  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.
