  Unsupervised denoising is a crucial challenge in real-world imaging
applications. Unsupervised deep-learning methods have demonstrated impressive
performance on benchmarks based on synthetic noise. However, no metrics are
available to evaluate these methods in an unsupervised fashion. This is highly
problematic for the many practical applications where ground-truth clean images
are not available. In this work, we propose two novel metrics: the unsupervised
mean squared error (MSE) and the unsupervised peak signal-to-noise ratio
(PSNR), which are computed using only noisy data. We provide a theoretical
analysis of these metrics, showing that they are asymptotically consistent
estimators of the supervised MSE and PSNR. Controlled numerical experiments
with synthetic noise confirm that they provide accurate approximations in
practice. We validate our approach on real-world data from two imaging
modalities: videos in raw format and transmission electron microscopy. Our
results demonstrate that the proposed metrics enable unsupervised evaluation of
denoising methods based exclusively on noisy data.
