PAKAN: Pixel Adaptive Kolmogorov-Arnold Network Modules for Pansharpening

Haoyu Zhang; Haojing Chen; Zhen Zhong; Liangjian Deng

cs.CVMar 16, 2026

PAKAN: Pixel Adaptive Kolmogorov-Arnold Network Modules for Pansharpening

Authors: Haoyu Zhang, Haojing Chen, Zhen Zhong, Liangjian Deng

Organizations: University of Electronic Science and Technology of China

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.

Figures & tables

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.

Methods	WV3				QB				GF2
Methods	PSNR $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	Q8 $\uparrow$	PSNR $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	Q4 $\uparrow$	PSNR $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	Q4 $\uparrow$
MTF-GLP-FS	32.963	5.316	4.700	0.833	32.709	7.792	7.373	0.835	41.565	1.655	1.589	0.897
BDSD-PC	32.970	5.428	4.697	0.829	32.550	8.085	7.513	0.831	41.205	1.681	1.667	0.892
TV	32.381	5.692	4.855	0.795	32.136	7.510	7.690	0.821	41.262	1.911	1.737	0.907
PNN	37.313	3.677	2.681	0.893	36.942	5.181	4.468	0.918	45.096	1.048	1.057	0.960
PanNet	37.346	3.613	2.664	0.891	34.678	5.767	5.859	0.885	46.268	0.997	0.919	0.967

Table 1: Comparisons on WV3, QB, and GF2 reduced-resolution datasets, each with 20 samples, respectively. Best: bold , and second-best: underline .

Methods	WV3 (Reduced-resolution)				WV3 (Full-resolution)
Methods	PSNR $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	Q8 $\uparrow$	D ${}_{\lambda}\downarrow$	D ${}_{s}\downarrow$	HQNR $\uparrow$
PanNet	37.346	3.613	2.664	0.891	0.017	0.047	0.937
PanNet*	37.962	3.590	2.642	0.894	0.016	0.046	0.939
FusionNet	38.047	3.324	2.465	0.904	0.024	0.036	0.941
FusionNet*	38.528	3.210	2.382	0.911	0.021	0.032	0.947
U2Net	39.117	2.888	2.150	0.920	0.020	0.028	0.952

Table 2: Quantitative results on the WV3, GF2 and QB datasets at both reduced and full resolutions, * denotes the backbone equipped with PAKAN modules. (Best: bold )

Figure 5: HQNR map comparison on representative full-resolution samples and qualitative residual comparison on representative reduced-resolution samples.

PA	KAN	WV3				QB				GF2
PA	KAN	PSNR $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	Q8 $\uparrow$	PSNR $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	Q4 $\uparrow$	PSNR $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	Q4 $\uparrow$
$\times$	$\times$	39.117	2.888	2.150	0.920	38.065	4.642	3.987	0.931	49.404	0.714	0.632	0.982
$\checkmark$	$\times$	39.174	2.867	2.135	0.921	38.246	4.505	3.773	0.935	49.571	0.693	0.615	0.984
$\times$	$\checkmark$	39.191	2.877	2.144	0.921	38.342	4.592	3.889	0.937	49.799	0.696	0.625	0.985
$\checkmark$	$\checkmark$	39.238	2.856	2.119	0.921	38.520	4.439	3.698	0.939	49.913	0.668	0.595	0.987

Table 3: Module ablation study on WV3, QB, and GF2 reduced-resolution datasets, each with 20 samples. Best: bold , and second-best: underline . (PA: pixel adaptive)

1D	2D	WV3				QB				GF2
1D	2D	PSNR $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	Q8 $\uparrow$	PSNR $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	Q4 $\uparrow$	PSNR $\uparrow$	SAM $\downarrow$	ERGAS $\downarrow$	Q4 $\uparrow$
$\checkmark$	$\times$	39.162	2.876	2.141	0.920	38.217	4.556	3.812	0.934	49.603	0.699	0.620	0.984
$\times$	$\checkmark$	39.198	2.865	2.129	0.921	38.371	4.487	3.744	0.937	49.781	0.684	0.607	0.985
$\checkmark$	$\checkmark$	39.238	2.856	2.119	0.921	38.520	4.439	3.698	0.939	49.913	0.668	0.595	0.987

Table 4: KAN ablation study on WV3, QB, and GF2 reduced-resolution datasets, each with 20 samples. Best: bold , and second-best: underline .

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RAFNet: Region-Aware Fusion Network for Pansharpening

Jianing Zhang, Zijian Zhou, Kai Sun

College of Artificial Intelligence, Xi’an Jiaotong University, Xi’an 710049, China · School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China

Dynamic Convolution Frequency-Domain Feature Learning Multi-Scale Feature Fusion Remote Sensing Convolutional Neural Networks

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Pansharpening aims to generate high-resolution multispectral (HRMS) images by fusing low-resolution multispectral (LRMS) and high-resolution panchromatic (PAN) images. Although deep learning has advanced this field, mainstream frequency-based methods relying on standard scaled dot-product attention suffer from quadratic computational complexity and fail to exploit the inherent regional sparsity of remote sensing imagery. Furthermore, existing spatial enhancement strategies typically employ static convolution kernels, which struggle to adapt to the complex frequency and regional variations of PAN and MS images. To address these bottlenecks, we propose a Region-Aware Fusion (RAFNet) Network that synergistically models spatial and frequency information. Specifically, we design a Spatial Adaptive Refinement (SAR) module that leverages the discrete wavelet transform (DWT) for directional frequency separation and K-means clustering for regional partitioning, which enables the dynamic construction of region-specific adaptive convolution kernels, achieving spatially and frequency-adaptive feature enhancement. Moreover, we introduce a Clustered Frequency Aggregation (CFA) module based on a sparse attention mechanism guided by the semantic clusters, which executes a region-aware sparse attention strategy that drastically reduces computational redundancy while ensuring high-quality frequency feature extraction. In addition we integrated these modules into a progressive, multi-level spatial-frequency network architecture to facilitate robust interaction and accurate image reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that the proposed RAFNet significantly outperforms state-of-the-art pansharpening methods in both reduced- and full-resolution assessments. The code is available at https://github.com/PatrickNod/RAFNet.

Abstract

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