2023/10/01 by T. Mitchell Roddenberry, Roddenberry, T. Mitchell, Vishwanath Saragadam +5 · 4 citations
Computer Science · Engineering · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Electrical engineering #Image and Signal Denoising Methods #Image and Video Processing (eess.IV) #Neural Networks and Applications #Signal Processing (eess.SP) #Ultrasonics and Acoustic Wave Propagation #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2310.00545
openalex publication_date 2023/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively represent signals in a way that couples spatial and spectral features of the signal that is not obvious in the usual discrete representation, paving the way for continuous signal processing and machine learning approaches that were not previously possible. Although INRs using sinusoidal activation functions have been studied in terms of Fourier theory, recent works have shown the advantage of using wavelets instead of sinusoids as activation functions, due to their ability to simultaneously localize in both frequency and space. In this work, we approach such INRs and demonstrate how they resolve high-frequency features of signals from coarse approximations done in the first layer of the MLP. This leads to multiple prescriptions for the design of INR architectures, including the use of complex wavelets, decoupling of low and band-pass approximations, and initialization schemes based on the singularities of the desired signal.