Wave scattering from buried non-metallic mine-like targets is modeled using the finite difference frequency domain method to determine the feasibility of identifying mines from shape features. It is shown that for constant cross-sectional target area - approximately 100 cm$+2$/ - the scattered fields of targets with widely varying shape but roughly the same height- to-width aspect ratio at 500 MHz are virtually indistinguishable regardless of burial depth. However, for GPR frequencies above 700 MHz the same selection of targets buried at a depth of 5 cm can indeed be discriminated by shape. It is deduced that while low GPR sensing frequencies may help to detect shallow anomalies, they do not supply any useful information about the shape details - particularly the edges - of the buried non-metallic mine-like targets. Higher frequencies provide significant additional information that can be used for target reconstruction. Based on the intuition generated from this scattering study, we develop a non-linear inverse scattering algorithm based on a low dimensional parameterization of the unknown object and the background. In particular, we use polynomials to represent the contrast in the real and imaginary parts of the object and background complex permittivities. The boundary separating the target from the unknown background is described using a periodic, quadratic B-spline curve whose control points can be individually manipulated. A greedy-type approach is used to minimize a regularized least-squares cost function in order to estimate the control point locations as well as the contrast expansion coefficients.
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