Nonparametric Bayesian Learning Driven Dynamic Group Sparse Regularization for Transient Signal Enhancement

Transient signal characteristics contain crucial information about the operating status of equipment, and their precise enhancement is crucial for monitoring complex conditions such as bearing faults and radar interference. The core challenge lies in extracting the dynamic evolution patterns of weak transient components from high noise and nonstationary observations. To address the limitations of traditional methods, which are constrained by fixed state assumptions, struggle to analyze multiscale transient mechanisms, and are prone to amplitude distortion in nonstationary signals, this article proposes an adaptive enhancement framework for transient signals based on hidden state dynamic inference. Utilizing the hierarchical Dirichlet process (DP) hidden semi-Markov model (HDP-HSMM), our method automatically identifies hidden state types and duration distributions through nonparametric Bayesian inference, overcoming traditional methods’ reliance on predefined state counts. We also introduce a dynamic allocation strategy for group sparse regularization parameters that enhances multiple transient components based on signal structure priors. A nonconvex group sparse dictionary residual regularization algorithm is designed to ensure optimization convergence while avoiding L1 norm underestimation of signal amplitudes. Experimental validation using bearing fault impact signals and data from a dual-channel MIMO RF transceiver shows that our method outperforms traditional convex optimization and nonconvex regularization techniques in transient signal enhancement, demonstrating robustness and applicability in complex operating conditions.