让傅里叶编码神经表示自适应调节局部频率，提升图像与3D重建质量。
Adaptive Local Frequency Filtering for Fourier-Encoded Implicit Neural Representations
- 引入空间可变参数α(x)动态调控傅里叶成分，实现不同位置的低通、带通、高通切换。
- 在2D图像、3D形状和稀疏数据上，重建精度更高且收敛速度比固定频率快。
- 学习到的α(x)能直观展示信号在不同区域的频率偏好，利于理解非平稳信号建模。
傅里叶编码隐式神经表示（INRs）在从离散样本建模连续信号方面表现出强大能力。然而，传统傅里叶特征映射在整个空间域使用固定频率，难以适应具有空间变化局部谱的信号，常导致高频细节收敛缓慢。为此，我们提出一种自适应局部频率滤波方法。该方法引入空间可变参数α(𝐱)，调节编码的傅里叶分量，实现在不同空间位置平滑切换低通、带通和高通行为。我们从神经正切核（NTK）角度分析该滤波器的影响，并提供其重塑有效核谱的NTK启发式解释。在2D图像拟合、3D形状表示和稀疏数据重构任务上的实验表明，所提方法在重建质量和优化速度上均优于固定频率基线。此外，学习到的α(𝐱)提供了空间频率偏好直观可视化，有助于解释模型在非平稳信号上的行为。结果表明，自适应局部频率调制是傅里叶编码INRs的有效增强。
原文摘要 · Abstract (English)
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 $α(\mathbf{x})$ 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 $α(\mathbf{x})$ 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.
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