🤖 AI Summary
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.
📝 Abstract
Real-world time-series data in industrial sensing, healthcare, and energy systems is often corrupted by a mixture of Gaussian noise and occasional large-magnitude impulse outliers. For tasks that depend on local shape, such as ECG morphology analysis and battery degradation monitoring, the main requirement is not only low reconstruction error but also preservation of derivative peaks and task-critical features. We propose Cascade-KDE, a training-free restoration framework for corrupted time series. The method first estimates a two-dimensional temporal-amplitude density, then applies a Density-Truncated Robust Expectation to limit the influence of distant abnormal points, and finally refines the sequence through an exponential cascade with adaptive stopping. This design aims to improve robustness under out-of-distribution impulse corruptions while keeping the restored trajectory close to the original local structure. Across several benchmark datasets, the proposed method shows consistent gains over classical filters and representative learning-based baselines on curve fidelity, derivative preservation, downstream classification, and runtime efficiency. These results suggest that bounded density-based restoration is a practical option for feature-preserving preprocessing in noisy time-series pipelines.