When solving inverse problems, one has to deal with numerous potential sources of model inexactnesses, like object motion, calibration errors, or simplified data models. Regularized Sequential Subspace Optimization (ReSeSOp) allows to compensate for such inaccuracies within the reconstruction step by employing consecutive projections onto suitably defined subspaces. However, this approach relies on a priori estimates for the model inexactness levels which are typically unknown. In dynamic imaging applications, where inaccuracies arise from the unpredictable dynamics of the object, these estimates are particularly challenging to determine in advance. To overcome this limitation, we propose a learned version of ReSeSOp which allows to approximate inexactness levels on the fly. The proposed framework generalizes established unrolled iterative reconstruction schemes to inexact forward operators and is particularly tailored to the structure of dynamic problems. We also present a comprehensive mathematical analysis regarding the effect of dependencies within the forward problem, clarifying when and why dividing the overall problem into subproblems is essential. The proposed method is evaluated on various examples from dynamic imaging, including datasets from a rheological CT experiment, brain MRI, and real-time cardiac MRI. The respective results emphasize improvements in reconstruction quality while ensuring adequate data consistency.

翻译：在求解逆问题时，必须处理众多潜在的模型非精确性来源，例如物体运动、校准误差或简化的数据模型。正则化序列子空间优化（ReSeSOp）通过连续投影到适当定义的子空间上，能够在重建步骤中补偿此类不精确性。然而，该方法依赖于模型非精确性水平的先验估计，而这类估计通常是未知的。在动态成像应用中，不精确性源于物体的不可预测动态，这些估计值尤其难以预先确定。为克服此限制，我们提出一种学习型ReSeSOp方法，能够实时逼近非精确性水平。该框架将成熟的展开式迭代重建方案推广至非精确前向算子情形，并特别针对动态问题的结构进行定制。我们还提出了关于前向问题内部依赖效应的完整数学分析，阐明了何时以及为何需要将整体问题分解为子问题。所提方法在动态成像的多个示例中得到验证，包括流变学CT实验数据集、脑部MRI数据和实时心脏MRI数据。相应结果在确保充分数据一致性的同时，凸显了重建质量的提升。