基于变分偏微分方程的图像去噪及其快速算法

发布时间：2018-07-04 08:47

本文选题：图像处理 + 图像去噪　；参考：《南京邮电大学》2015年硕士论文

【摘要】：图像中的噪声不仅严重恶化了图像的质量,损害了图像中一些重要的细节特征,甚至使图像变得十分模糊,这些问题都为后续图像处理工作带来很大的挑战。然而,传统的图像去噪方法已经不能满足人们获取高质量、高清晰图像的要求。在图像去噪中,偏微分方程的方法经过二十多年的不断发展,现已成为现代应用数学研究热点之一。本文关注的是基于变分法和偏微分方程方法的图像去噪及其快速数值求解方法。主要研究内容及创新点如下:(1)介绍几种常见的基于变分偏微分方程的去噪方法(如:PM模型、TV模型、自适应TV模型以及四阶YK模型),并简要分析上述模型的优缺点。另外,还介绍一些快速算法(如:对偶算法、Split Bregman算法和ADMM算法)。(2)利用直接变分法,得到泊松去噪模型(Le模型)解的一重要框式约束。然后,结合ADMM算法给出Le模型带框式约束的快速数值求解方法(这里称之为CADMM算法),并分析所提算法的收敛性。最后,数值仿真实验验证该算法的有效性与可行性。(3)结合自适应TV去噪模型,提出自适应的图像泊松去噪模型(?-Le模型)。然后,利用ADMM算法,给出?-Le模型的一快速算法。最后,数值仿真实验验证该算法的有效性与可行性。
[Abstract]:The noise in the image not only seriously deteriorates the image quality, damages some important details in the image, but also makes the image blur. These problems bring great challenges to the subsequent image processing. However, the traditional image denoising method can not meet the requirements of obtaining high quality and high definition images. In image denoising, the method of partial differential equation (PDE) has been developed continuously for more than 20 years, and has become one of the hotspots in modern applied mathematics. This paper focuses on image denoising and its fast numerical solution based on variational method and partial differential equation method. The main contents and innovations are as follows: (1) several common denoising methods based on variational partial differential equations (such as: PM model / TV model, adaptive TV model and fourth-order YK model) are introduced, and the advantages and disadvantages of these models are briefly analyzed. In addition, some fast algorithms, such as split Bregman algorithm and). (2 algorithm, are introduced to obtain an important frame constraint of Poisson denoising model (Le model) by using direct variational method. Then, a fast numerical solution of Le model with frame constraints (called CADMM algorithm) is presented with ADMM algorithm, and the convergence of the proposed algorithm is analyzed. Finally, the effectiveness and feasibility of the proposed algorithm are verified by numerical simulation. (3) combined with adaptive TV denoising model, an adaptive image Poisson denoising model (PS-Le model) is proposed. Then, using ADMM algorithm, we give a fast algorithm of Le model. Finally, the effectiveness and feasibility of the algorithm are verified by numerical simulation.
【学位授予单位】：南京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175;TP391.41

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