Graph spectral clustering of convolution artefacts in radio interferometric images

The starting point for deconvolution methods in radio astronomy is an estimate of the sky intensity called a dirty image. These methods rely on the telescope point spread function so as to remove artefacts which pollute it. In this work, we show that the intensity field is only a partial summary statistic of the matched filtered interferometric data, which we prove is spatially correlated on the celestial sphere. This allows us to define a sky covariance function. This previously unexplored quantity brings us additional information that can be leveraged in the process of removing dirty image artefacts. We demonstrate this using a novel unsupervised learning method. The problem is formulated on a graph: each pixel interpreted as a node, linked by edges weighted according to their spatial correlation. We then use spectral clustering to separate the artefacts in groups, and identify physical sources within them.