  Convolutional Neural Networks (CNNs) are highly effective for image
reconstruction problems. Typically, CNNs are trained on large amounts of
training images. Recently, however, un-trained CNNs such as the Deep Image
Prior and Deep Decoder have achieved excellent performance for image
reconstruction problems such as denoising and inpainting, \emph{without using
any training data}. Motivated by this development, we address the
reconstruction problem arising in accelerated MRI with un-trained neural
networks. We propose a highly optimized un-trained recovery approach based on a
variation of the Deep Decoder and show that it significantly outperforms other
un-trained methods, in particular sparsity-based classical compressed sensing
methods and naive applications of un-trained neural networks. We also compare
performance (both in terms of reconstruction accuracy and computational cost)
in an ideal setup for trained methods, specifically on the fastMRI dataset,
where the training and test data come from the same distribution. We find that
our un-trained algorithm achieves similar performance to a baseline trained
neural network, but a state-of-the-art trained network outperforms the
un-trained one. Finally, we perform a comparison on a non-ideal setup where the
train and test distributions are slightly different, and find that our
un-trained method achieves similar performance to a state-of-the-art
accelerated MRI reconstruction method.
