Empirical Characterization of Re-Identification Risk and Diagnostic Utility Under Gerchberg–Saxton Spectral Transformation in Medical Imaging

Medical images contain anatomical identifiers that persist beyond explicit metadata removal. We empirically characterize how Gerchberg–Saxton (GS) transformation affects subject-identification risk and diagnostic signal across two modalities and four adversary classes. We evaluate transformation impact on OASIS-1 brain MRI and NIH-CXR chest radiography using ResNet18 and DenseNet121, measuring diagnostic utility via subject-level AUC and subject-identification risk under cross-domain and in-domain supervised re-identification (closed-set), embedding-based linkage (open-set), and reconstruction-based inversion using U-Net and diffusion posterior sampling. Cross-domain supervised re-identification collapses to near-chance by GS-10% (OASIS-1 ResNet18: 0.6% [95% CI: 0.0–0.9]; NIH-CXR DenseNet121: 0.6% [0.3–0.8]), from respective RAW baselines of 83.9% and 72.4%. Reconstruction models achieve high perceptual fidelity (U-Net SSIM: 0.937 [0.932–0.942] at GS-0%) but do not restore RAW-baseline re-identification accuracy despite direct training exposure to all evaluation subjects. In-domain supervised and embedding-based re-identification decline consistently across masking levels, with modality-dependent magnitudes. Diagnostic AUC reductions remain within 3.6–6.1 percentage points at GS-50%. GS transformation produces a consistent empirical asymmetry between subject-identification risk reduction and diagnostic signal retention across modalities, architectures, and adversary classes. Masking strength p tunes this asymmetry, yielding a range of empirical operating points. Results reflect empirical evaluation under assessed adversary classes and do not constitute formal privacy guarantees.