ELIPPS：部分自监督下逆问题的精确学习

中文摘要 AI 辅助

在欠采样逆问题（如稀疏视角计算机断层扫描）中，仅收集少量测量数据，这减少了辐射暴露、采集时间和成本，并且还可以解决某些采集安排不可行的问题。此类问题的大多数基于学习的方法需要以完全采样的测量和真实图像形式进行监督，而这些数据的获取成本高昂甚至不可行。为克服这一问题，我们提出了ELIPPS（部分自监督下逆问题的精确学习），一种针对欠采样逆问题的不完全自监督训练范式，该范式既不需要真实图像，也不需要完全采样的测量。ELIPPS仅从固定不完全监督集上的不完全前向测量中学习。我们的理论表明，当数据分布在特定变换下不变时，最小化掩蔽经验风险等价于最小化完全自监督风险，即针对完整、无噪声测量的风险。该等价性对于任意等变假设类都是精确的，并且适用于信号相关噪声，如低剂量断层扫描的对数前泊松统计，以及对数变换计数模型（直至可量化的偏差）。当底层覆盖条件仅在离散网格上近似满足时，我们给出了关于相关框架常数和逆问题不可约误差的稳定性估计。我们通过利用旋转和反射不变性在计算机断层扫描中实现了ELIPPS。在我们的实验中，ELIPPS显著优于朴素的掩蔽监督，并达到了与使用完整干净测量训练的参考模型相同数量级的精度。

英文摘要

In undersampled inverse problems (such as sparse-view computed tomography), only a small number of measurements are collected, which reduces radiation exposure and acquisition time and cost, and can also address the inaccessibility of certain acquisition arrangements. Most learning-based methods for such problems require supervision in the form of fully sampled measurements and ground-truth images, which are costly or even infeasible to acquire. To overcome this issue, we propose \emph{Exact Learning for Inverse Problems from Partial Self-supervision} (ELIPPS), an incomplete self-supervised training paradigm for undersampled inverse problems that requires neither ground-truth images nor fully sampled measurements. ELIPPS learns solely from incomplete forward measurements on a fixed incomplete supervision set. Our theory shows that when the data distribution is invariant under certain transformations, minimizing a masked empirical risk is equivalent to minimizing the full self-supervised risk, i.e. the risk against the complete, noise-free measurement. The equivalence is exact for arbitrary equivariant hypothesis classes and holds for signal-dependent noise such as the pre-log Poisson statistics of low-dose tomography, and for the log-transformed count model up to a quantifiable bias. When the underlying coverage condition is only approximately satisfied on a discrete grid, we give a stability estimate in terms of the associated frame constants and the irreducible error of the inverse problem. We realize ELIPPS for computed tomography by exploiting rotation and reflection invariance. In our experiments, ELIPPS substantially outperforms naive masked supervision and reaches the same order of accuracy as a reference model trained with full clean measurements.

发表机构

• University of Innsbruck（因斯布鲁克大学）
• Yeungnam University（庆北国立大学）

机构由 AI 辅助整理，请以论文原文为准。