Abstract
Online optimisation facilitates the solution of dynamic inverse problems, such as image stabilisation, fluid flow monitoring, and dynamic medical imaging. In this paper, we improve upon previous work on predictive online primal-dual methods on two fronts. Firstly, we provide a more concise analysis that symmetrises previously unsymmetric regret bounds, and relaxes previous restrictive conditions on the dual predictor. Secondly, based on the latter, we develop several improved dual predictors. We numerically demonstrate their efficacy in image stabilisation and dynamic positron emission tomography.
Abstract (translated)
在本文中，我们在两个方面超过了以往关于预测在线初始-对偶方法的工作。首先，我们提供了更简洁的分析，对称化了之前不对称的后悔的上界，并放宽了之前对对偶预测器的限制条件。其次，基于后者的研究，我们开发了几个改进的对偶预测器。我们用数值方式证明了它们在图像稳定和动态正电子发射断层扫描中的有效性。
URL
https://arxiv.org/abs/2405.02497
