On divergence approximations for unsupervised training of deep denoisers based on Stein's unbiased risk estimator

Recently, there have been several works on unsupervised learning for training deep learning based denoisers without clean images. Approaches based on Stein's unbiased risk estimator (SURE) have shown promising results for training Gaussian deep denoisers. However, their performance is sensitive to hyper-parameter selection in approximating the divergence term in the SURE expression. In this work, we briefly study the computational efficiency of Monte-Carlo (MC) divergence approximation over recently available exact divergence computation using backpropagation. Then, we investigate the relationship between smoothness of nonlinear activation functions in deep denoisers and robust divergence term approximations. Lastly, we propose a new divergence term that does not contain hyper-parameters. Both unsupervised training methods yield comparable performance to supervised training methods with ground truth for denoising on various datasets. While the former method still requires roughly tuned hyper parameter selection, the latter method removes the necessity of choosing one.