# Euler-inspired Decoupling Neural Operator for Efficient Pansharpening

arXiv: https://arxiv.org/abs/2604.12463 · HTML: https://mlsanity.com/paper/2604.12463/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 53 references that are in the map.
- First posted on arXiv 14 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [FusionMamba: Dynamic Feature Enhancement for Multimodal Image Fusion with Mamba](https://mlsanity.com/paper/2404.09498/) (2024)
- [Deep Gradient Projection Networks for Pan-sharpening](https://mlsanity.com/paper/2103.04584/) (2021)
- [HyperTransformer: A Textural and Spectral Feature Fusion Transformer for Pansharpening](https://mlsanity.com/paper/2203.02503/) (2022)
- [Remote Sensing Image Fusion Based on Two-stream Fusion Network](https://mlsanity.com/paper/1711.02549/) (2017)
- [Local-Global Transformer Enhanced Unfolding Network for Pan-sharpening](https://mlsanity.com/paper/2304.14612/) (2023)
- [SWIFT: A General Sensitive Weight Identification Framework for Fast Sensor-Transfer Pansharpening](https://mlsanity.com/paper/2507.20311/) (2025)

## Abstract (arXiv)

Pansharpening aims to synthesize high-resolution multispectral (HR-MS) images by fusing the spatial textures of panchromatic (PAN) images with the spectral information of low-resolution multispectral (LR-MS) images. While recent deep learning paradigms, especially diffusion-based operators, have pushed the performance boundaries, they often encounter spectral-spatial blurring and prohibitive computational costs due to their stochastic nature and iterative sampling. In this paper, we propose the Euler-inspired Decoupling Neural Operator (EDNO), a physics-inspired framework that redefines pansharpening as a continuous functional mapping in the frequency domain. Departing from conventional Cartesian feature processing, our EDNO leverages Euler's formula to transform features into a polar coordinate system, enabling a novel explicit-implicit interaction mechanism. Specifically, we develop the Euler Feature Interaction Layer (EFIL), which decouples the fusion task into two specialized modules: 1) Explicit Feature Interaction Module, utilizing a linear weighting scheme to simulate phase rotation for adaptive geometric alignment; and 2) Implicit Feature Interaction Module, employing a feed-forward network to model spectral distributions for superior color consistency. By operating in the frequency domain, EDNO inherently captures global receptive fields while maintaining discretization-invariance. Experimental results on the three datasets demonstrate that EDNO offers a superior efficiency-performance balance compared to heavyweight architectures.