PIN: Prolate Spheroidal Wave Function-based Implicit Neural Representations

Implicit Neural Representations (INRs) provide a continuous mapping between signal coordinates and their values. The performance of INRs heavily depends on the choice of nonlinear activation functions, which has led to increased interest in encoding signals using diverse activations. Despite recent progress, existing INRs struggle with fine-scale representation, often introducing noise-like artifacts over smooth regions and showing poor generalization to unseen coordinates.

To address these limitations, we propose PIN — Prolate Spheroidal Wave Function-based Implicit Neural Representations — which leverages the optimal space-frequency concentration of Prolate Spheroidal Wave Functions (PSWFs) as a nonlinear mechanism in INRs. Experimental results demonstrate that PIN not only excels at representing images and 3D shapes but also significantly outperforms state-of-the-art methods in generalization tasks such as image inpainting, novel view synthesis, edge detection, and denoising.