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.
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