Uncertainty quantification in super-resolution guided wave array imaging using a variational Bayesian deep learning approach

Super-resolution guided wave array imaging has shown to be a feasible tool to detect and image sub-wavelength defects. However, research gaps remain in effectively quantifying and understanding the uncertainties in super-resolution imaging. In this study, we present a Bayesian deep learning approach to quantify and interpret various uncertainties in super-resolution guided wave array imaging. Specifically, we implement a Monte Carlo (MC) dropout scheme in the multi-scale deep learning models for approximate Bayesian inference to effectively quantify uncertainties in super-resolution subwavelength defect imaging. Furthermore, we decompose the total predictive uncertainty into distinct uncertainty sources: aleatoric uncertainty inherent in the data and epistemic uncertainty associated with the Bayesian deep learning model. From the experimental study, we observe that the two types of uncertainty (aleatoric and epistemic) in super-resolution guided wave array imaging can be successfully quantified using the multi-scale Bayesian deep learning approach. We further discuss the effectiveness of the Bayesian deep learning approach in small-data cases and compare the super-resolution imaging performance with a non-Bayesian (deterministic) deep learning approach.