基于图像分解的图像修复算法

摘要

针对传统变分模型在修复图像时易产生"阶梯效应"与细节模糊等问题,提出了一种基于图像分解的自适应二阶总广义变分和分数阶变分的图像修复算法.首先将待修复的目标图像分解为卡通部分与纹理部分,其中卡通对应目标图像的低、中频部分,因此利用抑制"阶梯效应"较好的二阶总广义变分模型对其进行修复;纹理对应其高频部分,因此利用对细节部分有增强效果的分数阶变分模型对其进行修复.由于文中所提到的修复模型均与线性鞍点结构下求取最优值的模型类似,因此在算法上均采用基于预解式的原始对偶算法对新模型进行求解.另外,为了取得更好的修复效果,文中设计了一个边缘指示算子来自适应地控制新模型的扩散,以更好地保护修复图像的边缘细节.实验结果表明:相比传统的TV、TGV修复模型,新模型的修复效果在主观视觉上显得更加自然,且在峰值信噪比与相关系数等客观评价指标上均有提高.%As traditional variational model in repairing images ie easy to produce "staircase effect"or fuzzy details,it is proposed an adaptive second -order total generalized variational and fractional variational image restoration algo-rithm based on image decomposition.First of all,the target image is decomposed into the cartoon part and texture part,the cartoon part corresponds to the low,intermediate frequency of the target image,therefore the second -order total generalized variational model which has a better inhibition of "staircase effect"is used to repair;the texture part corresponds to the high frequency,so the fractional order variational model which has the enhancement effect on the details is used to repair.As the mentioned repair model is similar to the optimal value of the linear saddle points,the algorithm adopts primitive duality algorithm based on preliminary solution for the new model.In addition,in order to obtain better repair effect,a edge indicator operator is designed to adaptively control the spread of the new model,to protect the edge details of the restoration image better.The experimental results show that compared with the tradi-tional TV,TGV repair model,the repairing effect of the new model appears more natural on the subjective visual,and the peak signal -to -noise ratio and correlation coefficient of the objective evaluation index are also increased.