Differentiable Operator Calibration for Coded Aperture Snapshot Spectral Imaging

Coded aperture snapshot spectral imaging (CASSI) acquires hyperspectral data cubes in a single shot but requires accurate knowledge of the forward measurement operator -- the coded aperture mask position, orientation, and dispersive element parameters -- for high-quality reconstruction. In practice, manufacturing tolerances and assembly drift introduce operator mismatch that degrades reconstruction by 10-17 dB. We present a differentiable calibration framework that models CASSI mismatch as a 6-parameter perturbation (spatial shift, rotation, dispersion slope and axis angle) and recovers these parameters through a two-stage pipeline: (1) a hierarchical beam search over a coarse parameter grid (~38 s/scene), followed by (2) a joint gradient refinement using differentiable PyTorch modules -- including a straight-through estimator for integer dispersion offsets and an unrolled GAP-TV solver with gradient checkpointing (~366 s/scene). Central to our approach is an enlarged grid forward model with 4x spatial and 2x spectral oversampling (217 bands), providing sub-pixel sensitivity to mismatch parameters. Validated on 10 KAIST hyperspectral scenes under a three-scenario protocol, our method achieves a calibration gain of +5.06 dB, recovering 30% of the 16.60 dB mismatch loss. When combined with oracle correction using mask-aware deep networks (MST-L), the recovery reaches +7.99 dB (75.5% of mismatch loss), demonstrating the synergy between calibration and learned reconstruction.