PrivSTD: Differentially Private Spatio-temporal Trajectory Density Data Publication

Spatio-temporal trajectory density data is widely used in urban analytics, mobility studies, and epidemiology. While differential privacy enables the release and analysis of such data, providing useful privacy guarantees for high-resolution density data remains challenging. Existing approaches typically perturb density data in the spatial domain, making it difficult to preserve spatio-temporal correlations and causing severe utility loss at fine granularity. We propose PrivSTD, a differentially private method for high-resolution spatio-temporal density release. PrivSTD applies the Discrete Cosine Transform to transform density data into the frequency domain, where low-frequency components capture spatial correlations and temporal smoothness. To suppress noise-dominated frequencies, we introduce a Benjamini-Hochberg FDR-based adaptive truncation mechanism that preserves statistically significant structure at no additional privacy cost. PrivSTD further employs a control variate-enhanced Recorrupted-to-Recorrupted denoising model to reconstruct high-quality density estimates. Experiments show that PrivSTD consistently outperforms existing methods, achieving 1.12×-53.89× lower error (6.12× on average) across all datasets.