Recently, implicit neural representations (INR) have made significant strides in various vision-related domains, providing a novel solution for Multispectral and Hyperspectral Image Fusion (MHIF) tasks. However, INR is prone to losing high-frequency information and is confined to the lack of global perceptual capabilities. To address these issues, this paper introduces a Fourier-enhanced Implicit Neural Fusion Network (FeINFN) specifically designed for MHIF task, targeting the following phenomena: The Fourier amplitudes of the HR-HSI latent code and LR-HSI are remarkably similar; however, their phases exhibit different patterns. In FeINFN, we innovatively propose a spatial and frequency implicit fusion function (Spa-Fre IFF), helping INR capture high-frequency information and expanding the receptive field. Besides, a new decoder employing a complex Gabor wavelet activation function, called Spatial-Frequency Interactive Decoder (SFID), is invented to enhance the interaction of INR features. Especially, we further theoretically prove that the Gabor wavelet activation possesses a time-frequency tightness property that favors learning the optimal bandwidths in the decoder. Experiments on two benchmark MHIF datasets verify the state-of-the-art (SOTA) performance of the proposed method, both visually and quantitatively. Also, ablation studies demonstrate the mentioned contributions. The code will be available on Anonymous GitHub (https://anonymous.4open.science/r/FeINFN-15C9/) after possible acceptance.

翻译：近期，隐式神经表示（INR）在多个视觉相关领域取得了显著进展，为多光谱与高光谱图像融合（MHIF）任务提供了新颖的解决方案。然而，INR容易丢失高频信息，且受限于全局感知能力的缺失。为解决这些问题，本文针对MHIF任务提出了一种傅里叶增强的隐式神经融合网络（FeINFN），目标针对以下现象：高分辨率高光谱图像（HR-HSI）潜在编码与低分辨率高光谱图像（LR-HSI）的傅里叶振幅极为相似，但相位却呈现不同模式。在FeINFN中，我们创新性地提出了一种空间与频率隐式融合函数（Spa-Fre IFF），帮助INR捕获高频信息并扩大感受野。此外，我们发明了一种采用复Gabor小波激活函数的新型解码器，称为空间-频率交互解码器（SFID），以增强INR特征的交互性。特别地，我们进一步从理论上证明了Gabor小波激活具有时频紧密性，有利于在解码器中学习最优带宽。在两个基准MHIF数据集上的实验验证了所提方法在视觉和定量指标上均达到了当前最优（SOTA）性能。同时，消融研究证实了上述贡献。代码将在可能接收后发布于匿名GitHub（https://anonymous.4open.science/r/FeINFN-15C9/）。