论文标题
与不完善的前向操作员和一般噪声模型的反问题的变分正规化
Variational regularisation for inverse problems with imperfect forward operators and general noise models
论文作者
论文摘要
我们研究了不完美的正向操作员的反问题的变异正则化方法，这些错误可以按订单间隔以班克晶格的部分顺序进行建模。我们对一般数据保真度术语和正则化功能的存在和凸双重性进行分析。对于A-Priori和A-posteriori参数选择规则，我们都可以从Bregman距离方面获得正则解决方案的收敛速率。我们的结果适用于诸如Wasserstein距离，F-Diverence，规范以及这些的总和和虚拟卷积之类的保真度术语。
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and convex duality for general data fidelity terms and regularisation functionals. Both for a-priori and a-posteriori parameter choice rules, we obtain convergence rates of the regularized solutions in terms of Bregman distances. Our results apply to fidelity terms such as Wasserstein distances, f-divergences, norms, as well as sums and infimal convolutions of those.
