【作者】 郑钰辉；

【导师】 夏德深；

【作者基本信息】 南京理工大学 ， 模式识别与智能系统， 2009， 博士

【摘要】 计算机技术推动着滚滚的历史车轮驶入了富有挑战的信息时代。随着这一时代的发展,科学研究与实际应用对信号质量的要求与日俱增,为此,先进的数字信号处理技术受到了广泛关注。滤波是数字信号处理中一项重要的研究课题,一方面其能有效地抑制噪声;另一方面滤波方法在理论上与正则化方法以及图像建模理论有着紧密的联系,对滤波方法的研究还能促进其它信号复原问题的解决。论文着重于空域自适应滤波的理论方法及其应用研究。在理论方法方面,分别开展了总变差(Total Variation,TV)自适应保真权系数的构造方法,张量驱动的曲率保持偏微分方程(Partial Differential Equation,PDE)滤波方法,基于预选择的非局部平均滤波方法,基于各向异性扩散PDE的结构张量平滑方法的研究;在方法应用方面,分别开展了斜模式遥感图像复原框架及去模糊方法的研究。论文取得的主要成果与创新理论如下:1)提出了结合局部结构信息的TV自适应保真权系数的构造方法。研究分析了已有的保真权系数构造方法,指出了这些方法本质上在寻求局部结构描述子。讨论了局部结构描述子应满足的2个基本条件,即鲁棒性与高精度性,指出了非线性结构张量是一种优良的局部结构描述子,利用非线性结构张量构造了TV自适应保真权系数。实验结果表明,引入了本文自适应保真权系数的TV滤波方法不仅能很好地去除噪声还能较好地保持图像中目标的几何结构,同时滤波速度较快。2)提出了加权型曲率保持PDE滤波方法。深入分析了目前流行的张量驱动PDE滤波方法,指出了张量驱动的曲率保持PDE滤波方法未考虑各积分曲线可能经历不同的图像结构,如此影响了其对图像边缘的保持能力。在此基础上,利用局部图像方向信息为不同积分曲线设计了相应的权重,得到了一种张量驱动的加权型曲率保持PDE滤波方法。实验结果显示本文方法在滤波的同时能较好地保持图像中边缘与曲率结构,且对图像具有一定的增强能力。3)深入研究了基于预选择的非局部平均滤波方法,指出了目前已提出的方法在提取图像片特征方面存有的不足。利用二维主成分分析(Two-dimensional PrincipalComponent Analysis,2DPCA)提出了一种有效的非局部平均滤波方法。该方法对基于预选择的非局部平均滤波方法的贡献有:(1)用于提取各图像片特征向量的面向图像片的2DPCA;(2)基于相似距离直方图的相似集自动选取方法;(3)相似距离权重参数自适应选取方法。实验结果表明,本文方法对弱梯度、人脸、以及纹理图像均能取得良好的滤波效果。4)提出了基于加权型曲率保持PDE的结构张量平滑方法。分析了已有的基于各向异性扩散的结构张量平滑方法,指出了这些方法在平滑张量场时容易破坏结构张量数据中的重要信息,如此造成了所得非线性结构张量不能较好地提取图像中的2维结构信息。将第3章提出的加权型曲率保持PDE图像滤波方法扩展到张量场得到了一种加权型曲率保持PDE张量场平滑方法,继而用该方法平滑结构张量得到了新的非线性结构张量。实验结果表明,本文方法生成的非线性结构张量能较好地提取图像局部2维结构信息。5)基于图像链优化设计理论,提出了斜模式遥感图像地面复原框架。重点论述了2维采样定理与倒易晶胞理论,用此分析了遥感图像中混叠的起因。利用有效分辨率模型与自适应倒易晶胞研究了斜模式图像获取系统的系统传递函数、混叠、噪声的分布,指出了在欠采样条件下,斜模式采样系统所获图像中存在有用的错位频谱。进一步提出了可通过提高系统截止频率得到上述错位频谱,并以此提高斜模式遥感图像有效分辨率的新观点。在此观点下给出了斜模式遥感图像复原框架,该框架依次由如下4步组成:(1)生成自适应倒易晶胞,(2)提取有效频谱,(3)上采样,(4)去模糊。6)提出了两种斜模式遥感图像去模糊方法。首先将TV模型中的数据保真项定义在斜模式自适应倒易晶胞上,建立了一种基于自适应倒易晶胞的TV正则化模型,并用第1章提出的方法构造了自适应权系数。进一步地,为使上述模型具备更好的图像复原能力,将梯度保真项引入到该模型得到了一种改进的基于斜模式自适应倒易晶胞的TV正则化模型,并分析指出了梯度保真项具有高频信息补偿能力。实验结果显示本章提出的两种TV正则化模型去模糊效果良好。两种方法中,改进的基于自适应倒易晶胞的TV模型得到的斜模式遥感图像复原结果视觉更清晰,信噪比值更高。更多还原

