Period-conscious Time-series Reconstruction under Local Differential Privacy
For practitioners collecting periodic user-generated streams (e.g., gait, audio) from edge devices, CPR enables accurate reconstruction under LDP, a critical privacy-preserving technique.
The paper tackles the problem of reconstructing periodic time series under local differential privacy (LDP), where noise corrupts spectral peaks and phase alignment. The proposed CPR framework achieves lower reconstruction error than baselines, especially under tight privacy budgets, on two real-world datasets.
Periodic patterns are fundamental cues in multimedia signals and systems, including repetitive motion in video (e.g., gait cycles), rhythmic and pitch-related structure in audio, and recurring textures in image sequences. When such user-generated streams are collected from edge devices, local differential privacy (LDP) is appealing because it perturbs data before upload; however, the injected noise can corrupt spectral peaks and induce phase drift, making period estimation unreliable and degrading reconstruction quality. We propose \textbf{CPR} (\textit{Cycle and Phase Recovery}), a period-aware reconstruction framework for periodic time series under LDP. CPR performs multi-scale period probing and multi-consensus selection to suppress noise-induced spectral interference, then aggregates perturbed samples at matched within-cycle phase positions to stabilize phase alignment across cycles. To recover the underlying per-phase values, CPR combines EM-based denoising with kernel density estimation, improving robustness under tight privacy budgets. Experiments on two real-world periodic datasets demonstrate that CPR better preserves periodic structure and consistently achieves lower reconstruction error than representative LDP baselines, especially in the low-$ε$ regime.