uR2D2: an unsupervised learning formulation of the R2D2 paradigm for Radio-interferometric Imaging

In radio interferometry (RI), images are typically formed from observed visibility data by iterative algorithms. These alternate a major cycle --computing a residual image representing the discrepancy between the observed and model data--, with a minor cycle --leveraging an image model to update the sky image based on the current data residual. The recently introduced "Residual-to-Residual Deep neural network (DNN) series for high-Dynamic-range imaging" (R2D2) paradigm is a learned and automated version of the traditional algorithm CLEAN, encapsulating the minor cycles in U-Net DNNs rather than simple thresholding operations requiring hyperparameter tuning. R2D2 was demonstrated to deliver much higher precision and faster processing than state-of-the-art image reconstruction algorithms, from CLEAN to optimisation algorithms such as uSARA. This performance stems from training a distinct DNN for each minor cycle, in a supervised manner, on a dataset of ground-truth images. Supervised learning, however, comes with its own challenge --an uncertain capability to generalise beyond the manifold of ground-truth images and observation settings sampled by the training dataset.

To address this challenge, we propose an unsupervised version of R2D2. Firstly, uR2D2 inherits R2D2’s automation and iterative structure. It encapsulates its minor cycles in U-Net DNNs, but dispenses with a ground-truth dataset by optimising its DNNs on the observed visibility data. More precisely, uR2D2 regularises the inverse problem by promoting invariance to the choice of data preconditioner: (i) inputting the set of Briggs-weighted data residual images alongside the current reconstruction, rather than a single Briggs weighting; and (ii) imposing that the reconstruction satisfies a data-fidelity constraint for all Briggs weightings simultaneously. Moreover, since each reconstruction depends on the DNN weights initialisation, a deep ensemble of runs yields per-pixel epistemic uncertainty maps. Finally, we demonstrate on simulated data and on real VLA observations of the celebrated radio galaxy Cygnus A that uR2D2’s reconstruction quality across high-dynamic-range settings is competitive with uSARA, and validate the deep-ensemble uncertainty maps against the true error maps in simulation.