  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.
