Continuous Syndrome Forensics for Proactive Image Manipulation Localization and Reconstruction

The proliferation of generative AI motivates proactive image forensics capable of accurately localizing manipulations and reconstructing visually plausible semantic content. However, existing proactive defenses primarily rely on empirical deep learning, lacking principled algebraic foundations and remaining fragile under global distortions. While classical coding theories offer rigorous paradigms, their direct adaptation to natural images is non-trivial: finite-field error-correction codes are not directly applicable to continuous-valued pixels without discretization, and tools like classical compressive sensing commonly require strict global sparsity that fails under large-area edits, alongside dense linear projections that degrade visual quality. To bridge this gap, we propose Continuous Syndrome Forensics (CSF), which extends syndrome-based verification to the continuous spatial domain. By imposing block-wise algebraic invariants, CSF introduces an algebraically structured formulation for tamper localization without global sparse-recovery optimization. Although it is effective for small edits, directly applying CSF to natural images suffers from host self-interference and remains underdetermined under large-area manipulations. To address these challenges, we further introduce SyndromeMark, a network-augmented framework. SyndromeMark leverages the continuous syndrome residual proposed in CSF as an algebraically anchored spatial prior to guide both localization and reconstruction. Specifically, this prior enables a localization network to separate tampering from host-texture leakage, while guiding a reconstruction network to synthesize contextually plausible content consistent with the algebraic constraint. Extensive evaluations show that SyndromeMark improves robustness over the evaluated proactive baselines under severe post-processing distortions, supports both localization and semantic reconstruction, and remains resilient in the adaptive surrogate setting.