  Generative models, such as GANs, learn an explicit low-dimensional
representation of a particular class of images, and so they may be used as
natural image priors for solving inverse problems such as image restoration and
compressive sensing. GAN priors have demonstrated impressive performance on
these tasks, but they can exhibit substantial representation error for both
in-distribution and out-of-distribution images, because of the mismatch between
the learned, approximate image distribution and the data generating
distribution. In this paper, we demonstrate a method for reducing the
representation error of GAN priors by modeling images as the linear combination
of a GAN prior with a Deep Decoder. The deep decoder is an underparameterized
and most importantly unlearned natural signal model similar to the Deep Image
Prior. No knowledge of the specific inverse problem is needed in the training
of the GAN underlying our method. For compressive sensing and image
superresolution, our hybrid model exhibits consistently higher PSNRs than both
the GAN priors and Deep Decoder separately, both on in-distribution and
out-of-distribution images. This model provides a method for extensibly and
cheaply leveraging both the benefits of learned and unlearned image recovery
priors in inverse problems.
