Valkonen Tuomo, Pock Thomas
1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK.
2Department of Mathematical Sciences, University of Liverpool, Liverpool, UK.
J Math Imaging Vis. 2017;59(3):394-414. doi: 10.1007/s10851-016-0692-2. Epub 2016 Dec 15.
We propose several variants of the primal-dual method due to Chambolle and Pock. Without requiring full strong convexity of the objective functions, our methods are accelerated on subspaces with strong convexity. This yields mixed rates, with respect to initialisation and (1 / ) with respect to the dual sequence, and the residual part of the primal sequence. We demonstrate the efficacy of the proposed methods on image processing problems lacking strong convexity, such as total generalised variation denoising and total variation deblurring.
我们提出了几种源于尚博勒（Chambolle）和波克（Pock）的原始对偶方法的变体。在不需要目标函数具有完全强凸性的情况下，我们的方法在具有强凸性的子空间上得到了加速。这产生了混合速率，相对于初始化是 ，相对于对偶序列以及原始序列的残差部分是 。我们在缺乏强凸性的图像处理问题上证明了所提出方法的有效性，例如全广义变分去噪和全变差去模糊。
