  Fast and accurate MRI image reconstruction from undersampled data is crucial
in clinical practice. Deep learning based reconstruction methods have shown
promising advances in recent years. However, recovering fine details from
undersampled data is still challenging. In this paper, we introduce a novel
deep learning based method, Pyramid Convolutional RNN (PC-RNN), to reconstruct
images from multiple scales. Based on the formulation of MRI reconstruction as
an inverse problem, we design the PC-RNN model with three convolutional RNN
(ConvRNN) modules to iteratively learn the features in multiple scales. Each
ConvRNN module reconstructs images at different scales and the reconstructed
images are combined by a final CNN module in a pyramid fashion. The multi-scale
ConvRNN modules learn a coarse-to-fine image reconstruction. Unlike other
common reconstruction methods for parallel imaging, PC-RNN does not employ coil
sensitive maps for multi-coil data and directly model the multiple coils as
multi-channel inputs. The coil compression technique is applied to standardize
data with various coil numbers, leading to more efficient training. We evaluate
our model on the fastMRI knee and brain datasets and the results show that the
proposed model outperforms other methods and can recover more details. The
proposed method is one of the winner solutions in the 2019 fastMRI competition.
