Bayesian hierarchical hyper-Laplacian priors for high-resolution defect imaging in pipe structures

The sparse defect imaging using guided waves for pipe structures has attracted a lot of attention due to its intuitive way of defect localization. However, there exist few attempts to employ the lp norm (p < 1) in sparse imaging to improve imaging performance. In this study, a new sparse imaging method based on Bayesian hierarchical hyper-Laplacian prior is proposed for pipe defect detection. A hyper-Laplacian prior is considered to obtain a sparser resolution, which aims at improving the imaging performance including defect imaging resolution and defect detection accuracy. A solid theoretical framework is constructed and derived to represent the hyper-Laplacian prior and to adaptively estimate all model parameters. Meanwhile, a two-step discretizing strategy is designed to reduce the computational cost. The experimental results demonstrate the superiority of the proposed method.