【作者】 刘红毅；

【导师】 韦志辉；

【作者基本信息】 南京理工大学 ， 模式识别与智能系统， 2011， 博士

【摘要】 图像在获取和传输过程中,不可避免地会受到噪声污染,致使图像质量下降,严重影响了后续图像处理工作(如图像超分辨率、图像分割、图像识别、特征提取等)。为了提高图像质量,为后续图像处理提供更可靠真实的图像,对图像进行去噪处理就成为图像处理中一项基础而重要的研究工作。图像去噪的目的是根据观察到的降质图像估计恢复原始真实图像,即在去除噪声同时更好保持图像中的重要结构信息。研究如何更好保持图像的边缘、纹理等重要结构信息的图像去噪模型和算法具有重要的理论意义和实用价值。本论文以刻画边缘和纹理的图像先验建模为出发点,利用小波变换、核回归及非局部均值等图像去噪方法,重点研究方法中的纹理、边缘等结构保持问题,提出一系列的结构保持的图像去噪模型和新算法。取得的主要成果及创新点如下：(1)提出一种新的基于小波系数相关性的图像去噪方法。利用小波系数多尺度相关性及小波系数极大值,定义两种基于最大子结点的相关系数,结合小波阈值进行图像去噪,并且将定义的相关系数推广到分数阶B样条小波域。理论分析和实验结果均表明,所提出相关系数在小波分解的高频子带可以很好地刻画图像结构,因而在去噪过程中保留了更多的边缘与纹理等结构信息,提高了去噪图像的质量。(2)针对基于正则性指数图像去噪方法的不足,提出正则性指数和图像全变差(Total Variation, TV)正则先验结合的图像去噪模型。该模型利用小波系数与信号正则性之间的关系,在小波分解的不同尺度,通过改变小波系数来提高图像局部正则性。有效克服了正则性指数去噪算方法在图像边缘处所产生的Gibbs现象,具有较好的边缘结构保持和噪声滤除性能。推广传统小波阈值与TV最小结合的变分模型到分数阶B样条小波,建立分数阶B样条小波域的TV去噪模型。通过分数阶B样条小波闽值和TV范数的结合,得到了对于纹理和边缘等几何结构都有良好保持性能的去噪图像。(3)利用结构张量矩阵刻画像素局部梯度结构信息,设计了一种新的数据自适应核函数,提出一种基于结构张量的自适应核回归图像去噪及插值模型。理论和实验表明：本文模型能够准确估计图像中的边缘方向,因而在图像去噪和插值中能够有效重建图像的边缘和纹理等几何结构,视觉效果良好；同时,本文模型的均方误差达到了最小,进一步验证了算法的有效性。针对Steering核回归模型对于细尺度边缘的不稳定性,应用两种更加鲁棒的核函数,提出两种边缘保持的核回归模型。与高斯核函数相比较,新的核函数具有更快的衰减性。当像素点属于细尺度边缘时,新的核函数对边缘附近像素赋予了更小权重,保证了去噪图像中的边缘细节更加清晰,消除了高斯核函数所出现的伪边缘现象。实验结果证明所提出模型对于纹理较少,细节丰富的图像具有很好重建效果。(4)耦合Patch相似性保真和非局部TV正则性先验,提出一种新的图像去噪变分模型。该模型利用非局部迭代去噪图像和真实图像间的Patch相似性建立保真项,从而保证了所产生的去噪图像和真实图像之问具有结构相似性。非局部TV正则项进一步保证了图像中边缘及细小纹理结构的有效保持。与现有相关方法相比较,实验结果表明,所提出方法在去噪同时能够有效保持图像中的边缘及纹理结构信息,特别是对于受噪声污染比较严重的图像,去噪性能和结构保持性能都达到了最好。(5)利用图像中Patch自相似性,结合TV正则先验,提出自适应非局部Patch自相似性正则化模型。与现有非局部权函数计算方法不同,本文利用改进的结构张量矩阵,构造具有自适应和方向性的权函数,得到了对于图像中Patch自相关性的准确估计,从而保证了图像中的纹理等几何结构信息的有效保持。在数值解法上,采用了分裂Bregman迭代进行求解,提高了算法效率。同时将去噪模型推广到图像恢复,实验结果证明了所提出算法在结构保持方面的有效性。更多还原

【Abstract】 An image is usually corrupted by noise in its acquisition and transmission. The degraded image severely affects the following image processing, such as image superresolution, image segmentation, image recognition, feature extraction. Thus, image denoising becomes a fundamental and important image processing for improving the quality of image. The goal of image denoising is to get a clearer and richer detailed image. Preserving the important structures such as edges and textures has important theoretical significance and application values.It is well-known that image structures are important for visual perception.Hence; this paper mainly focuses on image denoising model for edge-preservation and texture-preservation. Several new image denoising methods are proposed based on wavelet transform, kernel regression and nonlocal means, respectively. The main achievements and innovations are as follows:(1) Using the scale correlation and maxima modulus of wavelet coefficients, we define two new wavelet correlation coefficients based on maxima child nodes, and propose a new scale correlation based image denoising method. Furthermore; we extend these definitions to fractional B-spine wavelet coefficients. Both theoretical and experimental results demonstrate that the proposed correlation coefficients can capture the structure information in high frequency sub bands. So more edges and textures are kept in the denoised image and the quality of denoised image is improved.(2) To overcome the shortcomings of the regularity exponent based image denoising model, a new image denoising model combing the regularity exponent and image total variation (TV) is proposed. The model fully utilizes the relationship between wavelet coefficients and signal regularity. So the image regularity is modified by changing the wavelet coefficients in different scales. The noise is reduced while sharp edges are preserved; meanwhile, the Gibbs phenomenon is disappeared.With the fractional B-spline wavelet instead of the traditional wavelet, we establish a denoising algorithm based on the fractional B-spline wavelet and total variation. In this case, edges and textures are both maintained in the denoised image.(3) An adaptive kernel regression model based on structure tensor is proposed. The structure tensor, which can exploit the local gradient structure information, provides information to achieve a data-adaptive kernel function. Due to the accurate estimation of edge orientations, edges and textures structure information are well preserved and a better visual effects are achieved during denoising and interpolation. Meanwhile, the RMSE is also proved the effectiveness of the algorithm.To overcome the shortcomings of Steering kernel regression, two more robust kernel functions are applied to kernel regression, which are robust to micro-edges. On the image edges, the kernel functions have a faster decay, and the weight of pixels are assigned a small value. Thus it discourages the pseudo-edges. Experimental results of image denoising and interpolation show that the efficiency of the proposed models, especially to the image with less textures and more edge details.(4) We propose a novel nonlocal TV variation model, where the fidelity term is based on the Patch similarity, and regularity term is nonlocal TV priori. The iterative nonlocal provides structure similarity between noisy and denoised images; while the nonlocal TV preserves the edge and texture details. Compared with other related denoising methods, the proposed model can preserve more structure information in denoised image, especially to the image with much noise.(5) Combining the nonlocal Patch similarity regularization with TV regularization, we propose a new nonlocal Patch self-similarity regularized image denoising model. The similarity of Patches are said to be accurate, by introducing adaptive structure tensor to compute weight function of nonlocal Patch similarity. So in the denoised image, more structural features can be retained. A simpler and more effective algorithm, Split Bregman algorithm, is used to solve the model iteratively. By extending the model to image restoration, our model improves the quality of restoration image and the efficiency of computational complexity.更多还原