  In this paper we introduce a natural image prior that directly represents a
Gaussian-smoothed version of the natural image distribution. We include our
prior in a formulation of image restoration as a Bayes estimator that also
allows us to solve noise-blind image restoration problems. We show that the
gradient of our prior corresponds to the mean-shift vector on the natural image
distribution. In addition, we learn the mean-shift vector field using denoising
autoencoders, and use it in a gradient descent approach to perform Bayes risk
minimization. We demonstrate competitive results for noise-blind deblurring,
super-resolution, and demosaicing.
