加权整体变分图像去噪模型的多重网格方法

摘要

加权整体变分图像去噪模型是整体变分模型图像去噪模型的改进，能更好的复原图像。在求解整体变分图像去噪模型中，对偶方法比原方法能更好的处理震荡和非光滑区域。为了建立加权整体变分模型对偶方法的快速算法，本文首先提出用多重网格方法对加权整体变分模型的对偶方程进行求解；然后对提出的多重网格方法进行收敛性分析，揭示出收敛困难的原因；最后为了达到收敛，对多重网格方法进行改进。实验结果表明，改进的多重网格方法比半隐式对偶方法收敛更快。%The weight total variation image denoising model is an improvement on total variation image denoising model, and the formal can restore image better. In sovling the total variation image denoising model, the dual method can deal with the oscillation and non-smoothness better than the primal method.In order to establish a fast algorithm for dual method of the weight total variation image denoising model, first, we propose to use the multigrid algorithm to solve the dual equation of the weight variational model; then we analyze the convergence rate of the proposed multigrid algortithm, showing why it has some difficulties in achiveing convergence; finally, to achieve convergence,we modified the multigrid algortithm. Experimental results show that the proposed algorithm converges faster than the semi-implicit method.