FUTON: Fourier Tensor Network for Implicit Neural Representations
This addresses the problem of inefficient and noisy signal encoding in implicit neural representations for applications like image processing, though it is incremental as it builds on existing INR frameworks with a novel hybrid approach.
The paper tackles the slow convergence, overfitting, and poor extrapolation of MLP-based implicit neural representations (INRs) by introducing FUTON, a Fourier tensor network that models signals as generalized Fourier series with low-rank tensor decomposition, resulting in outperforming state-of-the-art MLP-based INRs on image and volume representation while training 2–5 times faster.
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.