  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.
