Robust feature characterization and sparse reconstruction of rail acoustic emission signals under impulsive noise

Low-frequency (< 3000 Hz) acoustic emission sensing is ideal for long-distance railway monitoring due to its high propagation speed and low attenuation. However, heavy-tailed impulsive noise often compromises signal fidelity and monitoring reliability. Traditional correntropy matching pursuit (CMP) with Gaussian kernels is frequently ineffective against such interference, leading to the loss of critical transient features. This article proposes an α -stable CMP (ACMP) algorithm integrated with K-singular value decomposition (K-SVD) dictionary learning. ACMP utilizes a novel translation-invariant kernel derived from the α -stable distribution’s characteristic function and an adaptive residual-weighting mechanism within a half-quadratic framework to suppress impulsive outliers while preserving transient signatures. Evaluations included large-scale Monte Carlo simulations ( n = 100) and field-collected rail-gap signals with controlled α -stable noise. Statistical assessments (Friedman and Holm-corrected Wilcoxon tests) showed significant improvements over orthogonal matching pursuit and CMP with large effect sizes. Comparison with an adapted deep-learning (adaptive denoising autoencoder) baseline further demonstrated ACMP’s superior reconstruction fidelity under the investigated conditions. Time–frequency analyses confirmed an optimal balance between noise reduction and feature preservation. The primary innovations lie in the construction of the noise-matched α -stable kernel and its integration into a tailored residual-weighting strategy. As a lightweight preprocessing solution, ACMP addresses data transmission and storage bottlenecks in Internet of Things-based monitoring by compressing high-bandwidth signals via sparse representation, enabling bandwidth-efficient diagnostic information transfer without requiring continuous streaming of raw waveforms.