Recently developed deep-learning-based denoisers often outperform state-of-the-art conventional denoisers, such as the BM3D. They are typically trained to minimizethe mean squared error (MSE) between the output image of a deep neural networkand a ground truth image. In deep learning based denoisers, it is important to use high quality noiseless ground truth data for high performance, but it is often challenging or even infeasible to obtain noiseless images in application areas such as hyperspectral remote sensing and medical imaging. In this article, we propose a method based on Stein's unbiased risk estimator (SURE) for training deep neural network denoisers only based on the use of noisy images. We demonstrate that our SURE-based method, without the use of ground truth data, is able to train deep neural network denoisers to yield performances close to those networks trained with ground truth, and to outperform the state-of-the-art denoiser BM3D. Further improvements were achieved when noisy test images were used for training of denoiser networks using our proposed SURE-based method.

The usual minimization of the l2-loss between ground truth and training data is replaced by the minimization over an unbiased estimator over training data, sampled in a Monte-Carlo fashion. The submission highlights how previous techniques for unbiased parameter estimation can be translated into the CNNs and shows very intriguing results, training without ground truth data. A missing aspect that has to be addressed is the existence of minimizer of the SURE estimator (equation (13)) - it is easy to contruct simple (e.g. The function value is not necessarily bounded from below, and the infimum over (13) becomes minus infinity. How can such cases be excluded, either by assumptions on the data / the number of free parameters, or by additional regularization on theta?

Recently developed deep-learning-based denoisers often outperform state-of-the-art conventional denoisers, such as the BM3D. They are typically trained to minimizethe mean squared error (MSE) between the output image of a deep neural networkand a ground truth image. In deep learning based denoisers, it is important to use high quality noiseless ground truth data for high performance, but it is often challenging or even infeasible to obtain noiseless images in application areas such as hyperspectral remote sensing and medical imaging. In this article, we propose a method based on Stein's unbiased risk estimator (SURE) for training deep neural network denoisers only based on the use of noisy images. We demonstrate that our SURE-based method, without the use of ground truth data, is able to train deep neural network denoisers to yield performances close to those networks trained with ground truth, and to outperform the state-of-the-art denoiser BM3D.

Recent deep learning based denoisers are trained to minimize the mean squared error (MSE) between the output of a network and the ground truth noiseless image in the training data. Thus, it is crucial to have high quality noiseless training data for high performance denoisers. Unfortunately, in some application areas such as medical imaging, it is expensive or even infeasible to acquire such a clean ground truth image. We propose a Stein's Unbiased Risk Estimator (SURE) based method for training deep learning based denoisers without ground truth data. We demonstrated that our SURE based method only with noisy input data was able to train CNN based denoising networks that yielded performance close to that of the original MSE based deep learning denoisers with ground truth data.