WS-Net: Weak-Signal Representation Learning and Gated Abundance Reconstruction for Hyperspectral Unmixing via State-Space and Weak Signal Attention Fusion

Zekun Long; Ali Zia; Guanyiman Fu; Vivien Rolland; Jun Zhou

cs.CVMar 10, 2026

WS-Net: Weak-Signal Representation Learning and Gated Abundance Reconstruction for Hyperspectral Unmixing via State-Space and Weak Signal Attention Fusion

Authors: Zekun Long, Ali Zia, Guanyiman Fu, Vivien Rolland, Jun Zhou

Organizations: School of Information and Communication Technology, Griﬃth University, Brisbane, QLD 4111, Australia · School of Computing, Engineering and Mathematical Sciences, La Trobe University, Melbourne, VIC 3086, Australia · CSIRO Agriculture and Food, Canberra, ACT 2601, Australia

Abstract

Weak spectral responses in hyperspectral images are often obscured by dominant endmembers and sensor noise, resulting in inaccurate abundance estimation. This paper introduces WS-Net, a deep unmixing framework specifically designed to address weak-signal collapse through state-space modelling and Weak Signal Attention fusion. The network features a multi-resolution wavelet-fused encoder that captures both high-frequency discontinuities and smooth spectral variations with a hybrid backbone that integrates a Mamba state-space branch for efficient long-range dependency modelling. It also incorporates a Weak Signal Attention branch that selectively enhances low-similarity spectral cues. A learnable gating mechanism adaptively fuses both representations, while the decoder leverages KL-divergence-based regularisation to enforce separability between dominant and weak endmembers. Experiments on one simulated and two real datasets (synthetic dataset, Samson, and Apex) demonstrate consistent improvements over six state-of-the-art baselines, achieving up to 55% and 63% reductions in RMSE and SAD, respectively. The framework maintains stable accuracy under low-SNR conditions, particularly for weak endmembers, establishing WS-Net as a robust and computationally efficient benchmark for weak-signal hyperspectral unmixing.

Figures & tables

Fig. 1: Overview of the proposed WS-Net framework. (1) WFFE : A multi-resolution wavelet-fused module that captures spatial–spectral cues across scales and enhances low-reflectance signals via Haar and Symlet-3 convolutions. (2) Mamba SSM and Inverse Attention Fusion : A dual-branch backbone integrating Mamba state-space modelling for efficient long-range spectral propagation with inverse attention for selective weak-signal enhancement. (3) Sparsity-Aware Decoder : Reconstructs hyperspectral data from softmax-constrained abundance maps while enforcing sparsity and distributional separation through KL-divergence regularisation.

Fig. 2: Architecture of the proposed Mamba SSM and Inverse Attention Fusion module. The framework integrates a Mamba-based state-space branch for long-range spectral modelling with a weak-signal Weak Signal Attention branch that selectively amplifies low-energy features suppressed by noise. The Transformer pathway introduces a class token with patch-level attention to provide global contextual guidance for hyperspectral unmixing.

Fig. 3: Dataset visualizations: ( a ) Simulated dataset, ( b ) Samson dataset, ( c ) Apex dataset. For each dataset, we show (left) a pseudo-RGB image (R: 650 nm, G: 532 nm, B: 450 nm), (middle) representative endmember abundance maps (normalized; brighter indicates higher abundance), and (right) endmember spectral signatures (reflectance versus wavelength).

Fig. 4: Abundance maps generated using the jet colourmap for the synthetic dataset. Each small image represents the spatial distribution of a specific endmember.

Panel of Figure 5 — Fig. 5: Visual comparison synthetic dataset of endmember spectra obtained by different unmixing techniques. The blue curves correspond to the ground‐truth spectra, while the orange curves denote the spectra estimated by each method.

