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. The supplementary material of this paper can be found here. The talk is available here.

tqdm python 3.6
tensorflow 1.13 or lower
scipy 1.2.1 or lower
numpy v1.17 or lower
matplotlib v3.1.0

above prerequisites + pytorch 1.13 or lower

It is better to use Conda for installation of all dependecies.

to demonstrate the performance of RARE with freath-breath 4D MRI, you can run the RARE by typing

$ python demo_RARE_np.py

or

$ python demo_RARE_torch.py

The per iteration results will be stored in the ./Results folder. The torch-mcnufft is a more efficient implementation using gpu backend. (Thanks wjgancn for his help in pytorch-mcnufft.)

The training code for artifact-to-artifact (A2A) convolutional neural network is coming soon. The pre-trained models are stored under the ./models folder. Feel free to download and test it.

If you find the paper useful in your research, please cite the paper:

@ARTICLE{Liu.etal2020,
  author={J. {Liu} and Y. {Sun} and C. {Eldeniz} and W. {Gan} and H. {An} and U. S. {Kamilov}},
  journal={IEEE Journal of Selected Topics in Signal Processing}, 
  title={RARE: Image Reconstruction using Deep Priors Learned without Ground Truth}, 
  year={2020},
  volume={14},
  number={6},
  pages={1088-1099},
  publisher={IEEE}
}