深度伪近端映射：一种用于迭代重建的自监督数据拟合代理
Deep Pseudo-Proximal Map: A Self-Supervised Data-Fitting Agent for Iterative Reconstruction
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- Purdue University（普渡大学）
- Oak Ridge National Laboratory（橡树岭国家实验室）
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中文总结 AI 辅助
提出深度伪近端映射，一种自监督数据拟合代理，将数据拟合近端映射重构为最小均方误差估计，无需真实图像训练，在去模糊、超分辨率和XCT上达到1% NRMSE，且XCT速度提升18倍。
中文摘要 AI 辅助
针对逆成像问题的迭代算法将重建过程分解为交替的子问题，其中一个子问题需要评估数据拟合近端映射。在许多实际情况下，该近端映射没有解析解，因此必须在每次迭代中通过内循环求解器进行近似，从而增加了外部重建循环的成本。为了解决这个问题，我们提出了伪近端映射（PPM），将数据拟合近端映射重新表述为合成概率模型的最小均方误差估计。我们将深度PPM实现为仅在采样的高斯噪声上训练的自监督神经网络，无需真实训练图像。对于任何前向模型$A$及其转置$A^T$可评估的算子，深度PPM均可训练，并且当$A$为线性时，可证明其与近端映射等价。我们在高斯去模糊和4倍超分辨率（其中近端映射有解析解）以及X射线计算机断层扫描（XCT，其中无解析解）上验证了深度PPM。作为迭代重建方法中的数据拟合代理，深度PPM在所有三种算子下将参考重建的NRMSE误差控制在1%以内，对于XCT，它用单次网络评估取代了内共轭梯度循环，速度提升18倍。
英文摘要
Iterative algorithms for inverse imaging problems split reconstruction into alternating subproblems, one of which requires evaluating the data-fitting proximal map. In many practical cases, this proximal map has no analytic solution and so must be approximated by an inner loop solver at every iteration, compounding the cost of the outer reconstruction loop. To address this, we propose the pseudo-proximal map (PPM), a reformulation of the data-fitting proximal map as the minimum mean square error estimate of a synthetic probabilistic model. We implement the deep PPM as a self-supervised neural network trained only on sampled Gaussian noise, requiring no ground-truth training images. The deep PPM can be trained for any operator for which the forward model $A$ and its transpose $A^T$ can be evaluated, with provable equivalence to the proximal map when $A$ is linear. We validate the deep PPM on Gaussian deblurring and 4x super-resolution, where the proximal map has an analytic solution, and on X-ray computed tomography (XCT), where no analytic solution exists. Used as the data-fitting agent within an iterative reconstruction method, the deep PPM reproduces the reference reconstruction to within 1% NRMSE for all three operators, and for XCT, it replaces the inner conjugate-gradient loop with a single network evaluation that is 18x faster.
