Learned iterative reconstructions hold great promise to accelerate tomographic imaging with empirical robustness to model perturbations. Nevertheless, an adoption for photoacoustic tomography is hindered by the need to repeatedly evaluate the computational expensive forward model. Computational feasibility can be obtained by the use of fast approximate models, but a need to compensate model errors arises. In this work we advance the methodological and theoretical basis for model corrections in learned image reconstructions by embedding the model correction in a learned primal-dual framework. Here, the model correction is jointly learned in data space coupled with a learned updating operator in image space within an unrolled end-to-end learned iterative reconstruction approach. The proposed formulation allows an extension to a primal-dual deep equilibrium model providing fixed-point convergence as well as reduced memory requirements for training. We provide theoretical and empirical insights into the proposed models with numerical validation in a realistic 2D limited-view setting. The model-corrected learned primal-dual methods show excellent reconstruction quality with fast inference times and thus providing a methodological basis for real-time capable and scalable iterative reconstructions in photoacoustic tomography.
翻译:学习迭代重建有很大的潜力来加速断层成像,并以经验稳健性应对模型扰动。但是,使用快速近似模型在光声断层成像中需要反复评估计算昂贵的正演模型,从而遇到了一系列困难。通过将模型校正嵌入到学习的原始-对偶框架中,本文推进了学习重建中的方法论和理论基础。在这里,模型校正与学习的更新算子在数据空间中联合学习,与一个以展开的端到端学习迭代重建方法相结合的图像空间中相互耦合。我们提出的模型允许扩展到一个原始-对偶深度平衡模型,提供固定点收敛以及减少训练的内存要求。我们在一个现实的2D 有限视野设定中提供了这些方法的理论和经验的细节和验证。模型校正的学习原始-对偶方法在快速推断时间和卓越的重建质量方面表现出色,因此为光声断层成像中的实时可行和可扩展的迭代重建提供了方法论基础。