Removing the Representation Error of GAN Image Priors Using the Deep Decoder

Generative models, such as GANs, have demonstrated impressive performance as natural image priors for solving inverse problems such as image restoration and compressive sensing. Despite this performance, they can exhibit substantial representation error for both in-distribution and out-of-distribution images, because they maintain explicit low-dimensional learned representations of a natural signal class. In this paper, we demonstrate a method for removing the representation error of a GAN when used as a prior in inverse problems by modeling images as the linear combination of a GAN 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.