Robustness of data-driven approaches in limited angle tomography

• DOI: 10.48550/arxiv.2403.11350
• Publication Date: 2025-01-29
• Authors: Yiran Wang; Yimin Zhong
• Keywords: FOS: Computer and information sciences; Computer Science - Machine Learning; 35R30; FOS: Mathematics; Mathematics - Numerical Analysis; Numerical Analysis (math.NA); Machine Learning (cs.LG)

The limited angle Radon transform is notoriously difficult to invert due to its ill-posedness. In this work, we give a mathematical explanation that data-driven approaches can stably reconstruct more information compared to traditional methods like filtered backprojection. In addition, we use experiments based on the U-Net neural network to validate our theory.