SplitIR: Operator-Splitting Reconstruction of Hidden Screen Content from Indirect Radiance

Can an ordinary camera recover the content of a hidden screen from the light it casts on a visible wall? Diffuse scattering weakens and mixes the screen's structural cues, obscuring the correspondence between wall evidence and the layout to be recovered. Successive refinements can then accumulate incompatible corrections in an unrestricted correction space and suppress the weak high-frequency cues that carry fine screen structure. We propose Operator-Splitting Reconstruction from Indirect Radiance (SplitIR), which separates reconstruction into potential assimilation and resolvent correction. The Potential Assimilation Module (PAM) uses a learned positive metric and bounded potential-guided transport to organize wall evidence into a coherent layout state. The Resolvent Correction Module (RCM) then analytically adjusts candidate corrections through a metric-aware proximal step and projects them into stage-conditioned feasible correction sets for local refinement. Across Screen, Chart, Password, and Website, SplitIR achieves the best PSNR, SSIM, and LPIPS among 22 representative baselines and reconstructs screen layouts, chart structures, and character patterns from diffuse wall observations. Ablations support the two-operator design, while controlled luminance and Gaussian-noise experiments show a persistent comparative advantage as observation quality degrades. Together, these results establish the initial feasibility of recovering hidden screen content with an ordinary camera observing wall radiance.