基于l_p正则化图像去模糊的快速广义迭代收缩算法

Image Deblurring via Fast Generalized Iterative Shrinkage Thresholding Algorithm for l_p Regularization

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.