Gaussian Process Modelling for Improved Resolution in Faraday Depth
  Reconstruction
  The incomplete sampling of data in complex polarization measurements from
radio telescopes negatively affects both the rotation measure (RM) transfer
function and the Faraday depth spectra derived from these data. Such gaps in
polarization data are mostly caused by flagging of radio frequency interference
and their effects worsen as the percentage of missing data increases. In this
paper we present a novel method for inferring missing polarization data based
on Gaussian processes (GPs). Gaussian processes are stochastic processes that
enable us to encode prior knowledge in our models. They also provide a
comprehensive way of incorporating and quantifying uncertainties in regression
modelling. In addition to providing non-parametric model estimates for missing
values, we also demonstrate that Gaussian process modelling can be used for
recovering rotation measure values directly from complex polarization data, and
that inferring missing polarization data using this probabilistic method
improves the resolution of reconstructed Faraday depth spectra.
