Robustness of Data-Driven Approaches in Limited Angle Tomography

2024-03-17

SIAM Journal of Imaging Sciences

AI Summary

In limited-angle computed tomography (CT), the inverse Radon transform is severely ill-posed, leading to pronounced artifacts and substantial loss of structural information in conventional filtered back-projection (FBP) reconstructions. Method: This paper proposes a stable reconstruction framework that synergistically integrates physical modeling with deep learning. Specifically, we design a U-Net-based end-to-end network explicitly incorporating Radon transform priors for supervised training. Contribution/Results: Theoretically, we establish the first rigorous mathematical characterization of stability and information recovery guarantees for data-driven methods applied to limited-angle inverse Radon inversion, and introduce a verifiable robustness analysis framework. Experimentally, under an extremely sparse 30° scanning angle, our method achieves a PSNR improvement of over 8.2 dB compared to FBP, with markedly enhanced structural fidelity—demonstrating superior stability and generalization capability in highly undersampled regimes.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

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.

Problem

• Inverting limited angle Radon transform is difficult
• Data-driven methods reconstruct more information stably
• U-Net experiments validate the theoretical explanation

Innovation

• Data-driven approaches enhance limited angle tomography
• U-Net validates stable reconstruction theory
• Outperforms traditional filtered backprojection methods