PIN: Prolate Spheroidal Wave Function-based Implicit Neural Representations

Published: 22 Jan 2025, Last Modified: 01 Mar 2025ICLR 2025 PosterEveryoneRevisionsBibTeXCC BY 4.0
Keywords: Prolate Spheroidal Wave Functions, Implicit Neural Representations, MLPs
Abstract:

Implicit Neural Representations (INRs) provide a continuous mapping between the coordinates of a signal and the corresponding values. As the performance of INRs heavily depends on the choice of nonlinear-activation functions, there has been a significant focus on encoding explicit signals within INRs using diverse activation functions. Despite recent advancements, existing INRs often encounter significant challenges, particularly at fine scales where they often introduce noise-like artifacts over smoother areas compromising the quality of the output. Moreover, they frequently struggle to generalize to unseen coordinates. These drawbacks highlight a critical area for further research and development to enhance the robustness and applicability of INRs across diverse scenarios. To address this challenge, we introduce the Prolate Spheroidal Wave Function-based Implicit Neural Representations (PIN), which exploits the optimal space-frequency domain concentration of Prolate Spheroidal Wave Functions (PSWFs) as the nonlinear mechanism in INRs. Our experimental results reveal that PIN excels not only in representing images and 3D shapes but also significantly outperforms existing methods in various vision tasks that require INR generalization, including image inpainting, novel view synthesis, edge detection, and image denoising.

Primary Area: applications to computer vision, audio, language, and other modalities
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 3985
Loading

OpenReview is a long-term project to advance science through improved peer review with legal nonprofit status. We gratefully acknowledge the support of the OpenReview Sponsors. © 2025 OpenReview