【Abstract】 Computer technologies have moved the wheel of history into the ambitious information age. With the developments of the age, the needs of scientific researches and practical applications for high quality signals are becoming more evident. Thus, advanced digital signal technologies have gained wide interests. In the field of digital processing, filtering is a most important research subject, on the one hand, it can be able to suppress noise effectively, and on the other hand, the study of filtering can promote solution of other signal restoration problems due to that filtering is very closely associated with regularization method and image modeling theory in the terms of theory.This paper mainly focuses on the studies of the spatial adaptive filtering theoretic methods and theirs applications. In the terms of theoretic methods, we have respectively studied methods of designing adaptive fidelity coefficients, tensor-driven curvature preserving PDE based image filtering methods, preselection based non-local means image filtering methods and anisotropic diffusion PDE based structure tensor smoothing methods; In the terms of applications, we have respectively studied restoration framework and deblurring methods for tilting mode satellite image. Main innovation theory and research results have been proposed as following:1) A local structure information based method for designing the adaptive fidelity coefficients in TV model is proposed. At first, informed methods for computing the adaptive fidelity coefficients are systematically discussed and pointed out that they were trying to search local structure descriptors in essence. Then we present two requirements of local structure descriptors, which are robustness and high accuracy, and indicate that nonlinear structure tensor is an excellent local structure descriptor. After this the adaptive fidelity coefficients are constructed by nonlinear structure tensor. Experimental results show that the TV filtering method with our new adaptive fidelity coefficients is capable of sufficiently preserving geometric information such as edges and corners in addition to its effectiveness for image filtering meanwhile the speed of filtering is fast.2) A weighted curvature-preserving PDE based filtering method is proposed. At first, informed tensor-driven PDE based filtering methods are systematically analyzed. Then, the tensor-driven curvature-preserving PDE filtering method is pointed out that it can not preserve image edge very well due to that the method did not take into account the differences between integral curves. Based on this, we employ local image directional information to design weight coefficients for different integral curve, and present a new tensor-driven curvature-preserving PDE. Experimental results indicate that new method shows superior performance on preserving image edge and curvature geometric structure, meanwhile the method has some image enhancement ability.3) The informed preselection based nonlocal means filters are analyzed intensively, and pointed out that they all had defects in terms of feature extraction from image patch. We employ 2DPCA to extract feature from image patch and propose an efficient nonlocal means filter. Mainly, our contributions to the preselection based nonlocal means filter are: (l)patch-oriented 2DPCA for extracting features from image patches; (2)automatic selection of the similar sets based on the histogram of similarity distance.(3)adaptive determination of the similar weight coefficient parameter. Experimental results show that our method can achieve better filtering results in a variety of images, such as weak gradient image, face image and texture image.4) A structure tensor smoothing method based on the weighted curvature-preserving PDE is proposed. At first, informed anisotropic diffusion based structure tensor smoothing methods are analyzed and pointed out that the smoothing methods can not preserve 2D structure information in structure tensor data leading to that corresponding nonlinear structure tensor are deficient in extracting 2D structure information form image. Then, the image filtering method proposed in the third chapter of this thesis is extended to tensor field, and yield a weighted curvature-preserving PDE based tensor field filtering method. At last, structure tensor is smoothed by the new filtering method and produces a new nonlinear structure tensor. Experimental results indicate that new nonlinear structure tensor can be able to extract local 2D structure information from image well.5) A restoration framework for tilting mode satellite image based on the theory of theory of optimum design for image chain is proposed. At first, 2D sampling theorem and reciprocal cell theory are discussed especially, and employed to analyze the cause of aliasing in satellite image. Then, the distribution of the systemic modulation transfer function, noise and aliasing of acquisition system of tilting mode satellite image, is studied by using efficient resolution model and adaptive reciprocal cell, and we point out that there could be available malposed frequency spectrum in the tilting mode satellite image, in the context of undersampling. Based on this, a viewpoint that the malposed frequency spectrum can be acquired by increasing systemic cut-off frequency in tilting mode imaging system is proposed. At last, under such condition, we present a restoration framework consisting of four successive steps of generating adaptive reciprocal cell, extracting efficient frequency spectrum, upsampling and deblurring.6) Two deblurring methods are proposed for titling mode satellite image. At first, the data-fitting term of TV model is rewrite in the fourier domain and defined on the titling mode adaptive reciprocal cell, thus a adaptive reciprocal cell based TV regularization model(ARCTV) is constructed, which also employs the method presented in chapter1 in this thesis to compute the adaptive weight coefficients. Then, in order to improve the deblurring capacity of the ARCTV model, a gradient-fitting term is introduced into it and yields a modification. Future, the gradient-fitting is analyzed and pointed out that it has the ability of compensating high frequency information. Experimental results show that the two proposed methods can achieve good deblured results and the deblurred results by the modified ARCTV method are better, both in visual effect and SNR values.更多还原