一种组稀疏高阶变分的图像复原模型

A Higher Order Total Variation with Group Sparsity Restricted Term for Image Restoration

为了更好地利用图像的稀疏性以提高变分模型的图像复原性能,在自适应高阶变分模型中对图像的一阶梯度加以组稀疏限制,建立一种非凸的组稀疏高阶变分模型。为实现该非凸模型的优化求解,采用交替方向乘子法将模型的极小化问题分解成多变量的子问题,进而采用IRL1与MM算法分别求解高阶变分与组稀疏极小化问题,实现退化图像的复原处理。通过对比实验证明,提出的组稀疏高阶变分模型有效利用图像的自相似性与稀疏性,能更好地复原图像的结构与纹理信息,消除了阶梯现象的影响,获得了更高的峰值信噪比与结构相似度,图像复原性能更优。

In order to enhance restoration performance of total variation and use sparsity to reconstruct image information,the group sparse representation of image’s gradient is used to restrict the adaptivity high-order total variational model,and a novel non-convex group sparse high-order variational model is proposed.To optimize the non-convex model,IRL1 and majorization-minimization iterative algorithms are respectively used to minimize higher order total variation and sparse subproblems of the alternating direction method of multipliers.The experimental results in terms of peak signal-to-noise ratio and structure similarity index measure show that the proposed model eliminates staircase artifact,recovers more structure and texture,and shows better performance than the compared models by utilizing the self-similarity and sparsity of images.