s is a very crucial step to produce a good reconstruction.

Conclusions
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We have employed the Gaussian process with a hierarchical prior to computed tomography using limited projection data. The method was implemented to estimate the x-ray attenuation function from the measured data produced by the Radon transform. The performance has been tested on simulated and real data, with promising results shown. Unlike algorithms commonly used for the limited x-ray tomography problem that require manual tuning of prior parameters, the proposed GP method offers an easier set up as it takes into account the prior parameters as a part of the estimation. Henceforth, it constitutes a promising and user-friendly strategy.

The most important part of the GP model is the selection of the covariance function, since it stipulates the properties of the unknown function. As such, it also leaves most room for improvement. Considering the examples in Section \[sec:expResults\], a common feature of the target functions is that they consist of a number of well-defined, separate regions. The function values are similar and thus highly correlated within the regions, while the correlation is low at the edges where rapid changes occur. This kind of behavior is hard to capture with a stationary covariance function that models the correlation as completely dependent on the distance between the input locations. A non-stationary alternative is provided by, for example, the neural network covariance function, which is known for its ability to model functions with non-smooth features [@Rasmussen2006]. The basis function approximation method employed in this work is only applicable to stationary covariance functions, but other approximations can of course be considered.

Despite its success, the computational burden of the proposed algorithm is relatively high. To solve this problem, speed-up strategies are available, such as implementing parallelized GPU code, optimizing the covariances of the sampling strategy, or by changing the MCMC