The Spectral Bias of the Deep Image Prior
This provides insights into the spectral bias of neural networks for researchers in image processing and deep learning, but it is incremental as it builds on prior work analyzing the deep image prior.
The paper investigates why the deep image prior helps in denoising natural images, showing that convolution layers decouple frequency components and fit lower frequencies first, making early stopping act as a low-pass filter.
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.