We propose a new MR image reconstruction method that systematically enforces data consistency while also exploiting deep-learning imaging priors. The prior is specified through a convolutional neural network (CNN) trained to remove undersampling artifacts from MR images without any artifact-free ground truth. The results on reconstructing free-breathing MRI data into ten respiratory phases show that the method can form high-quality 4D images from severely undersampled measurements corresponding to acquisitions of about 1 minute in length. The results also highlight the improved performance of the method compared to several popular alternatives, including compressive sensing and UNet3D.
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