Tomography的同时重建与不确定性量化
Simultaneous Reconstruction and Uncertainty Quantification for Tomography
AI总结：
针对Tomography中因不适定性导致缺乏ground truth时解质量难以量化的问题，提出基于Gaussian process modeling的方法，在实现与现有实用方法相当重建效果的同时，高效量化解的不确定性。
摘要：
Tomographic reconstruction尽管对广泛的应用产生了革命性影响，但其不适定性导致由于有限且含噪的测量而不存在唯一解。因此，在缺乏ground truth的情况下，量化解的质量极为可取却研究不足。在本研究中，我们通过Gaussian process modeling应对这一挑战，通过选择kernels和noise models，灵活且显式地融入关于样本特征和实验噪声的先验知识。我们提出的方法不仅产生了与现有实用重建方法（例如，用于逆问题的regularized iterative solver）相当的重建，还提供了一种量化解不确定性的高效方式。我们在各种图像上展示了所提方法的能力，并展现了其在各种噪声存在时进行不确定性量化的独特能力。
英文摘要：
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.
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