基于混合非凸性二阶全变分和重叠组稀疏的非盲图像去模糊算法

Non⁃blind image deblurring based on hybrid non⁃convex second⁃order total variation and the overlapping group sparse

为了解决凸性全变分正则化模型会使重构结果出现非闭合轮廓和非齐整边缘等缺点,设计了混合非凸性全变分耦合重叠组稀疏的图像去模糊算法。重叠组稀疏正则化项很好地考虑了相邻元素之间相互交叉的关系,非凸性二阶l p范数正则化项较好保持了图像的边缘形状信息,同时将这两个正则约束项融入到全变分函数中,可以准确地恢复边缘结构特征以及消除平滑区的阶梯效应和振铃效应。最后,为实现非凸性高阶模型的优化求解,提出了变量分裂法,将该模型分离成4个子问题,然后借助重加权l1交替方向法来完成图像去模糊的计算。测试数据显示,相比当前图像复原技术,所提算法具备更为理想的去模糊效果,复原图像表现出更高的峰值信噪比和结构相似度,可以更有效地恢复出边缘形状信息和纹理细节。

In order to solve the problem as non⁃closed contour and non⁃uniform edge of reconstruction results in convex total variational regularization model,a mode of image deblurring based on hybrid non⁃convex second⁃order total variation and overlapping group sparse is proposed.Overlapping group sparse regularization item well considering the cross relationship between adjacent elements,non convexity second⁃order lp norm regularization item better keep the edge of the image shape information,and the two regular constraint into total variation method at the same time,which can accurately restore edge structure characteristics and eliminate the staircase effect and smooth ringing effect.Finally,in order to achieve the optimal solution of the non⁃convex higher⁃order model,the variable splitting method is proposed to separate the model into four sub⁃problems,and then the method of a re⁃weighted l1 alternating direction method is used to complete the calculation of image deblurring.The test data show that compared with the current image restoration technology,the proposed algorithm has better deblurring effect,the restored image shows higher peak signal⁃to⁃noise ratio and structural similarity,which can recover edge shape information and texture details more effectively.