基于l_p正则化图像去模糊的快速广义迭代收缩算法

发布时间：2018-03-14 00:38

本文选题：图像去模糊　切入点：lp正则化　出处：《武汉大学学报(理学版)》2017年06期 　论文类型：期刊论文

【摘要】：将图像去模糊问题转化为求解l_p正则化的非凸优化问题,提出了一种求解l_p正则化问题的快速广义迭代收缩算法(FGISA,fast generalized iterative shrinkage thresholding algorithm).该算法通过对广义迭代收缩算法(GISA,generalized iterative shrinkage thresholding algorithm)的梯度项添加一个加权矩阵,并结合Nesterov梯度加速方法达到加快算法收敛速度的目的.由于加权矩阵仅仅与模糊矩阵有关,并且不随迭代过程变化,因此,与GISA相比FGISA并不增加算法的计算复杂度.文章给出了算法收敛性的理论分析.实验结果表明FGISA算法在收敛速度和图像恢复效果方面对GISA算法均有较大的改进.
[Abstract]:The problem of image de-blurring is transformed into a non-convex optimization problem for solving LP regularization. A fast generalized iterative contraction algorithm for solving LP regularization problem is proposed. The algorithm is generalized iterative shrinkage thresholding algorithm. The algorithm adds a weighted matrix to the gradient term of generalized iterative shrinkage thresholding algorithm. Combined with the Nesterov gradient acceleration method, the convergence rate of the algorithm is accelerated. Because the weighting matrix is only related to the fuzzy matrix and does not change with the iterative process, so, Compared with GISA, FGISA does not increase the computational complexity of the algorithm. The theoretical analysis of the convergence of the algorithm is given in this paper. The experimental results show that the FGISA algorithm has a great improvement on the GISA algorithm in terms of convergence speed and image restoration effect.
【作者单位】：五邑大学数学与计算科学学院;武汉理工大学计算机科学与技术学院;
【基金】：国家高技术研究发展(863)计划(2015AA015403) 国家自然科学基金(11601393) 湖北省自然科学基金重点项目(2015CFA059) 中央高校基本科研业务费资助(175110001) 湖北省科技支撑计划(2014BAA146) 广东省自然科学基金(2015A030313646,2016A030313005) 广东省教育厅研究生教育创新教育类项目(2016SFKS_40) 五邑大学青年基金(2015zk09)资助项目
【分类号】：TP391.41

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