Boosting AI-Generated Biomedical Images with Confidence through Advanced Statistical Inference

Generative artificial intelligence (AI) has transformed the biomedical imaging field through image synthesis, addressing challenges of data availability, privacy, and diversity in biomedical research. This paper proposes a novel nonparametric method within the functional data framework to discern significant differences between the mean and covariance functions of original and synthetic biomedical imaging data, thereby enhancing the fidelity and utility of synthetic data. Focusing on surface-based synthetic imaging data, our approach employs triangulated spherical splines to address spatial heterogeneity. A key contribution is the construction of simultaneous confidence regions (SCRs) to rigorously quantify uncertainty in original-synthetic differences. The asymptotic properties of the proposed SCRs are established, providing exact coverage probabilities and demonstrating equivalence to those derived from noise-free imaging data. Simulation studies validate the coverage properties of the SCRs and evaluate the size and power of the associated hypothesis tests. The proposed method is applied to compare the original and synthetic brain imaging data from the Human Connectome Project, where it highlights significant differences between original and synthetic images. We demonstrate that a straightforward transformation can align the mean and covariance functions of synthetic images with those of the original data, improving their reliability and utility for biomedical research applications.