无需配对数据，用自监督方法实现少角度CT重建
TomoSelfDEQ: Self-Supervised Deep Equilibrium Learning for Sparse-Angle CT Reconstruction
- 基于深度平衡网络，直接在欠采样投影数据上训练
- 仅需16个投影角度即达当前最优重建效果
- 理论保证自监督与有监督训练等效，适合医疗数据场景
深度学习已成为解决成像中逆问题的强大工具，包括计算机断层扫描（CT）。然而，多数方法需要带有真实图像的成对训练数据，这在医学应用中难以获取。我们提出TomoSelfDEQ，一种用于少角度CT重建的自监督深度平衡（DEQ）框架，可直接在欠采样测量数据上训练。理论上证明，在合理假设下，我们的自监督更新与包含（可能非酉）前向算子（如CT前向映射）的全监督训练一致。在少角度CT数据上的数值实验验证了这一结论，且表明TomoSelfDEQ优于现有自监督方法，在仅16个投影角度时即达到当前最优性能。
原文摘要 · Abstract (English)
Deep learning has emerged as a powerful tool for solving inverse problems in imaging, including computed tomography (CT). However, most approaches require paired training data with ground truth images, which can be difficult to obtain, e.g., in medical applications. We present TomoSelfDEQ, a self-supervised Deep Equilibrium (DEQ) framework for sparse-angle CT reconstruction that trains directly on undersampled measurements. We establish theoretical guarantees showing that, under suitable assumptions, our self-supervised updates match those of fully-supervised training with a loss including the (possibly non-unitary) forward operator like the CT forward map. Numerical experiments on sparse-angle CT data confirm this finding, also demonstrating that TomoSelfDEQ outperforms existing self-supervised methods, achieving state-of-the-art results with as few as 16 projection angles.
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