兰州大学机构库 >数学与统计学院
图像恢复中几种分裂算法的研究
Alternative TitleSeveral splitting methods for image restoration
孙莉
Thesis Advisor钟承奎 ; 魏婷
2012-05-30
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name博士
Keyword去噪 平均曲率模型 分裂模型 阶梯效应 交错网格 线性化全局高斯--赛德尔迭代 非线性多重网格法 彩色图像去噪 通道耦合 去模糊
Abstract图像恢复是图像处理中最基本和初步的问题之一, 它的主要目的是从观测图像中恢复出一个``真实''的图像. 目前最主要的图像恢复方法大致分为四个类型:变分方法、偏微分方程方法、随机方法、小波和空间-尺度分析. 其中偏微分方程方法在图像恢复领域得到了广泛的应用, 因为在数学物理领域偏微分方程已成为描述、建模以及模拟物理动态过程强有力的工具. 再者许多变分问题和正则化逼近问题都可以通过形式上的欧拉--拉格朗日方程进行有效计算. 本文结合最优化理论、凸分析、变分原理和偏微分方程把高阶的平均曲率模型给予推广和改进, 使导出的新模型在保证图像恢复质量的同时降低了原模型所产生的偏微分方程的强非线性性和算法的强正则性. 为了能快速地求解变分模型, 我们着重研究一种非线性多重网格算法. 实验结果说明了改进模型和数值算法的有效性和优越性.
Other AbstractImage restoration is the most basic and preliminary image processing problem. The aim of image restoration is to remove the noise efficiently and recover the ``true'' image. In recent years, research in the field of image restoration mainly falls into four categories: variational method; partial differential equations; stochastic modeling and wavelet and space-scale analysis. Partial differential equations(PDEs) have been achieved successful applications in the image processing, since PDEs in classical mathematical physics are powerful tools to describe, model, and analyse many dynamic, and many variational problem or their regularized approximations can be effectively computed from the formal Euler-Lagrange equations. In this thesis, we extend and improve the existing higher order mean curvature model by combining optimization theory, convex analysis, variational principles and partial differential equations. The new model ensure the quality of the image restoration and reduce strong nonlinearity and regularization in the original model. In order to quickly solve the variational model, we design a nonlinear multigrid algorithm for solving the partial differential equations. Experimental results show that the new numerical algorithm is effective and superior.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224617
Collection数学与统计学院
Recommended Citation
GB/T 7714
孙莉. 图像恢复中几种分裂算法的研究[D]. 兰州. 兰州大学,2012.
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