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.

本文介绍了自然图像的一种先验算法 —— 深度图像先验，它使用卷积神经网络对随机输入进行输出，通过使用梯度下降来调整网络参数以使输出匹配观测值。该方法在一系列图像重建任务中表现良好。同时通过推导得出结论，该算法渐近等于一个平稳的高斯过程，这启发了贝叶斯推断的方法。通过使用随机梯度 Langevin 对后验推断实现去除过早终止的需要，并在去噪和修补任务中提高了结果表现。我们在一些一维和二维信号重建任务中验证了这些算法的实用价值。