Attributing Aliasing Artifacts in Dirty Intensity Fields to their Parent Source

Estimating intensity fields of stochastic phenomenons is of crucial interest in many scientific applications. Typical experimental setups involve an acquisition system, that subsequently filters and samples the probed intensity field. This equivalently defines a sampling operator, fully specified by the characteristics of the measuring device. Reconstruction of the intensity field can then be achieved by performing an interpolation step on the collected samples, with an interpolation operator ideally matched with the sampling operator. Sampling followed by interpolation can be shown to act as an orthogonal projection onto the unknown intensity field. For this reason, the reconstructed intensity field can in general differ quite substantially from the actual one, polluted by aliasing artifacts that complicate and often forbid the identification of features within it. Nonlinear algorithms such as CLEAN (acclamated in radio astronomy) have been proposed to recover the actual features from the aliased intensity field, but their convergence properties have not yet been fully assessed. In this work, we propose a novel method to locate sources within the recovered intensity field and attribute aliasing artifacts to their parent source, in the specific case of point source intensity fields. Rather than directly estimating the intensity field, we first reconstruct the underlying random field it characterises. We then estimate the second moment of this reconstructed random field, including its covariance function. We use the covariance function as a measure of resemblance of different parts of the intensity field. The problem is then formulated as a clustering problem on a graph: the intensity field is sampled on a fine grid, each grid point is interpreted as a node on a graph, and edges between nodes are weighted proportionally to their covariance. We then use spectral clustering to separate the artifacts in groups, and identify the actual sources in the field as the nodes with maximum intensity within each cluster. We conclude with an application of our method to the field of radio astronomy.