交替迭代法及其在图像恢复中的应用 Alternative Title Alternating Iteration Method and Its Application in Image Restoration 史琬滢 Subtype 学士 Thesis Advisor 黄玉梅 2019-04-30 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 学士 Degree Discipline 数学与应用数学 Keyword 交替迭代法 收敛速度 凸规划 图像恢复 总变分 Abstract 交替迭代法(ADM)是求解带有线性约束的凸优化问题的一种重要数值方法，这种方法将原问题目标函数等价分解为多个低维子问题进行迭代求解，从而高效地得到原优化问题的解。近年来，ADM法在图像处理、统计学习、连续介质力学、数学经济学等领域有着广泛的应用，因此对交替方向迭代法的研究具有重要的理论和实际意义。本文对交替迭代法及其收敛性进行了研究，表明了ADM法具有O(1/t)的收敛速度。同时利用交替迭代法求解了图像恢复的总变分模型，实验结果说明，交替迭代法能有效地应用于图像恢复问题的求解中，快速地得到具有高质量恢复结果的图像。 Other Abstract The alternating iteration method (ADM) is an important numerical method for solving convex optimization problems with linear constraints. This method decomposes the objective function of the original problem into several low-dimensional sub-problems for iterative solution. Thus, the solution of the original optimization problem can be obtained efficiently. In recent years, the ADM algorithm has been widely used in many fields, for instance, image processing, statistical learning, continuum mechanics, mathematical economics and so on. In this paper, the alternating iteration method and its related theories are studied. We provide a unified proof to show the O(1/t) convergence rate for ADM. Then we apply ADM to solving the total variation model for image restoration. The numerical experimental results show that the alternating iteration method can quickly restore the image, and it can get good visuals qualities. Pages 20 URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/342344 Collection 数学与统计学院 Affiliation 数学与统计学院 First Author Affilication School of Mathematics and Statistics Recommended CitationGB/T 7714 史琬滢. 交替迭代法及其在图像恢复中的应用[D]. 兰州. 兰州大学,2019.
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