Convolutional plug-and-play sparse optimization for impulsive blind deconvolution

Impulsive blind deconvolution (IBD) is a fundamental ill-posed inverse problem in fault diagnosis community. Current IBD methods mainly utilize the intrinsic prior knowledge of impulsive sources to design various regularization terms (e.g., kurtosis, sparsity) to alleviate its ill-posedness. However, the great potentiality of statistical distribution structures embedded in observation data hasn't been exploited to establish more effective model and algorithm for IBD problem. Leveraging recent plug-and-play (PnP) strategy, a convolutional sparse optimization framework (dubbed COPS) is proposed to address it. Firstly, based on the fact that the absolute envelope of Gaussian noises follows a Rayleigh distribution and sparse impulsive components can be viewed as its outliers, a noise-aware statistical threshold is introduced to design a data-driven sparse penalty. Secondly, from a Bayesian perspective, a mapping relation between residual distribution and model hyper-parameter is unveiled, and then an adaptive parameter penalty is established to dynamically select model hyper-parameters. Lastly, two penalties are plugged into ADMM solver by PnP strategy to guarantee algorithmic convergence. Comprehensive numerical simulations confirm the COPS's advantages in terms of robustness, convergence, scalability and effectiveness. Diagnostic results of planetary gearbox faults further corroborate the COPS retains better deconvolutional accuracy than the state-of-the-art IBD techniques.