3-D Voxel-Based Reconstruction of Multiple Objects Buried in Layered Media by VBIM Hybridized With Unsupervised Machine Learning

This article presents a novel hybrid electromagnetic inversion method. The traditional 3-D variational Born iterative method (VBIM) is combined with the unsupervised machine-learning expectation maximization (EM). In each iteration, VBIM first outputs the pseudo-randomly distributed model parameters in all discretized cells in the inversion domain. Then the EM algorithm is used to classify them and estimate the mean model parameter values of each homogeneous scatterer or subscatterer supposing that the reconstructed model parameters in all cells comply with the Gaussian mixture model (GMM). At last, partial cells in the inversion domain classified as “background” will be removed and the unknowns in the next VBIM iteration are reduced. This process is implemented iteratively until no “background” cell can be removed anymore and the data misfit between the measured scattered field and reconstructed field reaches the stop criterion. Finally, the mean value of the model parameter estimated by EM is mandatorily assigned for each homogeneous scatterer or subscatterer. Numerical examples show that the proposed hybrid method works efficiently for the reconstruction of isotropic, anisotropic, homogeneous, or inhomogeneous scatterers. It also has a certain antinoise ability.