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

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.

Hyperspectral unmixing decomposes mixed pixels into material endmembers and their abundances from contiguous spectral observations. In modular sensing pipelines, endmembers are often first identified and then treated as fixed during abundance estimation. When this fixed endmember prior is inaccurate, spatially structured mismatch arising from illumination changes, sensor artifacts, or material boundaries may be incorrectly captured by the abundance variables, leading to unstable decompositions. This study presents an interpretable stage-wise hyperspectral unmixing framework (I-HyperSU) under fixed endmember priors, which is explicitly decomposed into a fixed endmember matrix $\mathbf{A}$, an abundance block $\mathbf{X}$, and a structural residual refinement block $\mathbf{S}$. The X-block estimates abundances using FISTA with nonnegativity and sparsity enhancement, and a soft penalty that approximately enforces sum-to-one constraints. The S-block jointly applies low-rank SVD structural regularization and a lightweight deep image prior (DIP) to refine structured residuals. This staged design makes the interaction between abundance and residual components transparent and interpretable. Experiments on Samson, Urban, and Jasper Ridge datasets demonstrate that, under fixed and imperfect endmember priors, soft abundance relaxation consistently outperforms hard simplex projection. Under the default N-FINDR endmember prior, the proposed framework reduces the joint reconstruction error by 61.7%--69.5% compared with a fixed-$\mathbf{A}$ UCLS baseline, while keeping the abundance RMSE nearly unchanged, indicating that the residual refinement branch accounts for structured model mismatch without degrading the abundance estimates. For example, on Urban, the reconstruction SAM decreases from $5.99^\circ$ for the X-only model to $1.92^\circ$ for the full model.

Hyperspectral image (HSI) classification plays a vital role in remote sensing applications, including agriculture, environmental monitoring, and urban analysis. However, its performance remains challenged by high spectral redundancy, noise sensitivity, and the difficulty of jointly modeling local material composition and long-range spectral dependencies. To address this, we propose AGSA-Net, an abundance-guided self-attention network that explicitly integrates spectral unmixing priors into the classification process. AGSA Net first estimates physically meaningful subpixel abundance maps subject to non-negativity and sum-to-one constraints, regularized by hybrid linear-nonlinear reconstruction decoder. The learned abundances are then used to construct an abundance affinity prior that guides a spectral transformer to emphasize class-discriminative interactions, and the resulting transformer features are fused with compact abundance descriptors for final prediction; in contrast to existing approaches that use abundance as auxiliary or concatenated features. Experiments on Indian Pines, Augsburg, and Berlin demonstrate the benefit of incorporating abundance- guided contextual modeling, particularly in heterogeneous urban scenes. The source code and trained models are available at: https://github.com/nnuvi/AGSA-Net