  Magnetic resonance imaging (MRI) is known to be a slow imaging modality and
undersampling in k-space has been used to increase the imaging speed. However,
image reconstruction from undersampled k-space data is an ill-posed inverse
problem. Iterative algorithms based on compressed sensing have been used to
address the issue. In this work, we unroll the iterations of the primal-dual
hybrid gradient algorithm to a learnable deep network architecture, and
gradually relax the constraints to reconstruct MR images from highly
undersampled k-space data. The proposed method combines the theoretical
convergence guarantee of optimi-zation methods with the powerful learning
capability of deep networks. As the constraints are gradually relaxed, the
reconstruction model is finally learned from the training data by updating in
k-space and image domain alternatively. Experi-ments on in vivo MR data
demonstrate that the proposed method achieves supe-rior MR reconstructions from
highly undersampled k-space data over other state-of-the-art image
reconstruction methods.
