Period-conscious Time-series Reconstruction under Local Differential Privacy

TL;DR

This paper introduces CPR, a novel period-aware reconstruction framework for periodic time series under local differential privacy, improving spectral peak detection and phase alignment despite noise.

Contribution

CPR employs multi-scale period probing, phase aggregation, and EM-based denoising to enhance periodic signal reconstruction under local differential privacy constraints.

Findings

CPR achieves lower reconstruction error than baseline methods.

CPR better preserves periodic structures in noisy, privatized data.

Effective under tight privacy budgets, especially in low-epsilon regimes.

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-$\epsilon$ regime.