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PAKAN: Pixel Adaptive Kolmogorov-Arnold Network Modules for Pansharpening

Haoyu Zhang, Haojing Chen, Zhen Zhong, Liangjian Deng

Abstract

Pansharpening aims to fuse high-resolution spatial details from panchromatic images with the rich spectral information of multispectral images. Existing deep neural networks for this task typically rely on static activation functions, which limit their ability to dynamically model the complex, non-linear mappings required for optimal spatial-spectral fusion. While the recently introduced Kolmogorov-Arnold Network (KAN) utilizes learnable activation functions, traditional KANs lack dynamic adaptability during inference. To address this limitation, we propose a Pixel Adaptive Kolmogorov-Arnold Network framework. Starting from KAN, we design two adaptive variants: a 2D Adaptive KAN that generates spline summation weights across spatial dimensions and a 1D Adaptive KAN that generates them across spectral channels. These two components are then assembled into PAKAN 2to1 for feature fusion and PAKAN 1to1 for feature refinement. Extensive experiments demonstrate that our proposed modules significantly enhance network performance, proving the effectiveness and superiority of pixel-adaptive activation in pansharpening tasks.

PAKAN: Pixel Adaptive Kolmogorov-Arnold Network Modules for Pansharpening

Abstract

Pansharpening aims to fuse high-resolution spatial details from panchromatic images with the rich spectral information of multispectral images. Existing deep neural networks for this task typically rely on static activation functions, which limit their ability to dynamically model the complex, non-linear mappings required for optimal spatial-spectral fusion. While the recently introduced Kolmogorov-Arnold Network (KAN) utilizes learnable activation functions, traditional KANs lack dynamic adaptability during inference. To address this limitation, we propose a Pixel Adaptive Kolmogorov-Arnold Network framework. Starting from KAN, we design two adaptive variants: a 2D Adaptive KAN that generates spline summation weights across spatial dimensions and a 1D Adaptive KAN that generates them across spectral channels. These two components are then assembled into PAKAN 2to1 for feature fusion and PAKAN 1to1 for feature refinement. Extensive experiments demonstrate that our proposed modules significantly enhance network performance, proving the effectiveness and superiority of pixel-adaptive activation in pansharpening tasks.
Paper Structure (22 sections, 17 equations, 5 figures, 4 tables)

This paper contains 22 sections, 17 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Overview
  4. Notation and Problem Formulation
  5. KAN Preliminaries
  6. Adaptive KAN with Spatial and Spectral Coupling
  7. Weight Generation as Conditional Parameterization
  8. Factorized Adaptation: 2D and 1D Adaptive KAN
  9. Coupling Mechanism and Pixel-Adaptivity
  10. Complexity and Stability Considerations
  11. PAKAN 2to1: Feature Fusion Module
  12. PAKAN 1to1: Feature Refinement Module
  13. Connections to Pansharpening Physics
  14. Using PAKAN in Existing and New Networks
  15. Loss Function
  16. ...and 7 more sections

Figures (5)

  • Figure 1: Overview of PAKAN. Left: static KAN uses a single activation and lacks adaptivity across heterogeneous land covers, while our approach learns content-dependent activations. Middle: traditional KAN versus 2D/1D Adaptive KAN with dynamically generated weights. Right: qualitative comparison showing improved detail and spectral fidelity when PAKAN modules are embedded into U2Net.
  • Figure 2: Main architecture of the adaptive KAN components. Left: weight generation pipelines for 2D and 1D adaptive KANs, where the spatial branch produces pixel-wise weights from local features and the spectral branch produces channel-wise weights from global pooled context. Right: partial views of 1D and 2D Adaptive KANs that use the generated weights to modulate spline activations.
  • Figure 3: The overall design of our PAKAN 1to1 and 2to1 module. Channel mapping is explicitly set as 1to1: $C\rightarrow C$ and 2to1: $2C\rightarrow C$.
  • Figure 4: A brief illustration of PAKAN-U2Net.
  • Figure 5: HQNR map comparison on representative full-resolution samples and qualitative residual comparison on representative reduced-resolution samples.