We introduce the R2D2 Deep Neural Network (DNN) series paradigm for fast and scalable image reconstruction from highly-accelerated non-Cartesian k-space acquisitions in Magnetic Resonance Imaging (MRI). While unrolled DNN architectures provide a robust image formation approach via data-consistency layers, embedding non-uniform fast Fourier transform operators in a DNN can become impractical to train at large scale, e.g in 2D MRI with a large number of coils, or for higher-dimensional imaging. Plug-and-play approaches that alternate a learned denoiser blind to the measurement setting with a data-consistency step are not affected by this limitation but their highly iterative nature implies slow reconstruction. To address this scalability challenge, we leverage the R2D2 paradigm that was recently introduced to enable ultra-fast reconstruction for large-scale Fourier imaging in radio astronomy. R2D2's reconstruction is formed as a series of residual images iteratively estimated as outputs of DNN modules taking the previous iteration's data residual as input. The method can be interpreted as a learned version of the Matching Pursuit algorithm. A series of R2D2 DNN modules were sequentially trained in a supervised manner on the fastMRI dataset and validated for 2D multi-coil MRI in simulation and on real data, targeting highly under-sampled radial k-space sampling. Results suggest that a series with only few DNNs achieves superior reconstruction quality over its unrolled incarnation R2D2-Net (whose training is also much less scalable), and over the state-of-the-art diffusion-based "Decomposed Diffusion Sampler" approach (also characterised by a slower reconstruction process).

翻译：本文介绍了R22D深度神经网络系列范式，用于从磁共振成像中高度加速的非笛卡尔k空间采集中实现快速且可扩展的图像重建。尽管展开式DNN架构通过数据一致性层提供了稳健的图像形成方法，但在DNN中嵌入非均匀快速傅里叶变换算子在大规模训练时可能变得不切实际，例如在具有大量线圈的二维MRI或更高维成像中。采用与测量设置无关的即插即用去噪器与数据一致性步骤交替进行的方案不受此限制影响，但其高度迭代的特性导致重建速度缓慢。为应对这一可扩展性挑战，我们运用了近期在射电天文大规模傅里叶成像中实现超快速重建的R2D2范式。R2D2的重建结果被构建为一系列残差图像，这些图像通过以前次迭代数据残差为输入的DNN模块迭代估计输出。该方法可被理解为匹配追踪算法的学习版本。我们在fastMRI数据集上以监督方式顺序训练了一系列R2D2 DNN模块，并针对高度欠采样的径向k空间采样，在仿真和真实数据中验证了其二维多线圈MRI重建性能。结果表明，仅需少量DNN构成的系列即可实现优于其展开式变体R2D2-Net（其训练可扩展性也显著不足）的重建质量，同时超越基于扩散的先进方法“分解扩散采样器”（该方法的重建过程同样较为缓慢）。