Cascade-KDE: Training-Free Time-Series Restoration for Impulse Corruptions

Cascade-KDE is a training-free restoration framework for time-series data corrupted by Gaussian noise and large-magnitude impulse outliers. It estimates a two-dimensional temporal-amplitude density, applies Density-Truncated Robust Expectation to limit distant abnormal points, and refines the sequence via an exponential cascade with adaptive stopping. Designed for tasks like ECG morphology analysis and battery degradation monitoring, it preserves derivative peaks and local shape without requiring training. The method targets out-of-distribution impulse corruptions, ensuring robustness while maintaining original local structure. Benchmarks demonstrate its effectiveness.