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Regularization by denoising (RED) is an image reconstruction framework that uses an image denoiser as a prior. Recent work has shown the state-of-the-art performance of RED with learned denoisers corresponding to pre-trained convolutional neural nets (CNNs). In this work, we propose to broaden the current denoiser-centric view of RED by considering priors corresponding to networks trained for more general artifact-removal. The key benefit of the proposed family of algorithms, called regularization by artifact-removal (RARE), is that it can leverage priors learned on datasets containing only undersampled measurements. This makes RARE applicable to problems where it is practically impossible to have fully-sampled groundtruth data for training. We validate RARE on both simulated and experimentally collected data by reconstructing a free-breathing whole-body 3D MRIs into ten respiratory phases from heavily undersampled k-space measurements. Our results corroborate the potential of learning regularizers for iterative inversion directly on undersampled and noisy measurements.
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