Adaptive control of spectral bias in Untrained Neural Network Priors for inverse problems

Untrained Neural Network Priors (UNNPs) has turned out to be a flexible priors for inverse problem, requiring no external data for training. However, it suffers from overfitting due to the over-parameterization of the network work, leading to second performance degradation. A concurrent work mitigates this by uniformly bounding the spectral norms across all convolutional layers, failing to account for the varying influence of individual layers based on their depth. In this paper, we propose an adaptive approach to control the spectral bias in UNNPs, thus reducing overfitting. Inspired by the observation that spectral norms increase as the network processes higher frequencies, our method allows the spectral norms of convolutional layers to vary, with each norm guided toward a distinct upper limit. To achieve this, we propose to regulate spectral norm growth through guided gradient flow. By incorporating gradient flow dynamics into the UNNPs optimization process and utilizing an attenuated learning rate, we ensure that the spectral norms of convolutional layers converge to their respective limits. This strategy provides nuanced control over the fitting of higher frequencies while enhancing model robustness. We conducted extensive experiments on the Set9 and Set12 datasets focusing on denoising and inpainting tasks. The results demonstrate that our guided gradient flow approach effectively mitigates overfitting in the UNNPs model. This method not only enhances the model’s robustness but also shows superior performance compared to other variants.