  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 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 Gaussian process 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 Gaussian process 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.
