Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations

arXiv cs.CV / 4/6/2026

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Key Points

The paper proposes an adaptive local frequency filtering technique for Fourier-encoded implicit neural representations (INRs) to better handle signals whose local spectra vary across space.
By introducing a spatially varying modulation parameter α(x), the method smoothly transitions between low-pass, band-pass, and high-pass behaviors at different locations rather than using a fixed global set of Fourier frequencies.
The authors provide theoretical analysis from the neural tangent kernel (NTK) viewpoint, explaining how the filtering reshapes the effective kernel spectrum and affects optimization dynamics.
Experiments on 2D image fitting, 3D shape representation, and sparse data reconstruction show improved reconstruction quality and faster convergence versus fixed-frequency baselines.
The learned α(x) can be visualized to interpret the model’s spatially varying frequency preferences, offering an explanation for performance on non-stationary signals.

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.