The R2D2 Deep Neural Network (DNN) series was recently introduced for image formation in radio interferometry. It can be understood as a learned version of CLEAN, whose minor cycles are substituted with DNNs. We revisit R2D2 on the grounds of series convergence, training methodology, and DNN architecture, improving its robustness in terms of generalisability beyond training conditions, capability to deliver high data fidelity, and epistemic uncertainty. Firstly, while still focusing on telescope-specific training, we enhance the learning process by randomising Fourier sampling integration times, incorporating multi-scan multi-noise configurations, and varying imaging settings, including pixel resolution and visibility-weighting scheme. Secondly, we introduce a convergence criterion whereby the reconstruction process stops when the data residual is compatible with noise, rather than simply using all available DNNs. This not only increases the reconstruction efficiency by reducing its computational cost, but also refines training by pruning out the data/image pairs for which optimal data fidelity is reached before training the next DNN. Thirdly, we substitute R2D2's early U-Net DNN with a novel architecture (U-WDSR) combining U-Net and WDSR, which leverages wide activation, dense connections, weight normalisation, and low-rank convolution to improve feature reuse and reconstruction precision. As previously, R2D2 was trained for monochromatic intensity imaging with the Very Large Array (VLA) at fixed $512 \times 512$ image size. Simulations on a wide range of inverse problems and a case study on real data reveal that the new R2D2 model consistently outperforms its earlier version in image reconstruction quality, data fidelity, and epistemic uncertainty.

The ``Residual-to-Residual DNN series for high-Dynamic range imaging'' (R2D2) approach was recently introduced for Radio-Interferometric (RI) imaging in astronomy. R2D2's reconstruction is formed as a series of residual images, iteratively estimated as outputs of Deep Neural Networks (DNNs) taking the previous iteration's image estimate and associated data residual as inputs. In this work, we investigate the robustness of the R2D2 image estimation process, by studying the uncertainty associated with its series of learned models. Adopting an ensemble averaging approach, multiple series can be trained, arising from different random DNN initializations of the training process at each iteration. The resulting multiple R2D2 instances can also be leveraged to generate ``R2D2 samples'', from which empirical mean and standard deviation endow the algorithm with a joint estimation and uncertainty quantification functionality. Focusing on RI imaging, and adopting a telescope-specific approach, multiple R2D2 instances were trained to encompass the most general observation setting of the Very Large Array (VLA). Simulations and real-data experiments confirm that: (i) R2D2's image estimation capability is superior to that of the state-of-the-art algorithms; (ii) its ultra-fast reconstruction capability (arising from series with only few DNNs) makes the computation of multiple reconstruction samples and of uncertainty maps practical even at large image dimension; (iii) it is characterized by a very low model uncertainty.

Radio-interferometric (RI) imaging entails solving high-resolution high-dynamic range inverse problems from large data volumes. Recent image reconstruction techniques grounded in optimization theory have demonstrated remarkable capability for imaging precision, well beyond CLEAN's capability. These range from advanced proximal algorithms propelled by handcrafted regularization operators, such as the SARA family, to hybrid plug-and-play (PnP) algorithms propelled by learned regularization denoisers, such as AIRI. Optimization and PnP structures are however highly iterative, which hinders their ability to handle the extreme data sizes expected from future instruments. To address this scalability challenge, we introduce a novel deep learning approach, dubbed "Residual-to-Residual DNN series for high-Dynamic range imaging". R2D2's reconstruction is formed as a series of residual images, iteratively estimated as outputs of Deep Neural Networks (DNNs) taking the previous iteration's image estimate and associated data residual as inputs. It thus takes a hybrid structure between a PnP algorithm and a learned version of the matching pursuit algorithm that underpins CLEAN. We present a comprehensive study of our approach, featuring its multiple incarnations distinguished by their DNN architectures. We provide a detailed description of its training process, targeting a telescope-specific approach. R2D2's capability to deliver high precision is demonstrated in simulation, across a variety of image and observation settings using the Very Large Array (VLA). Its reconstruction speed is also demonstrated: with only few iterations required to clean data residuals at dynamic ranges up to 100000, R2D2 opens the door to fast precision imaging. R2D2 codes are available in the BASPLib library on GitHub.

Accompanying Part I, this sequel delineates a validation of the recently proposed AI for Regularisation in radio-interferometric Imaging (AIRI) algorithm on observations from the Australian Square Kilometre Array Pathfinder (ASKAP). The monochromatic AIRI-ASKAP images showcased in this work are formed using the same parallelised and automated imaging framework described in Part I: ``uSARA validated on ASKAP data''. Using a Plug-and-Play approach, AIRI differs from uSARA by substituting a trained denoising deep neural network (DNN) for the proximal operator in the regularisation step of the forward-backward algorithm during deconvolution. We build a trained shelf of DNN denoisers which target the estimated image-dynamic-ranges of our selected data. Furthermore, we quantify variations of AIRI reconstructions when selecting the nearest DNN on the shelf versus using a universal DNN with the highest dynamic range, opening the door to a more complete framework that not only delivers image estimation but also quantifies epistemic model uncertainty. We continue our comparative analysis of source structure, diffuse flux measurements, and spectral index maps of selected target sources as imaged by AIRI and the algorithms in Part I -- uSARA and WSClean. Overall we see an improvement over uSARA and WSClean in the reconstruction of diffuse components in AIRI images. The scientific potential delivered by AIRI is evident in further imaging precision, more accurate spectral index maps, and a significant acceleration in deconvolution time, whereby AIRI is four times faster than its sub-iterative sparsity-based counterpart uSARA.

We introduce the first AI-based framework for deep, super-resolution, wide-field radio-interferometric imaging, and demonstrate it on observations of the ESO~137-006 radio galaxy. The algorithmic framework to solve the inverse problem for image reconstruction builds on a recent ``plug-and-play'' scheme whereby a denoising operator is injected as an image regulariser in an optimisation algorithm, which alternates until convergence between denoising steps and gradient-descent data-fidelity steps. We investigate handcrafted and learned variants of high-resolution high-dynamic range denoisers. We propose a parallel algorithm implementation relying on automated decompositions of the image into facets and the measurement operator into sparse low-dimensional blocks, enabling scalability to large data and image dimensions. We validate our framework for image formation at a wide field of view containing ESO~137-006, from 19 gigabytes of MeerKAT data at 1053 and 1399 MHz. The recovered maps exhibit significantly more resolution and dynamic range than CLEAN, revealing collimated synchrotron threads close to the galactic core.