Learning Where Light Goes: Transport Routing and Coun- terfactual Recovery for Hidden Screen Reconstruction

Can an ordinary RGB camera recover the content of a hidden screen from the light it casts onto a wall? Diffuse propagation spreads each screen region across multiple measurement locations and mixes distant contributions, obscuring where weak evidence originates. The resulting ambiguity also allows plausible character strokes, boundaries and textures to enter a reconstruction without sufficient measurement support. We propose Transport Coupling and Counterfactual Recovery Learning (TCCRL) to connect evidence attribution with local structure verification. Screen-Wall Transport Coupling Learning learns a nonnegative sparse coupling shared across contents of each fixed capture geometry. The same coupling predicts measurement effects and routes wall evidence back to an initial screen state. Counterfactual Transport Verification and Selective Write-back then tests bounded local additions and deletions against complementary measurements and sequentially incorporates accepted changes. Across five screen-content benchmarks, TCCRL improves reconstruction fidelity and perceptual quality over 19 baselines. The recovered images preserve principal colours, regional layouts, page structure, chart outlines, character shapes and interface boundaries. These results establish the initial feasibility of hidden screen reconstruction from wall-mediated observations in fixed physical scenes.