  The "deep image prior" proposed by Ulyanov et al. is an intriguing property
of neural nets: a convolutional encoder-decoder network can be used as a prior
for natural images. The network architecture implicitly introduces a bias; If
we train the model to map white noise to a corrupted image, this bias guides
the model to fit the true image before fitting the corrupted regions.
  This paper explores why the deep image prior helps in denoising natural
images. We present a novel method to analyze trajectories generated by the deep
image prior optimization and demonstrate:
  (i) convolution layers of the an encoder-decoder decouple the frequency
components of the image, learning each at different rates
  (ii) the model fits lower frequencies first, making early stopping behave as
a low pass filter.
  The experiments study an extension of Cheng et al which showed that at
initialization, the deep image prior is equivalent to a stationary Gaussian
process.
