  Deep neural networks have been proved efficient for medical image denoising.
Current training methods require both noisy and clean images. However, clean
images cannot be acquired for many practical medical applications due to
naturally noisy signal, such as dynamic imaging, spectral computed tomography,
arterial spin labeling magnetic resonance imaging, etc. In this paper we
proposed a training method which learned denoising neural networks from noisy
training samples only. Training data in the acquisition domain was split to two
subsets and the network was trained to map one noisy set to the other. A
consensus loss function was further proposed to efficiently combine the outputs
from both subsets. A mathematical proof was provided that the proposed training
scheme was equivalent to training with noisy and clean samples when the noise
in the two subsets was uncorrelated and zero-mean. The method was validated on
Low-dose CT Challenge dataset and NYU MRI dataset and achieved improved
performance compared to existing unsupervised methods.
