  We present a novel, general-purpose method for deconvolving and denoising
images from gridded radio interferometric visibilities using Bayesian inference
based on a Gaussian process model. The method automatically takes into account
incomplete coverage of the uv-plane, signal mode coupling due to the primary
beam, and noise mode coupling due to uv sampling. Our method uses Gibbs
sampling to efficiently explore the full posterior distribution of the
underlying signal image given the data. We use a set of widely diverse mock
images with a realistic interferometer setup and level of noise to assess the
method. Compared to results from a proxy for point source- based CLEAN method
we find that in terms of RMS error and signal-to-noise ratio our approach
performs better than traditional deconvolution techniques, regardless of the
structure of the source image in our test suite. Our implementation scales as
O(np log np), provides full statistical and uncertainty information of the
reconstructed image, requires no supervision, and provides a robust, consistent
framework for incorporating noise and parameter marginalizations and foreground
removal.
