图像复原中非凸稀疏优化问题的快速算法

项目名称： 图像复原中非凸稀疏优化问题的快速算法

项目编号： No.11501584

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 李洽

作者单位： 中山大学

项目金额： 18万元

中文摘要： 图像复原是图像处理学科最基本与最重要的领域之一。近年来，基于稀疏表示的图像复原方法广泛地应用在图像复原问题中，并取得了很大的成功。快速求解对应的稀疏优化问题是基于稀疏表示的图像复原方法中的核心，也是目前国内外应用与计算数学界研究的热点问题。在本项目中，我们研究图像复原中三类非凸稀疏优化问题的快速算法，这三类优化问题均不能由现有的算法很好地求解。第一类优化问题产生基于稀疏表示的图像非盲复原问题，其特点是含有非凸稀疏度量函数，如L0模或Lp（0

中文关键词： 图像复原；非凸优化；稀疏表示

英文摘要： Image restoration is one of the fundamental and important areas of the imaging science. Recently, sparse representation based image restoration approaches are widely spread and achieve great success. Solving the corresponding sparse optimization problems becomes a very crucial issue in the sparse based image restoration methods and is now a hot research topic in the applied and computational mathematics. In this project, we study three categories of nonconvex sparse optimization problems arising from image restoration. The first category of problems comes from the sparsity based approaches for non-blind image restoration. The problems are nonconvex due to the nonconvex sparse promoting functions involved. For example, the L0 or Lp（0<p<1）norm. The second category of problems mainly comes from the sparsity based methods for blind image deconvolution. The problems are nonconvex since the fidelity terms involve the convolution of two variables. The third category of problems is large scale nonconvex sparse optimization problems which involve high dimensional images or large scale matrices We aim at developing fast and accurate optimization algorithms for these three classes of problems.

英文关键词： image restoration;nonconvex optimization;sparse representation