A new shape-based method for object localization and characterization from scattered field data

The problem of characterizing the geometric structure of an object buried in an inhomogeneous halfspace of unknown composition is considered. We develop a nonlinear inverse scattering algorithm based on a low-dimensional parameterization of the unknown object and the background. In particular, we use a low-order polynomial expansion to represent the spatial variations 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, We determine the unknown control point locations and contrast expansion coefficients using a greedy-type approach to minimize a regularized least-squares cost function. The regularizer used here is designed to constrain the geometric structure of the boundary of the object and is closely related to snake methods employed in the image processing community. We demonstrate the performance of our approach via extensive numerical simulation involving two dimensional (2-D), TMz scattering geometries. Our results indicate a strong ability to localize and estimate the shape of the object even in the presence of an unknown and inhomogeneous background.