Ligen Shi, Jun Qiu, Zengyu Pang, Yuhang Zheng, Lina Wu, Di He, Chang Liu
Implicit neural representations (INRs) commonly employ Fourier features to alleviate spectral bias and represent high-frequency signals. Fourier encodings, however, use the same frequency representation across spatial locations despite the spatially varying frequency content of natural signals. We propose Adaptive Frequency Implicit Neural Representation (AFINR), a spatially adaptive frequency-conditioning framework for Fourier encoded INRs. A sampling compatible Fourier dictionary first defines the explicit frequency support, and a learnable spatial control field then modulates the admitted Fourier components before decoding. The control field is parameterized in the discrete cosine transform (DCT) domain to provide a compact and continuously queryable spatial representation. AFINR can be combined with different coordinate decoders, including ReLU, SIREN, CAFE, and CAFE+. Experiments on Kodak and DIV2K show consistent average improvements across these decoder families. In particular, AFINR-CAFE+ improves CAFE+ by 3.95 dB on Kodak and 3.50 dB on DIV2K. Ablation studies characterize the effects of adaptive-field parameterization, DCT coefficient retention, and frequency-response parameters, while learned spatial responses show position-dependent use of the admitted Fourier components.
Wen Yan, Ligen Shi, Jun Qiu, Haimiao Zhang, Lina Wu, Chang Liu
Implicit Neural Representations (INRs) have emerged as a compelling paradigm for modeling multidimensional signals by mapping continuous coordinates to signal values. However, Multi-Layer Perceptrons (MLP)-based INRs inherently suffer from spectral bias, which favors low-frequency components and suppresses the reconstruction of essential high-frequency details. While existing techniques, such as Fourier feature mappings, mitigate this issue, they often rely on sensitive manual tuning and are prone to spectral artifacts. In this paper, we propose a spatial-frequency-aware INR framework that combines an MLP branch with a Kolmogorov-Arnold network (KAN) branch for complementary frequency-oriented modeling. The MLP branch provides a low-frequency-oriented representation of smooth structures, whereas the KAN branch complements localized variations and fine details. To coordinate the two branches, we integrate the discrete wavelet transform (DWT) and inverse discrete wavelet transform (IDWT) into the output fusion stage. The outputs of the two branches are decomposed into wavelet coefficients, and the corresponding coefficients are additively fused before inverse wavelet reconstruction. A wavelet-domain band-separation regularization further penalizes high-frequency responses in the MLP branch and low-frequency responses in the KAN branch, thereby encouraging complementary frequency-oriented behavior. Experiments on 1D signals, 2D images, 3D volumes and signed distance functions, videos, and 4D light-fields demonstrate the applicability of the proposed representation across the evaluated signal modalities. Results demonstrate improved reconstruction fidelity across the evaluated signal modalities.