3D Fourier-based Global Feature Extraction for Hyperspectral Image Classification

Muhammad Ahmad

cs.CVMar 17, 2026

3D Fourier-based Global Feature Extraction for Hyperspectral Image Classification

Authors: Muhammad Ahmad

Organizations: SDAIA-KFUPM, Joint Research Center for Artificial Intelligence (JRCAI), King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia.

Abstract

Hyperspectral image classification (HSIC) has been significantly advanced by deep learning methods that exploit rich spatial-spectral correlations. However, existing approaches still face fundamental limitations: transformer-based models suffer from poor scalability due to the quadratic complexity of self-attention, while recent Fourier transform-based methods typically rely on 2D spatial FFTs and largely ignore critical inter-band spectral dependencies inherent to hyperspectral data. To address these challenges, we propose Hybrid GFNet (HGFNet), a novel architecture that integrates localized 3D convolutional feature extraction with frequency-domain global filtering via GFNet-style blocks for efficient and robust spatial-spectral representation learning. HGFNet introduces three complementary frequency transforms tailored to hyperspectral imagery: Spectral Fourier Transform (a 1D FFT along the spectral axis), Spatial Fourier Transform (a 2D FFT over spatial dimensions), and Spatial-Spatial Fourier Transform (a 3D FFT jointly over spectral and spatial dimensions), enabling comprehensive and high-dimensional frequency modeling. The 3D convolutional layers capture fine-grained local spatial-spectral structures, while the Fourier-based global filtering modules efficiently model long-range dependencies and suppress noise. To further mitigate the severe class imbalance commonly observed in HSIC, HGFNet incorporates an Adaptive Focal Loss (AFL) that dynamically adjusts class-wise focusing and weighting, improving discrimination for underrepresented classes.

Figures & tables

Fig. 1 : HSI cubes are first divided into 3D patches to preserve local and contextual dependencies. Three consecutive 3D Convolutional layers extract hierarchical features, while the GFNet layer enhances representations by transforming spatial-spectral data into the frequency domain. After normalization, a 3D FFT decomposes features into frequency components, where learnable global filters emphasize relevant information and suppress noise. The transformed features undergo regularization and pass through a Multilayer perceptron (MLP) block with AFL to handle class imbalances. A residual connection ensures stable gradient flow and feature preservation before dynamic fully connected layers generate the final class probabilities.

Data	Metric	MHSA	Wavelets	GFNet	SpFT	SFT	SFL	AFL
IP	$\kappa$	96.21	97.06	94.22	97.26	97.66	97.92	98.24
	OA	96.68	98.46	92.14	97.60	97.95	96.11	98.45
	AA	95.05	95.69	93.67	96.47	96.35	96.78	97.16
HC	$\kappa$	97.49	95.51	95.73	97.75	97.83	98.67	99.10
	OA	97.85	97.38	96.48	98.07	98.15	98.87	99.23
	AA	95.75	97.76	94.12	96.73	96.44	97.92	98.71

TABLE I : Quantitative comparison of different frequency and attention-based configurations, including SFL (SFL + SSFT) and the proposed AFL (AFL + SSFT).

Class	SF	HViT	WFormer	Mamba	WMamba	HGFNet
1	98.4307	99.3383	98.4755	96.9197	96.0255	99.7183
2	99.2001	98.1629	99.2528	83.8006	96.0007	99.6396
3	94.3807	98.6000	85.4754	78.0283	94.8668	99.7472
4	99.8879	99.5517	97.9454	95.6294	99.2528	99.7385
5	97.8333	99.1666	97.1666	73.0000	63.8333	99.6666
6	92.6301	86.4518	81.5975	35.3045	76.8314	96.1606

TABLE II : Class-wise accuracy and overall performance metrics on HC Dataset .

Panel of Figure 4 — Fig. 2 : Visual comparison of classification maps on the HC dataset. (a) Ground truth maps: (b–g) predicted maps from competing models and our proposed HGFNet.

Class	SF	HViT	WFormer	Mamba	WMamba	HGFNet
1	95.6521	100	86.9565	4.3478	65.2173	67.3913
2	95.0980	92.5770	93.1372	42.2969	81.5126	95.4481
3	97.1084	96.6265	98.3132	18.0722	77.3493	99.6385
4	94.0677	85.5932	91.5254	3.3898	50.8474	100
5	97.1074	99.5867	98.7603	33.0578	84.7107	97.9296
6	97.8082	98.6301	98.0821	86.5753	87.9452	100

TABLE III : Class-wise accuracy and overall performance metrics on IP Dataset .

Panel of Figure 6 — Fig. 3 : Predicted ground truth maps for the Indian Pines dataset.

Class	SF	HViT	WFormer	Mamba	WMamba	HGFNet
1	99.4159	99.5584	99.7008	86.8660	95.1709	99.2592
2	93.6788	91.3439	94.9886	64.1799	88.3826	98.9749
3	97.7087	98.5519	99.6333	88.9011	93.3644	99.2484
4	99.7121	98.8033	99.8860	98.8731	99.7427	99.9693
5	91.9588	95.5934	96.1724	79.4467	76.5519	95.2717
6	98.2808	99.5466	99.8967	91.1845	98.9272	99.8788

TABLE IV : Class-wise accuracy and overall performance metrics on HH Dataset .

Panel of Figure 8 — Fig. 4 : Predicted ground truth maps for the HH dataset.

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Hyperspectral Image Classification Hybrid CNN-Transformer Architectures Expert Routing Multi-Scale Feature Fusion Mixture-of-Experts Models

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Deep learning methods, including Convolutional Neural Networks, Transformers and Mamba, have achieved remarkable success in hyperspectral image (HSI) classification. Nevertheless, existing methods exhibit inflexible integration of local-global representations, inadequate handling of spectral-spatial scale disparities across heterogeneous bands, and susceptibility to the Hughes phenomenon under high-dimensional sample heterogeneity. To address these challenges, we propose Local-Global Expert Spatial-Spectral Transformer (LGEST), a novel framework that synergistically combines three key innovations. The LGEST first employs a Deep Spatial-Spectral Autoencoder (DSAE) to generate compact yet discriminative embeddings through hierarchical nonlinear compression, preserving 3D neighborhood coherence while mitigating information loss in high-dimensional spaces. Secondly, a Cross-Interactive Mixed Expert Feature Pyramid (CIEM-FPN) leverages cross-attention mechanisms and residual mixture-of-experts layers to dynamically fuse multi-scale features, adaptively weighting spectral discriminability and spatial saliency through learnable gating functions. Finally, a Local-Global Expert System (LGES) processes decomposed features via sparsely activated expert pairs: convolutional sub-experts capture fine-grained textures, while transformer sub-experts model long-range contextual dependencies, with a routing controller dynamically selecting experts based on real-time feature saliency. Extensive experiments on four benchmark datasets demonstrate that LGEST consistently outperforms state-of-the-art methods.

Abstract

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