Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations

TL;DR

This paper introduces an adaptive local frequency filtering method for Fourier-encoded implicit neural representations, enabling better modeling of signals with spatially varying spectra and improving convergence and reconstruction quality.

Contribution

It proposes a spatially varying frequency modulation parameter, analyzed via NTK, that enhances Fourier-encoded INRs by adaptively shaping local spectral properties.

Findings

Improved reconstruction quality across 2D and 3D tasks.

Faster convergence compared to fixed-frequency methods.

Learned frequency modulation provides interpretable spatial frequency preferences.

Abstract

Fourier-encoded implicit neural representations (INRs) have shown strong capability in modeling continuous signals from discrete samples. However, conventional Fourier feature mappings use a fixed set of frequencies over the entire spatial domain, making them poorly suited to signals with spatially varying local spectra and often leading to slow convergence of high-frequency details. To address this issue, we propose an adaptive local frequency filtering method for Fourier-encoded INRs. The proposed method introduces a spatially varying parameter $\alpha(\mathbf{x})$ to modulate encoded Fourier components, enabling a smooth transition among low-pass, band-pass, and high-pass behaviors at different spatial locations. We further analyze the effect of the proposed filter from the neural tangent kernel (NTK) perspective and provide an NTK-inspired interpretation of how it reshapes the effective kernel spectrum. Experiments on 2D image fitting, 3D shape representation, and sparse data reconstruction demonstrate that the proposed method consistently improves reconstruction quality and leads to faster optimization compared with fixed-frequency baselines. In addition, the learned $\alpha(\mathbf{x})$ provides an intuitive visualization of spatially varying frequency preferences, which helps explain the behavior of the model on non-stationary signals. These results indicate that adaptive local frequency modulation is a practical enhancement for Fourier-encoded INRs.