[论文解读] Content-Aware Frequency Encoding for Implicit Neural Representations with Fourier-Chebyshev Features

Junbo Ke, Yangyang Xu+2 more|arXiv (Cornell University)|Mar 1, 2026

Handwritten Text Recognition Techniques被引用 0

一句话总结

CAFE 通过并行线性编码器与 Hadamard 融合为隐式神经表示自适应地合成丰富的频谱，并通过 Chebyshev 特征（CAFE+）扩展以提升低频稳定性和高频细节。

ABSTRACT

Implicit Neural Representations (INRs) have emerged as a powerful paradigm for various signal processing tasks, but their inherent spectral bias limits the ability to capture high-frequency details. Existing methods partially mitigate this issue by using Fourier-based features, which usually rely on fixed frequency bases. This forces multi-layer perceptrons (MLPs) to inefficiently compose the required frequencies, thereby constraining their representational capacity. To address this limitation, we propose Content-Aware Frequency Encoding (CAFE), which builds upon Fourier features through multiple parallel linear layers combined via a Hadamard product. CAFE can explicitly and efficiently synthesize a broader range of frequency bases, while the learned weights enable the selection of task-relevant frequencies. Furthermore, we extend this framework to CAFE+, which incorporates Chebyshev features as a complementary component to Fourier bases. This combination provides a stronger and more stable frequency representation. Extensive experiments across multiple benchmarks validate the effectiveness and efficiency of our approach, consistently achieving superior performance over existing methods. Our code is available at https://github.com/JunboKe0619/CAFE.

研究动机与目标

• 解决隐式神经表示（INRs）中的光谱偏差，阻碍高频细节的捕捉。
• 将频率合成负担从 MLP 转移到可学习的编码阶段。
• 实现从扩展的频率集合中自适应选择与任务相关的频率。

提出的方法

• 用傅里叶特征对输入进行编码，并通过 N 条并行线性层传递。
• 通过 Hadamard 积将并行投影融合，形成 CAFE 编码特征。
• 可选地将傅里叶特征和 Chebyshev 特征结合（CAFE+），以增强低频和高频表示。
• 将得到的特征输入至 MLP 主干以进行信号重建。
• 提供理论分析，显示扩展的频率可接受性：CW：CAFE 可合成 O(M^N 3^{N-1}) 个频率，且 Chebyshev 特征使低频表示更鲁棒。

实验结果

研究问题

• RQ1 自适应、编码阶段的频率合成是否能提升 INR 的性能，相较于固定的傅里叶基底？
• RQ2 将傅里叶特征与 Chebyshev 特征结合（CAFE+）如何影响跨频段的稳定性与重建？
• RQ3 并行线性层数量对表现力与训练成本有何影响？
• RQ4 在二维/三维 INR 任务与 NeRFs 中，CAFE 与 Chebyshev 成分对性能提升的贡献程度如何？

主要发现

• CAFE 明确扩展了可表示的频谱空间，超越固定的傅里叶基底，从而更好地捕捉高频细节。
• CAFE+ 结合傅里叶-Chebyshev 特征可获得更强的低频稳定性并改进高频拟合。
• 在多项任务中，CAFE 与 CAFE+ 相较于基线（如 SIREN、WIRE、FINER、SCONE、SL2A）在 PSNR/IoU/类似 PSNR 的指标上表现更优。
• 在 CAFE 中增加并行线性层数量可提升性能，达到饱和点前训练成本呈线性增长。
• Chebyshev 特征提供鲁棒的低频表示，能很好地补充傅里叶特征，降低低频噪声。