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

Forward model mismatch -- sub-pixel mask misalignment and dispersion drift between the coded aperture and detector -- is unavoidable in deployed CASSI systems, yet even moderate perturbations degrade state-of-the-art mask-guided transformers (MST) by over 16 dB. We present a self-supervised two-stage differentiable calibration pipeline that recovers 5-parameter mismatch from a single measurement and nominal mask alone, requiring no ground truth. Stage 1 performs a coarse hierarchical grid search scored by GPU-accelerated GAP-TV; Stage 2 applies gradient refinement through an unrolled differentiable forward operator using a Straight-Through Estimator (STE) for integer dispersion offsets. The pipeline is self-supervised, requiring only the measurement and nominal mask -- no ground truth scene. Evaluating five reconstruction methods (GAP-TV, MST-S, MST-L, HDNet, PnP-HSICNN) across four scenarios on 10 KAIST scenes, we uncover a mask-sensitivity spectrum: mask-guided transformers suffer catastrophic degradation (>15 dB) yet recover ~48% of the oracle gap after calibration, while deep prior methods (HDNet) show inherent robustness with moderate degradation (~10 dB). Code and results are publicly available.