Cascade-KDE: Robust Time-Series Restoration under Out-of-Distribution Impulse Corruptions
This work addresses the challenge of simultaneously achieving low reconstruction error and faithful preservation of critical local features—such as derivative peaks—in real-world time series corrupted by a mixture of Gaussian noise and out-of-distribution impulsive anomalies. To this end, the authors propose a training-free recovery framework that uniquely integrates two-dimensional (time–amplitude) kernel density estimation with density-truncated robust expectation to suppress anomaly influence, complemented by an adaptively terminated exponential cascade mechanism for fine-grained signal restoration. Extensive experiments on multiple benchmark datasets demonstrate that the proposed method significantly outperforms conventional filters and learning-based baselines in terms of waveform fidelity, derivative preservation, downstream classification accuracy, and computational efficiency, thereby unifying robustness with accurate retention of local structural characteristics.