Physics-guided topology-aware safeguarded unfolding for low-sampling computational ghost imaging

Low-sampling computational ghost imaging reduces acquisition burden but is highly sensitive to real-system mismatch and structural errors. We propose a physics-guided, topology-aware safeguarded unfolding method for 64 × 64 reconstruction from 300 Cake-Cutting-ordered Hadamard single-exposure measurements (7.3242% sampling). Pattern-wise calibration and physical backprojection establish a real-measurement baseline; topology-error prediction then localizes bounded logit-domain corrections, while residual-aware gating, backtracking, and acceptance criteria constrain multistage updates. On the independent ALL200 real-measurement test set, Dice/clDice/PSNR reach 0.8850/0.8716/16.0130 dB versus 0.8420/0.8691/13.8974 dB for TV-CS, and the mean reconstruction time decreases from 0.1630 s to 0.1206 s. Relative to the physics-adapted U-Net, clDice increases by 0.0417, and the background false-positive rate decreases from 0.0343 to 0.0175.