紧框架分析模型下的模糊图像盲复原

Blind image restoration based on analysis model under tight frame

在基于稀疏表示模型的图像盲复原问题中,模糊核估计与稀疏模型的选取是影响盲复原性能的两个关键因素。针对传统基于稀疏表示盲复原方法的不足,本文提出一种基于紧框架分析模型的图像盲复原方法。该方法将盲复原问题分裂为两个迭代的子问题,分别是基于梯度图像的模糊核估计与基于紧框架分析模型的非盲图像复原。在核估计问题中,提出同时约束核稀疏性及一阶微分平滑特性,进一步提高了核估计精度。在紧框架非盲图像复原问题中,提出一种基于Moreau envelope函数的数值计算方法,有效地解决紧框架复原模型的不可微和不可分离性。实验结果表明,本文复原方法在图像细节恢复与客观评价指标方面均优于传统复原算法。

In blind image restoration based on the sparse representation model,kernel estimation and the selection of the sparse model are two significant factors that affect the blind restoration. Considering the imperfections of the conventional blind restoration method based on sparse representation,we propose a novel blind restoration method based on the tight-frame analytical model. This novel method divides the blind restoration problem into two iterative subproblems： kernel estimation based on the gradient image,and non-blind image restoration based on the tightframe model. In the kernel estimation,we propose constraining simultaneously the sparsity of the kernel and the smoothness of the first-order differential of the kernel,which further improves the accuracy of the kernel estimation.In the non-blind image restoration subproblem,we propose a numerical algorithm based on the Moreau envelope function,which can solve the nondifferentiability and inseparability of the tight-frame restoration model. The experimental results show that the proposed method is superior to the conventional methods in relation to both the recovery of image detail and the objective assessment indicators.