Using multiobjective optimization to reconstruct interferometric data

Abstract

In very long baseline interferometry (VLBI), signals recorded at multiple antennas are combined to form a sparsely sampled virtual aperture with an effective diameter set by the largest separation between the antennas. Due to the sparsity of the sampled aperture, VLBI imaging constitutes an ill-posed inverse problem. Various algorithms have been employed to deal with the VLBI imaging, including the recently proposed multiobjective evolutionary algorithm by decomposition (MOEA/D) described in the first paper of this series. Among the approaches to the reconstruction of the image features in total intensity from sparsely sampled visibilities, extensions to the polarimetric and the temporal domain are of great interest for the VLBI community in general and the Event Horizon Telescope Collabroration (EHTC) in particular. Based on the success of MOEA/D in presenting an alternative claim of the image structure in a unique, fast, and largely unsupervised way, we study the extension of MOEA/D to polarimetric and time dynamic reconstructions in this paper. To this end, we utilized the multiobjective, evolutionary framework introduced for MOEA/D, but added the various penalty terms specific to total intensity imaging time-variable and polarimetric variants, respectively. We computed the Pareto front (the sample of all non-dominated solutions) and identified clusters of close proximities. We tested MOEA/D with synthetic data sets that are representative for the main science targets and instrumental configuration of the EHTC and its possible successors. We successfully recovered the polarimetric and time-dynamic signature of the ground truth movie (even with relative sparsity) and a set of realistic data corruptions. MOEA/D has been successfully extended to polarimetric and time-dynamic reconstructions and, specifically, in a setting that would be expected for the EHTC. It offers a unique alternative and independent claim to the already existing methods, along with a number of additional benefits, namely: it is the first method that effectively explores the problem globally and compared to regularized maximum likelihood (RML) methods. Thus, it waives the need for parameter surveys. Hence, MOEA/D is a novel, useful tool to characterize the polarimetric and dynamic signatures in a VLBI data set robustly with a minimal set of user-based choices. In a consecutive work, we will address the last remaining limitation for MOEA/D (the number of pixels and numerical performance), so that MOEA/D can firmly solidify its place within the VLBI data reduction pipeline.