The classic regularization theory for solving inverse problems is built on the assumption that the forward operator perfectly represents the underlying physical model of the data acquisition. However, in many applications, for instance in microscopy or magnetic particle imaging, this is not the case. Another important example represent dynamic inverse problems, where changes of the searched-for quantity during data collection can be interpreted as model uncertainties. In this article, we propose a regularization strategy for linear inverse problems with inexact forward operator based on sequential subspace optimization methods (SESOP). In order to account for local modelling errors, we suggest to combine SESOP with the Kaczmarz’ method. We study convergence and regularization properties of the proposed method and discuss several practical realizations. Relevance and performance of our approach are evaluated at simulated data from dynamic computerized tomography with various dynamic scenarios.

用于解决反问题的经典正则化理论是建立在以下假设之上的：前向运算符完美地代表了数据采集的基础物理模型。然而，在许多应用中，例如在显微镜或磁性粒子成像中，情况并非如此。另一个重要的例子是动态逆问题，其中数据收集过程中搜索量的变化可以解释为模型不确定性。在本文中，我们提出了一种基于顺序子空间优化方法（SESOP）的具有不精确前向算子的线性逆问题的正则化策略。为了解决局部建模错误，我们建议将SESOP与Kaczmarz方法结合使用。我们研究了该方法的收敛性和正则化性质，并讨论了一些实际的实现。我们的方法的相关性和性能是根据来自具有各种动态场景的动态计算机断层扫描的模拟数据进行评估的。