A Bayesian Perspective on the Deep Image Prior

Zezhou Cheng; Matheus Gadelha; Subhransu Maji; Daniel Sheldon

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arXiv · 1904.07457

A Bayesian Perspective on the Deep Image Prior

Zezhou Cheng·Matheus Gadelha·Subhransu Maji·Daniel Sheldon

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Abstract

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.

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Zezhou Cheng, Matheus Gadelha, Subhransu Maji, Daniel Sheldon. 2019-04-16. A Bayesian Perspective on the Deep Image Prior. https://arxiv.org/abs/1904.07457

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