变参式Tikhonov正则化图像复原算法

Varying-Parameter Tikhonov Regularization Image Restoration

正则化方法是近年来流行的图像复原算法。研究了周期边界条件下Tikhonov正则化的预处理共轭梯度算法,提出了新的预处理矩阵和变化正则化参数的方法。正则化参数先取较大值,抑制复原图像中的噪声,得出收敛的结果来修正初始梯度;再取较小值,用来增强复原图像中的细节。对一组图像复原基准问题的实验结果表明,与当前流行的正则化图像复原算法比较,该算法的图像复原效果更佳。

Regularization is popular in image restoration recent years. We analyze the preconditioning conjugate gradient method with Tikhonov regularization under the periodic boundary conditions, and propose a new preconditioning matrix and the varying regularization parameter method. At first, we choose a larger regularization parameter to restrain the noise in the restored image, get a convergent result to modify the initial gradient. After that, we choose a smaller one to increase the details. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm performs favorably in comparison with several state-of-the-art regularization image restoration algorithms.