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.

翻译：我们提出了一种用于非笛卡尔磁共振图像重建的新方法。尽管展开式架构通过数据一致性层提供了鲁棒性，但在大规模场景下将测量算子嵌入深度神经网络（DNN）可能变得不切实际。另一种即插即用（PnP）方法中，去噪DNN对测量设置不可知，因此不受此限制影响且已被证明有效，但其高度迭代的特性同样影响可扩展性。为解决这一可扩展性挑战，我们借鉴了近期在天文成像中提出的“面向高动态范围成像的残差到残差DNN序列（R2D2）”方法。R2D2的重建结果由一系列残差图像构成，这些残差通过迭代方式估计，每次迭代的残差图像由DNN输出生成，该DNN以前次迭代的图像估计及对应的数据残差作为输入。该方法可被理解为匹配追踪算法的学习版本。我们通过仿真实验验证R2D2方法，考虑径向k空间采样采集序列。初步结果表明R2D2能够实现：（i）虽逊于其展开式变体R2D2-Net（因需嵌入基于NUFFT的数据一致性层而不可扩展）；（ii）重建质量优于采用基于FFT近似数据一致性层的可扩展版R2D2-Net；（iii）在仅需较少迭代次数的前提下，重建质量优于PnP方法。