Method	Magnetite	Mirabilite	Montmorillonite	Olivine	RMSE_Mean
FCLSU [ 31 , 33 ]	0.0151	0.0315	0.0198	0.0146	0.0205
Hyperweak [ 41 ]	0.0379	0.0436	0.1145	0.1784	0.0936
CNNAEU [ 25 ]	0.0162	0.0506	0.0166	0.0130	0.0241
DeepTrans [ 27 ]	0.0206	0.0153	0.0884	0.0137	0.0345
EDAA [ 28 ]	0.0155	0.0119	0.0106	0.0156	0.0134
EndNet [ 24 ]	0.0155	0.0140	0.0099	0.1526	0.0480

TABLE I: Root Mean Square Error (RMSE) comparison on the simulated S1 dataset. The S1 dataset is constructed by linearly mixing four materials—magnetite, mirabilite, montmorillonite, and olivine—under a strict linear mixing model. The table reports RMSE values for each endmember and their average (RMSE_Mean). Lower values indicate better abundance estimation accuracy. The best results are marked in red.

Method	Magnetite	Mirabilite	Montmorillonite	Olivine	SAD_Mean
FCLSU [ 31 , 33 ]	0.3300	0.0153	0.0343	0.1340	0.1284
Hyperweak [ 41 ]	0.0015	0.1202	0.0457	0.2456	0.1033
CNNAEU [ 25 ]	0.2194	0.0675	0.0244	0.0402	0.0879
DeepTrans [ 27 ]	0.1281	0.0508	0.0342	0.0762	0.0723
EDAA [ 28 ]	0.3381	0.0159	0.0155	0.0362	0.1014
EndNet [ 24 ]	0.3392	0.0187	0.0145	0.3617	0.1835

TABLE II: Spectral Angle Distance (SAD) comparison on the simulated S1 dataset. SAD is used to evaluate the angular similarity between the estimated and ground truth abundance vectors. The S1 dataset consists of hyperspectral pixels with 459 bands ranging from 400 nm to 2500 nm and includes challenging ternary mixtures involving low-reflectance materials. Lower SAD values represent more accurate abundance direction estimation. The best results are marked in red.

Panel of Figure 8 — Fig. 6: Performance comparison of different unmixing algorithms in terms of average and material-specific metrics. (a) Average RMSE across all materials. (b) Average SAD across all materials. (c) weak signal RMSE for Magnetite. (d) weak signal SAD for Magnetite. Lower values indicate better unmixing accuracy.

Fig. 7: Abundance maps generated using the jet colourmap for the Samson dataset. Each small image represents the spatial distribution of a specific endmember.

Panel of Figure 10 — Fig. 8: Visual comparison Samson dataset of endmember spectra obtained by different unmixing techniques. The blue curves correspond to the ground‐truth spectra, while the orange curves denote the spectra estimated by each method.

Method	Soil	Tree	Water	RMSE_Mean
FCLSU [ 31 , 33 ]	0.1076	0.0371	0.0158	0.0535
Hyperweak [ 41 ]	0.1576	0.2202	0.3589	0.2456
CNNAEU [ 25 ]	0.0164	0.0261	0.1040	0.0488
DeepTrans [ 27 ]	0.0712	0.0683	0.0930	0.0775
EDAA [ 28 ]	0.0197	0.0278	0.0656	0.0377
EndNet [ 24 ]	0.0036	0.0263	0.0145	0.0148

TABLE III: Root Mean Square Error (RMSE) comparison on the Samson dataset. RMSE is computed per endmember and averaged across three endmembers. Lower values indicate better estimation performance. The best results are shown in red.

Method	Soil	Tree	Water	SAD_Mean
FCLSU [ 31 , 33 ]	0.0260	0.0970	0.1461	0.0897
Hyperweak [ 41 ]	0.9229	0.0758	0.0282	0.3423
CNNAEU [ 25 ]	0.0559	0.0683	0.1012	0.0752
DeepTrans [ 27 ]	0.0120	0.0616	0.0898	0.0545
EDAA [ 28 ]	0.0674	0.0726	0.1400	0.0933
EndNet [ 24 ]	0.0124	0.0671	0.0619	0.0460

TABLE IV: Spectral Angle Distance (SAD) comparison on the Samson dataset. SAD measures angular similarity between predicted and ground truth abundance vectors. Lower values indicate better directional estimation. Best results are marked in red.

Fig. 9: Abundance maps generated using the jet colormap for the apex dataset. Each small image represents the spatial distribution of a specific endmember.

Panel of Figure 14 — Fig. 10: Visual comparison of endmember spectra obtained by different unmixing techniques. The blue curves correspond to the ground‐truth spectra, while the orange curves denote the spectra estimated by each method.

