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A non-destructive testing (NDT) application of X-ray computed tomography (CT) is inspection of subsea pipes in operation via 2D cross-sectional scans. Data acquisition is time-consuming and costly due to the challenging subsea environment. While reducing the number of projections in a CT scan yields time and cost savings, this compromises the reconstruction quality when conventional reconstruction methods are used. To address this issue we take a Bayesian approach to CT reconstruction and focus on designing an effective prior that introduces additional information to the problem. We propose a new class of structural Gaussian priors to enforce expected material properties in different regions of the reconstructed image based on available a-priori information about the pipe's layered structure. The prior is composed from Gaussian distributions, and we utilize this to propose an efficient computational strategy to sample the resulting posterior distribution. This is essential in practical NDT applications for fast processing of the large-scale data we see in CT. Numerical experiments with synthetic and real data show that the proposed structural Gaussian prior reduces artifacts and enhances contrast in the reconstruction, compared to using only a conventional Gaussian Markov random field prior or no prior information at all. Furthermore, we obtain uncertainty estimates that indicate the certainty of the reconstructions increase when more prior information is added. [ABSTRACT FROM AUTHOR]