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.

翻译：深度学习已成为解决成像逆问题（包括计算机断层扫描（CT））的强大工具。然而，大多数方法需要带有真实图像标签的配对训练数据，这在例如医学应用中可能难以获取。我们提出了TomoSelfDEQ，一个用于稀疏角度CT重建的自监督深度均衡（DEQ）框架，该框架直接在欠采样测量值上进行训练。我们建立了理论保证，表明在适当的假设下，我们的自监督更新与包含（可能非酉的）前向算子（如CT前向映射）的损失函数的全监督训练更新相匹配。在稀疏角度CT数据上的数值实验证实了这一发现，同时也表明TomoSelfDEQ优于现有的自监督方法，仅使用16个投影角度即可达到最先进的结果。