribution of thecoefficients,it can be seen that multiscale random field model is suitable for the modeling of thecoefficients.Traditional markov random field model has an isotropic structure and is not suitablefor the correlation structure of the M-band coefficients.The estimation of field model parametersis also time consuming and need a large amount of memory.In the reference of the random fieldmodel based on fuzzy logic,in this thesis,a spatially adatptive multiscale hidden markov randomfield is constructed for the M-band coefficients.In the model,the likelihood function is computedusing psudo likelihood and the ML-MAP algorithm is used for parameter estimation.Experimentsshow that compared with the performence of threadtholding algorithms,the denoising results is very excellent,especially in high level noise situation.更多还原