A Bayesian Perspective on the Deep Image Prior
This provides a theoretical foundation for the deep image prior, addressing a drawback for researchers in image processing, though it is incremental as it builds on existing methods.
The paper tackles the problem of image reconstruction by showing that the deep image prior is asymptotically equivalent to a Gaussian process prior, enabling a Bayesian inference approach that avoids early stopping and improves results for denoising and inpainting tasks.
The deep image prior was recently introduced as a prior for natural images. It represents images as the output of a convolutional network with random inputs. For "inference", gradient descent is performed to adjust network parameters to make the output match observations. This approach yields good performance on a range of image reconstruction tasks. We show that the deep image prior is asymptotically equivalent to a stationary Gaussian process prior in the limit as the number of channels in each layer of the network goes to infinity, and derive the corresponding kernel. This informs a Bayesian approach to inference. We show that by conducting posterior inference using stochastic gradient Langevin we avoid the need for early stopping, which is a drawback of the current approach, and improve results for denoising and impainting tasks. We illustrate these intuitions on a number of 1D and 2D signal reconstruction tasks.