Uncertainty Quantification in Inverse Scattering Problems With Bayesian Convolutional Neural Networks

Recently, tremendous progress has been achieved in applying deep learning schemes (DLSs) to solve inverse scattering problems (ISPs), where state-of-the-art performance has been attained. However, little attention has been paid to the uncertainty quantification of these deep-learning methods in solving ISPs. In other words, the error of the prediction is not known since the ground truth is not available in practice. In this article, a Bayesian convolutional neural network (BCNN) is used to quantify the uncertainties in solving ISPs. With Monte Carlo dropout, the proposed BCNN is able to directly predict the pixel-based uncertainties of the widely used DLSs in ISPs. To quantitatively evaluate the performance of uncertainty predictions, both correlation coefficient and nonlinear correlation distribution between the predicted uncertainty and true absolute error are calculated. The tests on both synthetic and experimental data show that the predictive uncertainty is highly correlated with true absolute error calculated from the ground truth. Besides, when DLSs fail to solve an ISP, the predicted uncertainty increases significantly, which offers a pixel-based “confidence level” in solving ISPs.