The R2D2 deep neural network series paradigm for fast precision imaging in radio astronomy

TL;DR

This work tackles fast, high-dynamic-range imaging in radio interferometry by introducing R2D2, a Residual-to-Residual DNN series that reconstructs images via a sequence of learned residual updates. The approach blends a learned version of matching pursuit with a Forward-Backward PnP framework, offering two incarnations: a fully data-driven R2D2 and a data-model-informed R2D2-Net (R3D3). Through telescope-specific, VLA-focused training on a large ground-truth database and MeqTrees-based RI data generation, R2D2 achieves state-of-the-art imaging precision with far fewer iterations than traditional methods, and deeper R2D2-Net variants further improve dynamic range. Comparisons against uSARA, AIRI, and CLEAN show consistent, substantial gains in SNR and logSNR, highlighting the method’s potential for fast, automated, high-fidelity RI imaging in next-generation instruments.

Abstract

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.

Figures (5)

• Figure 1: Illustration of the R2D2 algorithm. Both image iterates $\boldsymbol{x}^{(i-1)}$ and associated residual dirty images $\boldsymbol{r}^{(i-1)}$ are fed to R2D2 DNNs as input. R2D2 DNNs' output are then used to update the next image iterates. The sequence of the image iterates and corresponding residual dirty images are indicated with dashed red and green arrows, respectively. The sequence of the learned residual images are indicated with blue arrows.
• Figure 2: Illustration of the U-Net core architecture underpinning the different incarnations of the R2D2 algorithm. The convolutional layers of the network, represented as boxes, apply multi-channel convolutions, followed by down-sampling (contracting path) or up-sampling (expanding path). The outcome of these layers are 3D feature maps, whose dimensions are specified around the corresponding boxes: the 2D spatial dimension at the bottom center, and the number of feature channels at the outer edge.
• Figure 3: Selection of raw low-dynamic range images (linear scale; top row), and corresponding ground-truth images after pre-processing (logarithmic scale; bottom row). The training dataset includes medical images (first column), and optical astronomy images (second column). The validation dataset comprises images of giant radio galaxies (e.g., Messier 87; third column), and radio galaxy clusters (e.g., Abell 746; fourth column).
• Figure 4: A selection of simulated 2D Fourier sampling patterns with the antenna configuration of the VLA (top row) and resulting dirty images (linear scale; bottom row). The depicted dirty images correspond to the ground-truth images shown in Figure \ref{['fig:train_val']}.
• Figure 5: Results of the dataset pruning procedure. Evolution of the size of the training dataset shown as a fraction of the size of the initial training dataset, throughout the iterations of R2D2 and both R3D3 realizations ($\textrm{R3D3}^{\textrm{3L}}$, $\textrm{R3D3}^{\textrm{6L}}$).