The reconstruction of blood velocity in a vessel from contrast enhanced x-ray computed tomography projections is a complex inverse problem. It can be formulated as reconstruction problem with a partial differential equation constraint. A solution can be estimated with the a variational adjoint method and proper orthogonal decomposition (POD) basis. In this work, we investigate new inversion approaches based on PODs coupled with deep learning methods. The effectiveness of the reconstruction methods is shown with simulated realistic stationary blood flows in a vessel. The methods outperform the reduced adjoint method and show large speed-up at the online stage.

中文翻译：

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对比增强 X 射线计算机断层扫描血管血流重建的深度学习方法

从对比增强 X 射线计算机断层扫描投影重建血管中的血流速度是一个复杂的逆问题。它可以表述为具有偏微分方程约束的重构问题。可以使用变分伴随法和适当的正交分解 (POD) 基础来估计解。在这项工作中，我们研究了基于 POD 与深度学习方法相结合的新反演方法。通过模拟血管中真实的静态血流显示了重建方法的有效性。该方法优于简化伴随方法，并且在在线阶段显示出很大的加速。