Directional Positive-Definite Metric Consensus for Time-Modulated Hyperspectral Reconstruction

Time-modulated hyperspectral imaging records multiple spatially aligned measurements of the same scene under different spectral responses for reconstruction. However, correlations among these responses lead to nonuniform sensitivity across spectral directions, while existing reconstruction algorithms generally coordinate learned priors using shared scalar penalties. Here, we propose the Time-Modulated Calibration-Conditioned Spatial–Spectral Reconstruction Network (TCSS), an ADMM-inspired unfolding network built on Directional Positive-Definite Metric Consensus. Using calibration-derived directions in spectral space, TCSS constructs branch-specific positive-definite metrics that jointly control prior strength and spectral–spatial allocation across directions. Spectral-Shape-Guided Dual-Branch Reconstruction (SDBR) and Cross-Stage Reconstruction Increment Propagation (CSIP) further improve spatial–spectral prior extraction and information propagation across reconstruction stages. Extensive experiments show that TCSS achieves superior reconstruction performance with a compact architecture and generalizes consistently across datasets and the tested calibrated response sets. The code is released at https://anonymous.4open.science/r/test24/.