  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. Traditional
optimization-based reconstruction relies on regularization to address this
issue; however, it faces its own challenge because the type of regularizer and
choice of regularization parameter are a critical but difficult decision.
Moreover, traditional reconstruction yields point estimates for the
reconstruction with no further indication of the quality of the solution. In
this work we address these challenges by exploring Gaussian processes (GPs).
Our proposed GP approach yields not only the reconstructed object through the
posterior mean but also a quantification of the solution uncertainties through
the posterior covariance. Furthermore, we explore the flexibility of the GP
framework to provide a robust model of the information across various length
scales in the object, as well as the complex noise in the measurements. We
illustrate the proposed approach on both synthetic and real tomography images
and show its unique capability of uncertainty quantification in the presence of
various types of noise, as well as reconstruction comparison with existing
methods.