Method	Roof	Tree	Road	Water	RMSE_Mean
FCLSU [ 31 , 33 ]	0.0942	0.0554	0.1526	0.1746	0.1192
Hyperweak [ 41 ]	0.2131	0.1743	0.2109	0.4528	0.2628
CNNAEU [ 25 ]	0.0588	0.0385	0.0769	0.1233	0.0743
DeepTrans [ 27 ]	0.1200	0.0993	0.1776	0.0902	0.1218
EDAA [ 28 ]	0.0947	0.0701	0.0311	0.1702	0.0915
EndNet [ 24 ]	0.0337	0.0346	0.1071	0.1058	0.0703

TABLE V: Root Mean Square Error (RMSE) comparison on the APEX dataset. RMSE is computed for each endmember and averaged across all four. Lower is better. Best results are in bold red .

Method	Roof	Tree	Road	Water	SAD_Mean
FCLSU [ 31 , 33 ]	0.6900	0.2494	0.1471	0.5058	0.3981
Hyperweak [ 41 ]	0.0964	0.5448	0.1700	0.0964	0.6155
CNNAEU [ 25 ]	0.2649	0.1724	0.4133	0.0853	0.2340
DeepTrans [ 27 ]	0.0836	0.1295	0.0903	0.0434	0.0867
EDAA [ 28 ]	0.6943	0.3178	0.1633	0.1365	0.3280
EndNet [ 24 ]	0.2296	0.1550	0.0893	0.0839	0.1394

TABLE VI: Spectral Angle Distance (SAD) comparison on the APEX dataset. Lower is better. Best results are in bold red .

	Conv	Haar	Symlet-3	$a$ SAD	$a$ RMSE	$w$ SAD	$w$ RMSE
S1	✓			0.2675	0.2875	0.1792	0.2104
	✓	✓		0.0484	0.0638	0.1024	0.0874
	✓	✓	✓	0.0271	0.0181	0.0262	0.0152
Samson	✓			0.1025	0.0785	0.0957	0.1471
	✓	✓		0.0914	0.1470	0.1705	0.1142
	✓	✓	✓	0.0378	0.0736	0.0436	0.0153

TABLE VII: Ablation study of multi-resolution wavelet modules. Weak signal SAD (wSAD )and Weak signal RMSE (wRMSE) denote weak-signal errors.

ID	Variant	M	T	IAT	S1		Samson		APEX
ID	Variant	M	T	IAT	RMSE $\downarrow$	SAD $\downarrow$	RMSE $\downarrow$	SAD $\downarrow$	RMSE $\downarrow$	SAD $\downarrow$
V1	M only	✓	✗	✗	0.1742	0.2028	0.2141	0.2702	0.2204	0.3052
V2	T only	✗	✓	✗	0.0270	0.0252	0.0784	0.1025	0.1066	0.0871
V3	WAT only	✗	✗	✓	0.0281	0.0302	0.0544	0.0925	0.0981	0.0891
V4	M + T	✓	✓	✗	0.0762	0.1824	0.0612	0.0670	0.0745	0.0810
V5	M + WAT	✓	✗	✓	0.0527	0.0225	0.0478	0.0589	0.0621	0.0772

TABLE VIII: Ablation of Mamba state-space (M), Multihead Self-Patch Attention (T), and Weak Signal Attention (WAT) on three datasets. For each variant, we report the average RMSE and SAD on S1, Samson, and APEX.

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Hyperspectral Imaging

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Hyperspectral unmixing (HU) is crucial for analyzing hyperspectral imagery, yet achieving accurate unmixing remains challenging. While traditional methods struggle to effectively model complex spectral-spatial features, deep learning approaches often lack physical interpretability. Unrolling-based methods, despite offering network interpretability, inadequately exploit spectral-spatial information and incur high memory costs and numerical precision issues during backpropagation. To address these limitations, we propose DEQ-Unmix, which reformulates abundance estimation as a deep equilibrium model, enabling efficient constant-memory training via implicit differentiation. It replaces the gradient operator of the data reconstruction term with a trainable convolutional network to capture spectral-spatial information. By leveraging implicit differentiation, DEQ-Unmix enables efficient and constant-memory backpropagation. Experiments on synthetic and two real-world datasets demonstrate that DEQ-Unmix achieves superior unmixing performance while maintaining constant memory cost.

Abstract

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