用傅里叶张量网络加速隐式神经表示，提升图像与体积数据建模效果。
FUTON: Fourier Tensor Network for Implicit Neural Representations
- 将信号建模为傅里叶级数，系数由低秩张量参数化
- 在图像与体数据上训练速度提升2-5倍，性能超越主流MLP方法
- 适合需要快速收敛与良好外推能力的图像重建任务
隐式神经表示（INRs）已成为编码信号的强大工具，但主流的MLP架构常面临收敛慢、对噪声过拟合及外推性能差的问题。本文提出FUTON（傅里叶张量网络），将信号建模为广义傅里叶级数，其系数通过低秩张量分解参数化。FUTON以正交可分离基函数的加权组合隐式表达信号，融合了傅里叶基的平滑性与周期性偏好，以及低秩参数化的低维频谱结构约束。我们提供了通用逼近定理的理论保证，并推导出复杂度与谱分辨率及输入维度呈线性关系的推理算法。在图像与体数据表示任务中，FUTON持续优于现有MLP-based INRs，且训练速度提升2–5倍。在图像去噪、超分辨率等逆问题上，FUTON表现出更优的泛化能力与更快的收敛速度。
原文摘要 · Abstract (English)
Implicit neural representations (INRs) have emerged as powerful tools for encoding signals, yet dominant MLP-based designs often suffer from slow convergence, overfitting to noise, and poor extrapolation. We introduce FUTON (Fourier Tensor Network), which models signals as generalized Fourier series whose coefficients are parameterized by a low-rank tensor decomposition. FUTON implicitly expresses signals as weighted combinations of orthonormal, separable basis functions, combining complementary inductive biases: Fourier bases capture smoothness and periodicity, while the low-rank parameterization enforces low-dimensional spectral structure. We provide theoretical guarantees through a universal approximation theorem and derive an inference algorithm with complexity linear in the spectral resolution and the input dimension. On image and volume representation, FUTON consistently outperforms state-of-the-art MLP-based INRs while training 2--5$\times$ faster. On inverse problems such as image denoising and super-resolution, FUTON generalizes better and converges faster.
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