  We propose to leverage denoising autoencoder networks as priors to address
image restoration problems. We build on the key observation that the output of
an optimal denoising autoencoder is a local mean of the true data density, and
the autoencoder error (the difference between the output and input of the
trained autoencoder) is a mean shift vector. We use the magnitude of this mean
shift vector, that is, the distance to the local mean, as the negative log
likelihood of our natural image prior. For image restoration, we maximize the
likelihood using gradient descent by backpropagating the autoencoder error. A
key advantage of our approach is that we do not need to train separate networks
for different image restoration tasks, such as non-blind deconvolution with
different kernels, or super-resolution at different magnification factors. We
demonstrate state of the art results for non-blind deconvolution and
super-resolution using the same autoencoding prior.
