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. We show that the resulting method significantly outperforms conventional un-trained methods such as total-variation norm minimization, as well as naive applications of un-trained networks. Most importantly, we achieve on-par performance with a standard trained baseline, the U-net, on the FastMRI dataset, a dataset for benchmarking deep learning based reconstruction methods. While state-of-the-art trained methods still outperform our un-trained method, our work demonstrates that current trained methods only achieve a minor performance gain over un-trained methods, at the cost of a loss in robustness to out-of-distribution examples. Therefore, un-trained neural networks are a serious competitor to trained ones for medical imaging.
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