Alternative minimisation algorithm for non-local total variational image deblurring
Alternative minimisation algorithm for non-local total variational image deblurring
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DOI：
10.1049/iet-ipr.2009.0186
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发表时间：
2010-10
影响因子：
2.3
通讯作者：
Dai-Qiang Chen;Lizhi Cheng
中科院分区：
文献类型：
--
作者：
Dai-Qiang Chen;Lizhi Cheng
近年来，基于非局部正则化的变分模型取得了优于传统方法的结果，并且针对这些模型提出了许多迭代算法。目前，张晓群等人。提出了两种基于Bregman迭代求解非局部正则化问题的算法，这些算法收敛速度快，但每次迭代的计算量较大。在此，基于优化中的变量分裂和惩罚技术以及快速傅立叶变换的思想，作者提出了一种非局部全变分模型，并提出了该模型的快速迭代算法。在一定的假设下，证明了迭代算法的q线性收敛性。实验表明，该算法可以有效加快变分模型的执行速度，并通过惩罚参数的选择获得信噪比的提高。
Recently, variational models based on non-local regularisation obtain superior results over traditional methods, and many iterative algorithms have been proposed for these models. At present, Xiaoqun Zhang et al. proposed two algorithms based on Bregman iteration for solving non-local regularisation problems, these algorithms converge fast but the calculation quantity is large for each iterative step. Here, based on the idea of variable splitting and penalty techniques in optimisation and fast Fourier transform, the authors present a non-local total variational model and propose a fast iterative algorithm for the model. Under some assumption, q-linear convergence of the iterative algorithm is proved. Experiments demonstrate that the algorithm can efficiently speed up the execution of the variational model and obtain an improvement in signal-to-noise ratio through the selection of penalty parameters.