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：学习型迭代重建方法凭借对模型扰动的经验鲁棒性，在加速断层成像方面展现出巨大潜力。然而，其在光声断层成像中的应用受限于需反复评估计算代价高昂的正向模型。采用快速近似模型可实现计算可行性，但需补偿模型误差。本研究通过将模型校正嵌入学习型原始-对偶框架，推进了学习型图像重建中模型校正的方法论与理论基础。具体而言，模型校正与图像域中的学习型更新算子共同在数据域中联合学习，构成一种展开式端到端学习迭代重建方法。该框架可扩展至原始-对偶深度均衡模型，具有不动点收敛特性并降低训练内存需求。我们通过理论分析与真实二维有限视角场景下的数值验证，为所提模型提供了理论及经验依据。经过模型校正的学习型原始-对偶方法在保持快速推理速度的同时实现了卓越的重建质量，为光声断层成像中可实时部署且可扩展的迭代重建奠定了方法论基础。