Data-efficient linear hyperspectral imaging through risk-guided co-design
Computational hyperspectral imaging reconstructs spatial-spectral information from limited optical measurements. Linear reconstructors are efficient and interpretable, but often underperform deep nonlinear models, which typically require substantial training data and computational resources. Here we present a theory-guided encoding-reconstruction co-design framework that achieves, to our knowledge, state-of-the-art linear reconstruction performance. We establish a theory for the exact five-term decomposition of reconstruction risk and introduce a method for diagnosing the statistical-coverage lower bound within a fixed principal component analysis envelope, which together inform the optimized design of hyperspectral imaging systems. The framework applies across coded-aperture snapshot spectral imaging (CASSI), diffractive optical element imaging and spectral filter array imaging, achieving 34.76 dB mean PSNR in single-shot CASSI, outperforming a deep baseline by 9.43 dB with only five source scenes, and matching empirical cross-domain risk within 0.2%. Our results establish a data-efficient and theoretically grounded route to high-performance linear hyperspectral reconstruction, while providing a quantitative basis for identifying whether reconstruction is limited by optical encoding, reconstruction design or statistical coverage.