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.
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