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In this work, we consider the inverse problem of reconstructing the internal structure of an object from limited x-ray projections. We use a Gaussian process (GP) prior to model the target function and estimate its (hyper)parameters from measured data. In contrast to other established methods, this comes with the advantage of not requiring any manual parameter tuning, which usually arises in classical regularization strategies. Our method uses a basis function expansion technique for the GP which significantly reduces the computational complexity and avoids the need for numerical integration. The approach also allows for reformulation of come classical regularization methods as Laplacian and Tikhonov regularization as GP regression, and hence provides an efficient algorithm and principled means for their parameter tuning. Results from simulated and real data indicate that this approach is less sensitive to streak artifacts as compared to the commonly used method of filtered backprojection. [ABSTRACT FROM AUTHOR]