CAJ | 학술논문

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。
축보비철방법（GNC）화증엄랍격랑일대우재비철비광활도상회복중유교고적회복성능。연이분별사용저량충방법시GNC불능구보증전국수렴，증엄랍격랑일대우불능획득유효적초시치。위극복상술결함，본문통과전환원시문제위등식약속우화문제추출료일충기우GNC화증엄랍격랑일대우적조합도상회복방법，병대기수렴성엄격증명。해방법불부가이획득유효적초시치，동시불요구문제구유철성화광활성。경다지，일개자괄응능량함수통과대우질대이득도。실험결과표명추출적방법가이유효지제고도상회복질량화산법효솔。
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 .