【作者】 郭强；

【导师】 郁松年；

【作者基本信息】 上海大学 ， 计算机应用技术， 2010， 博士

【摘要】 受成像条件、外部噪声以及人为因素的影响,人们获取到的图像常常会出现不同程度的失真,如图像含有噪声、模糊不清。噪声和模糊的存在降低了图像的视觉质量,影响了图像的后续处理。为改善图像质量,尽可能减少失真对图像后续处理的影响,对图像进行去噪和去模糊处理就成为图像预处理过程中一项非常重要的工作。小波变换因其多分辨特性而被广泛应用于图像去噪和去模糊。然而,小波变换只能表示图像中的点状奇异,而不能有效地表示曲线奇异。新近出现的剪切波变换则有效地克服了小波变换的缺陷。本文深入研究了剪切波变换的相关性质,特别是图像剪切波系数的统计特性,并在此基础上提出了基于剪切波变换的图像去噪和去模糊方法。本文的主要工作和创新包括以下几个方面:(1)研究了离散剪切波变换的数值实现,并对其时间复杂度、冗余度、重构准确性以及稀疏性进行了分析。由于能够对图像进行多尺度和多方向分析是剪切波变换的主要特点,因此在分别分析图像多尺度变换和多方向变换的基础上,利用多尺度滤波器和伪极坐标傅里叶变换来分别实现剪切波多尺度和多方向分析的功能,从而对剪切波变换进行离散实现。(2)研究了基于剪切波的图像去噪和去模糊所涉及的三个关键问题,即估计方法、剪切波系数的先验模型以及系数间的相关性。图像去噪、去模糊问题理论上是一个估计问题,本文采用最大后验估计(MAP)对剪切波系数进行估计。针对剪切波系数的分布具有重尾性这一特点,提出了基于广义球等高指数分布的剪切波系数先验模型,将其作为MAP估计所需的先验知识,并对广义球等高指数分布的重尾性进行了理论证明。同时,以互信息为衡量标准,对剪切波系数间的相关性进行了量化分析,明确了剪切波的尺度和方向特征对系数间相关性的影响,为建立去噪模型提供了依据。(3)针对图像去噪问题,提出了三种剪切波去噪方法。在最大后验估计理论框架下,利用所建立的剪切波系数统计模型以及系数间的相关性,建立了三变量去噪模型。在假定变量具有相同标准差的情况下,由估计模型推出一种具有闭式解的去噪方法(方法1),该方法运行时间较短,去噪性能较好;对变量具有不同标准差的情况,给出了一种迭代去噪方法(方法2),与方法1相比该方法运行时间较长,但去噪效果好于方法1。同时,对去噪方法中的未知参数提出了相应的估计方法,并对所涉及到的迭代算法的收敛性进行了证明。在此基础上,将三变量模型推广为多变量模型,提出了方法3。实验结果验证了这三种方法的有效性。(4)针对图像去模糊问题,提出了一种基于邻近迭代算法的剪切波去模糊方法。利用剪切波系数的先验模型,通过最大后验估计理论导出图像去模糊模型。由于该去模糊模型对应于一个最优化问题,因此采用邻近迭代算法对其进行求解。给出了模型中相应参数的估计方法,对算法的收敛性进行了证明,并分析了算法的时间复杂度。与基于小波变换和曲线波变换的图像去模糊方法相比,本文方法具有更好的性能。更多还原

【Abstract】 Images are often corrupted by noise and blur due to the undesired conditions for im-age acquisition, processing and transmission. The noise and blur in images have severelydegraded image quality and affected the subsequent image processing tasks. Thus noise andblur reduction has been a very important pre-processing step for improving the quality ofimages. In the past decade, the wavelet transform has been successfully used in image de-noising and deblurring due to its multiresolution capability. However, despite its remarkablesuccess in dealing with pointwise singularities, the standard separable wavelet transformfails to provide an optimal sparse representation for images that contain other types of singu-larities. Shearlets, a new directional multiresolution transform, can efficiently represent thedirectional information of images.This thesis mainly investigates the properties of the shearlet transform, especially thestatistical characteristic for shearlet transform coefficients of natural images. Then new im-age denoising and deblurring methods are derived using maximum a posteriori (MAP) esti-mation theory with the proposed statistical model. The main achievements of this thesis areas follows:Firstly, after discussing the implementation of the discrete shearlet transform (DST),the computational complexity, redundancy, reconstruction accuracy and sparsity of the DSTare analyzed. Since multiscale and multidirectional decomposition of images is the mostimportant characteristic of the DST, we can implement the DST by performing the multi-scale and multidirectional decomposition steps separately as done in contourlets. One wayof achieving a multiscale and multidirectional decomposition is to use Laplacian pyramidfollowed by fast pseudo-polar Fourier transform.Secondly, estimation methods, coefficients statistical models and correlation betweencoefficients are key problems for image denoising and deblurring based on the shearlet trans-form. In this thesis, a comprehensive study of these three problems is given. In essence,image denoising and deblurring can be regarded as a standard estimation problem. We useMAP estimation theory to estimate the shearlet coefficients. In order to model the shearletcoefficients, we propose a probability model, generalized spherically contoured exponential(GSCE) model, which is used as prior information for MAP. Theoretical analysis is pre-sented to prove that GSCE is heavy-tailed. Furthermore, correlation between coefficients isanalyzed by using the mutual information as quantitative measure. The quantitative resultsare used to develop a image denoising model. Thirdly, three shearlet-based denoising methods are proposed for image noise reduction.According to the correlation characterization, GSCE is exploited to establish a trivariatemaximum a posteriori model. In the case of variates having the same standard deviation, asimple closed-form solution (Method I) is derived from this trivariate model. For variateswith different standard deviations, an iterative denoising method (Method II) is presented,and the convergence of the iterative algorithm is proved. Related parameters estimationmethods are given. Then we propose another denoising method (Method III) based on thegeneralized model. Experimental results demonstrate the efficiency of the proposed methods.Finally, a shearlet-based deblurring method using the proximal iteration is presentedfor image deblurring. Using the coefficients model and MAP, an image deblurring model isderived. Since this deblurring model is equivalent to an optimization problem, the proximaliterative algorithm is used to solve it. The parameters estimation methods, the computationalcomplexity and the convergence of the proximal iteration are presented. Experimental re-sults show that the proposed deblurring method obtains better performance than the existingwavelet-based and curvelet-based methods.更多还原