基于对偶两步模型的图像放大问题

项目名称： 基于对偶两步模型的图像放大问题

项目编号： No.11426137

项目类型： 专项基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 武婷婷

作者单位： 南京邮电大学

项目金额： 3万元

中文摘要： 本项目利用变分与偏微分方程及其数值计算领域的最新数学成果研究图像放大问题，具有鲜明的理工结合，数学与信息交叉的特色。本项目以解决基于对偶两步模型的图像放大问题中存在的关键问题为目的展开研究，主要创新点如下：1. 基于修正LOT模型的图像放大方法。考虑到Chambolle对偶策略中的对偶变量可以看作图像的法向量, 第一步中，我们通过计算对偶变量来代替经典LOT模型中的光滑化法向量。在第二步中, 我们采用快速的分裂Bregman迭代算法重构所求图像。2. 基于对偶TV-Stokes模型的图像放大方法。结合切向量的零散度条件，在第一步中构造出一个非线性TV-Stokes方程，数值计算中我们采用对偶策略进行求解，进而大幅度提高算法的效率。本项目的研究将在理论上有突破，算法上有创新，新的图像放大方法在运算速度和放大质量上都有提高，将具有更广泛的应用价值。

中文关键词： 两步模型；对偶策略；非精确ADMM；启发式算法；全局优化

英文摘要： By using the latest mathematics results of variational methods, PDE and numerical computation, we research image zooming problems in this project which indicates distinctive combinations of science and engineering, and overlapped characteristics between mathematics and information. In this project, we focus on the key issues of the image zooming problems based on two-step models using duality strategies. Main novelties are listed as follows: 1. The image zooming method based on modified LOT model. In the first method, instead of smoothing the normal vector directly as did in the first step of the classical LOT model, we reconstruct the unit normal vector by means of Chambolle's dual formulation. Then, we adopt the split Bregman iteration to obtain the zoomed image in the second step. 2. The image zooming method based on TV-Stokes model using a dual formulation. By imposing the divergence free condition on the tangential vector field, we get a nonlinear TV-Stokes equation in the first step. Furthermore, we adopt dual algorithms in the numerical experiments which will illustrate the efficiency of our proposed methods. The research of this project will have a breakthrough in theory and algorithms. The new image zooming methods are presented with fast computational speed, exhibit a better visual impression and have

英文关键词： Two-step model；Duality strategy；Inexact ADMM；Heuristic method；Global optimization