  We propose a new approach for non-Cartesian magnetic resonance image
reconstruction. While unrolled architectures provide robustness via
data-consistency layers, embedding measurement operators in Deep Neural Network
(DNN) can become impractical at large scale. Alternative Plug-and-Play (PnP)
approaches, where the denoising DNNs are blind to the measurement setting, are
not affected by this limitation and have also proven effective, but their
highly iterative nature also affects scalability. To address this scalability
challenge, we leverage the "Residual-to-Residual DNN series for high-Dynamic
range imaging (R2D2)" approach recently introduced in astronomical imaging.
R2D2's reconstruction is formed as a series of residual images, iteratively
estimated as outputs of DNNs taking the previous iteration's image estimate and
associated data residual as inputs. The method can be interpreted as a learned
version of the Matching Pursuit algorithm. We demonstrate R2D2 in simulation,
considering radial k-space sampling acquisition sequences. Our preliminary
results suggest that R2D2 achieves: (i) suboptimal performance compared to its
unrolled incarnation R2D2-Net, which is however non-scalable due to the
necessary embedding of NUFFT-based data-consistency layers; (ii) superior
reconstruction quality to a scalable version of R2D2-Net embedding an FFT-based
approximation for data consistency; (iii) superior reconstruction quality to
PnP, while only requiring few iterations.
