  Compressive sensing (CS) is an effective approach for fast Magnetic Resonance
Imaging (MRI). It aims at reconstructing MR images from a small number of
under-sampled data in k-space, and accelerating the data acquisition in MRI. To
improve the current MRI system in reconstruction accuracy and speed, in this
paper, we propose two novel deep architectures, dubbed ADMM-Nets in basic and
generalized versions. ADMM-Nets are defined over data flow graphs, which are
derived from the iterative procedures in Alternating Direction Method of
Multipliers (ADMM) algorithm for optimizing a general CS-based MRI model. They
take the sampled k-space data as inputs and output reconstructed MR images.
Moreover, we extend our network to cope with complex-valued MR images. In the
training phase, all parameters of the nets, e.g., transforms, shrinkage
functions, etc., are discriminatively trained end-to-end. In the testing phase,
they have computational overhead similar to ADMM algorithm but use optimized
parameters learned from the data for CS-based reconstruction task. We
investigate different configurations in network structures and conduct
extensive experiments on MR image reconstruction under different sampling
rates. Due to the combination of the advantages in model-based approach and
deep learning approach, the ADMM-Nets achieve state-of-the-art reconstruction
accuracies with fast computational speed.
