  Recently developed deep-learning-based denoisers often outperform
state-of-the-art conventional denoisers such as the BM3D. They are typically
trained to minimize the mean squared error (MSE) between the output image of a
deep neural network (DNN) and a ground truth image. Thus, it is important for
deep-learning-based denoisers to use high quality noiseless ground truth data
for high performance. However, it is often challenging or even infeasible to
obtain noiseless images in some applications. Here, we propose a method based
on Stein's unbiased risk estimator (SURE) for training DNN denoisers based only
on the use of noisy images in the training data with Gaussian noise. We
demonstrate that our SURE-based method, without the use of ground truth data,
is able to train DNN denoisers to yield performances close to those networks
trained with ground truth for both grayscale and color images. We also propose
a SURE-based refining method with a noisy test image for further performance
improvement. Our quick refining method outperformed conventional BM3D, deep
image prior, and often the networks trained with ground truth. Potential
extension of our SURE-based methods to Poisson noise model was also
investigated.
