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.
Image deblurring was formulated as an optimization problem regularized by l_p norm.A fast generalized iterative shrinkage thresholding algorithm（FGISA）was proposed to solve it.The FGISA algorithm accelerated the generalized iterative shrinkage thresholding algorithm（GISA）by multiplying a weighting matrix to the gradient function of the GISA together with the well-known Nesterov＇s strategy.Since the weighting matrix was only predetermined by the blur kernel and fixed,therefore,comparing with GISA,FGISA did not increase the computational complexity.Numerical experiments are presented that demonstrate the improved performance of the FGISA over GISA both in speed and accuracy.
出处
《武汉大学学报（理学版）》
CAS
CSCD
北大核心
2017年第6期551-556,共6页
Journal of Wuhan University:Natural Science Edition
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
关键词
图像去模糊
lp正则化
迭代收缩算法
加权矩阵
image deblurring
regularized
shrinkage thresholding algorithm
weighting matrix
