Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of ground truth, quantifying the solution quality is highly desirable but under-explored. In this work, we address this challenge through Gaussian process modeling to flexibly and explicitly incorporate prior knowledge of sample features and experimental noises through the choices of the kernels and noise models. Our proposed method yields not only comparable reconstruction to existing practical reconstruction methods (e.g., regularized iterative solver for inverse problem) but also an efficient way of quantifying solution uncertainties. We demonstrate the capabilities of the proposed approach on various images and show its unique capability of uncertainty quantification in the presence of various noises.

翻译：断层成像重建虽在广泛应用中产生了革命性影响，但其病态特性导致因有限且有噪声的测量数据而无法获得唯一解。因此，在缺乏真实数据的情况下，量化解的质量极具价值但尚未被充分探索。本研究通过高斯过程建模应对这一挑战，利用核函数与噪声模型的选择，灵活明确地融入样本特征与实验噪声的先验知识。所提出的方法不仅能获得与现有实用重建方法（如反问题的正则化迭代求解器）相当的重建结果，还能高效实现解的不确定性量化。我们通过多种图像验证了该方法的效能，并展示了其在各类噪声环境下进行不确定性量化的独特能力。