Period-conscious Time-series Reconstruction under Local Differential Privacy

2026-05-04

AI Summary

This work addresses the challenge of reconstructing periodic time series under local differential privacy (LDP), where injected noise often distorts spectral peaks and induces phase shifts, leading to inaccurate period estimation and degraded signal fidelity. To mitigate these issues, the paper proposes the CPR framework, which introduces, for the first time, explicit period and phase awareness into LDP-compliant time series reconstruction. CPR robustly identifies the true period through multi-scale period detection and multi-consensus selection, aligns perturbed samples according to their phase positions, and recovers the true values at each phase via an EM-based denoising step combined with kernel density estimation. Experiments on two real-world periodic datasets demonstrate that CPR significantly outperforms existing LDP methods, achieving lower reconstruction error and better preservation of periodic structure, especially under stringent privacy budgets (small ε).

Abstract

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.

Problem

• Local Differential Privacy
• Periodic Time Series
• Period Estimation
• Phase Drift
• Time-series Reconstruction

Innovation

• Local Differential Privacy
• Periodic Time Series
• Cycle and Phase Recovery
• Spectral Interference Suppression
• Phase Alignment