一种基于GNC和增广拉格朗日对偶的非凸非光滑图像恢复方法

A Method Based on the GNC and Augmented Lagrangian Duality for Nonconvex Nonsmooth Image Restoration

逐步非凸方法(GNC)和增广拉格朗日对偶在非凸非光滑图像恢复中有较高的恢复性能.然而分别使用这两种方法时GNC不能够保证全局收敛,增广拉格朗日对偶不能获得有效的初始值.为克服上述缺陷,本文通过转换原始问题为等式约束优化问题推出了一种基于GNC和增广拉格朗日对偶的组合图像恢复方法,并对其收敛性严格证明.该方法不仅可以获得有效的初始值,同时不要求问题具有凸性和光滑性.更多地,一个自适应能量函数通过对偶迭代而得到.实验结果表明推出的方法可以有效地提高图像恢复质量和算法效率.

The graduated nonconvex method （GNC） and augmented Lagrangian duality have superior restoration performance for nonconvex nonsmooth image restoration .However ,the global convergence of the general GNC could not be guaranteed and an effective initial value could not be obtained for the augmented Lagrangian duality when they are used separately .To overcome these drawbacks ,we propose a hybrid method based on the GNC and augmented Lagrangian duality by transforming the original problem into equality constrained optimization ,then its dual convergence has been strictly proven .The proposed method could get an effec-tive initial value and does not require the convexity and smoothness of the underlying problem .Moreover ,an adaptive energy func-tion is generated by the dual iterations .Experimental results show that the proposed method could enhance the quality of restored im-ages and the efficiency of algorithm effectively .