Inverse scattering with sparse Bayesian vector regression

A Bayesian formulation is employed to develop a sparse vector regression model. The model is used to characterize the connection between measured vector scattered-field data x and the underlying target responsible for these fields, characterized by the parameter vector t. The scattering data x may be measured at multiple positions and/or at multiple frequencies. The statistical model is trained using a set of data D = {xn, tn} n=1N established from a measurement and/or a forward model. Given observed scattered fields x, the model yields the expected target parameters t, as well as the associated accuracy of this estimate, defined in terms of 'error bars'. After developing the theory, we consider scattering from dielectric targets buried under a lossy half-space. We address examples for which the actual target responsible for the scattered fields is not matched to that used in the regression model, as well as scattering data with large additive noise.