P4NSU: Projection-Based Pretraining for Nonlinear Sparse Unmixing in Spectral Imaging

Accurate quantification of components with spectral imaging (e.g., hyperspectral and Raman) is fundamentally challenged by nonlinear mixing effects. To overcome the limitations of model-specific traditional algorithms, we propose P4NSU, a deep learning framework for projection-based pretraining of nonlinear sparse unmixing. P4NSU introduces a synergistic two-part strategy: hierarchical pretraining that distills large spectral libraries into compact, task-specific subsets and a learnable projection that maps spectra into a feature space where unmixing simplifies to a linear problem. Extensive evaluations on three synthetic data sets, generated using established three nonlinear models, demonstrate that P4NSU consistently outperforms state-of-the-art linear and nonlinear methods, achieving a 14-51% reduction in overall RMSE. Its practical utility is further validated on real-world data sets. For hyperspectral imaging of pigments, P4NSU attained the highest unmixing accuracy, particularly reducing the RMSE for the most spectrally ambiguous chalk by more than 40%. For Raman imaging of leukemia cells, P4NSU produced biochemically meaningful abundance maps that aligned with known subtypes; notably, utilizing these maps as features significantly enhanced automated classification performance, underscoring its dual strengths in accurate quantification and information distillation. Implemented as an open-source Python toolkit (https://github.com/Ryan21wy/P4NSU), P4NSU offers a robust and practical solution to advance quantitative analysis in spectral imaging across diverse fields.