Correcting Forward Model Mismatch in Coded Aperture Snapshot Spectral Imaging via Two-Stage Differentiable Calibration

Coded aperture snapshot spectral imaging (CASSI) captures a 3D hyperspectral cube from a single 2D measurement using a coded mask and spectral dispersion. Deep learning reconstructors such as MST achieve state-of-the-art quality (>34 dB) but assume perfect knowledge of the forward operator. In practice, sub-pixel mask misalignment and dispersion drift between the coded aperture and detector are unavoidable, yet even moderate mismatch degrades MST-L reconstruction by over 16 dB. We propose a two-stage differentiable calibration pipeline: (1) a coarse hierarchical grid search scored by GPU-accelerated GAP-TV, followed by (2) joint gradient refinement through an unrolled differentiable forward operator using a Straight-Through Estimator (STE) for integer dispersion offsets, plus a 1D grid search for dispersion slope recovery. The pipeline is self-supervised, requiring only the measurement and nominal mask -- no ground truth scene. On 10 KAIST benchmark scenes with injected 5-parameter mismatch, our method recovers significant quality for mask-aware methods through self-supervised calibration. We evaluate five reconstruction methods (GAP-TV, MST-S, MST-L, HDNet, PnP-HSICNN) across four scenarios, revealing a mask-sensitivity spectrum: mask-guided transformers suffer catastrophic degradation (>15 dB) but gain most from calibration (~3 dB), deep prior methods (HDNet) show moderate degradation (~10 dB) with inherent robustness, and iterative methods show graduated sensitivity.