Filtering In Implicit Neural Networks

Implicit neural networks (INNs) are very effective for learning data representation. However, most INNs inevitably generate over-smoothed patches or obvious noisy artifacts in the results when the data has many scales of details or a wide range of frequencies, leading to significant performance reduction. Adapting the result containing both noise and over-smoothed regions usually suffers from either over smoothing or noisy issues. To overcome this challenge, we propose a new framework, coined FINN, that integrated a \emph{filtering} module to the \emph{implicit neural network} to perform data fitting while filtering artifacts. The filtering module has a smoothing operator that acts on the intermediate results of the network and a recovering operator that brings distinct details from the input back to the regions overly smoothed. The proposed method significantly alleviates over smoothing or noisy issues. We demonstrate the advantage of the FINN on the image regression task, considering both real and synthetic images, and showcases significant improvement on both quantitative and qualitative results compared to state-of-the-art methods. Moreover, FINN yields better performance in both convergence speed and network stability. Source code is available at https://github.com/yixin26/FINN.