  With recent deep learning based approaches showing promising results in
removing noise from images, the best denoising performance has been reported in
a supervised learning setup that requires a large set of paired noisy images
and ground truth for training. The strong data requirement can be mitigated by
unsupervised learning techniques, however, accurate modelling of images or
noise variance is still crucial for high-quality solutions. The learning
problem is ill-posed for unknown noise distributions. This paper investigates
the tasks of image denoising and noise variance estimation in a single, joint
learning framework. To address the ill-posedness of the problem, we present
deep variation prior (DVP), which states that the variation of a properly
learnt denoiser with respect to the change of noise satisfies some smoothness
properties, as a key criterion for good denoisers. Building upon DVP, an
unsupervised deep learning framework, that simultaneously learns a denoiser and
estimates noise variances, is developed. Our method does not require any clean
training images or an external step of noise estimation, and instead,
approximates the minimum mean squared error denoisers using only a set of noisy
images. With the two underlying tasks being considered in a single framework,
we allow them to be optimised for each other. The experimental results show a
denoising quality comparable to that of supervised learning and accurate noise
variance estimates.
