A Theory-Guided Transformer for Interpretable Hyperspectral Unmixing

Hyperspectral unmixing (HU) is fundamental for conducting quantitative analyses in remote sensing, yet existing methods face a persistent tradeoff between model performance and physical interpretability. Although deep learning models achieve superior performance, even “gray-box” models that incorporate physical constraints still suffer from an intrinsically opaque decision-making process, which hinders their trustworthiness in critical applications. To address this challenge, this paper introduces a theory-guided unmixing framework aimed at enhancing mechanistic interpretability called the sparse and subspace-attentive transformer unmixing network (SSTU-Net). Unlike heuristic architectures, SSTU-Net is rigorously derived from the first principles of sparse rate reduction (SRR) theory. Its core modules—the multi-head subspace self-attention (MSSA) and the iterative shrinkage-thresholding algorithm (ISTA)—directly implement the essential mathematical steps of information compression and sparsification within the SRR theory, respectively. Extensive experiments on both synthetic and real hyperspectral datasets demonstrate that SSTU-Net achieves competitive performance compared to representative state-of-the-art methods—including advanced autoencoder-based networks (e.g., CyCU-Net and DAAN) and recent transformer-based unmixing architectures (e.g., DeepTrans and MAT-Net)—while strictly adhering to theoretically predicted evolutionary trajectories. More importantly, a series of specifically designed structural interpretability validation experiments mechanistically confirm the theoretically predicted behaviors, such as layer-wise information compression, feature sparsification, and subspace orthogonalization. These results reveal the internal working mechanisms of SSTU-Net, validating the feasibility and significant potential of our principled theory-guided framework for developing high-performance and trustworthy intelligent models in remote sensing.