The Spectral Bias of the Deep Image Prior

TL;DR

This paper investigates why the deep image prior effectively denoises images by analyzing how neural networks learn different frequency components over time, revealing a spectral bias towards low frequencies.

Contribution

It introduces a novel analysis method for deep image prior optimization trajectories and uncovers the spectral bias towards low frequencies during training.

Findings

Convolution layers decouple image frequency components.

Models learn lower frequencies faster, enabling early stopping as a low pass filter.

Deep image prior at initialization resembles a stationary Gaussian process.

Abstract

The "deep image prior" proposed by Ulyanov et al. is an intriguing property of neural nets: a convolutional encoder-decoder network can be used as a prior for natural images. The network architecture implicitly introduces a bias; If we train the model to map white noise to a corrupted image, this bias guides the model to fit the true image before fitting the corrupted regions. This paper explores why the deep image prior helps in denoising natural images. We present a novel method to analyze trajectories generated by the deep image prior optimization and demonstrate: (i) convolution layers of the an encoder-decoder decouple the frequency components of the image, learning each at different rates (ii) the model fits lower frequencies first, making early stopping behave as a low pass filter. The experiments study an extension of Cheng et al which showed that at initialization, the deep image prior is equivalent to a stationary Gaussian process.